186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung/* 286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * Copyright (C) 2013 The Android Open Source Project 386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * Licensed under the Apache License, Version 2.0 (the "License"); 586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * you may not use this file except in compliance with the License. 686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * You may obtain a copy of the License at 786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * http://www.apache.org/licenses/LICENSE-2.0 986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 1086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * Unless required by applicable law or agreed to in writing, software 1186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * distributed under the License is distributed on an "AS IS" BASIS, 1286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 1386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * See the License for the specific language governing permissions and 1486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * limitations under the License. 1586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung */ 1686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 1786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung#ifndef ANDROID_AUDIO_RESAMPLER_FIR_GEN_H 1886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung#define ANDROID_AUDIO_RESAMPLER_FIR_GEN_H 1986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 2086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungnamespace android { 2186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 2286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung/* 236582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * generates a sine wave at equal steps. 2486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 256582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * As most of our functions use sine or cosine at equal steps, 266582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * it is very efficient to compute them that way (single multiply and subtract), 276582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * rather than invoking the math library sin() or cos() each time. 286582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 296582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * SineGen uses Goertzel's Algorithm (as a generator not a filter) 306582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * to calculate sine(wstart + n * wstep) or cosine(wstart + n * wstep) 316582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * by stepping through 0, 1, ... n. 326582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 336582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * e^i(wstart+wstep) = 2cos(wstep) * e^i(wstart) - e^i(wstart-wstep) 346582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 356582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * or looking at just the imaginary sine term, as the cosine follows identically: 366582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 376582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * sin(wstart+wstep) = 2cos(wstep) * sin(wstart) - sin(wstart-wstep) 386582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 396582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Goertzel's algorithm is more efficient than the angle addition formula, 406582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * e^i(wstart+wstep) = e^i(wstart) * e^i(wstep), which takes up to 416582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4 multiplies and 2 adds (or 3* and 3+) and requires both sine and 426582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * cosine generation due to the complex * complex multiply (full rotation). 436582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 446582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * See: http://en.wikipedia.org/wiki/Goertzel_algorithm 4586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 4686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung */ 4786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 486582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hungclass SineGen { 496582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hungpublic: 506582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung SineGen(double wstart, double wstep, bool cosine = false) { 516582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung if (cosine) { 526582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mCurrent = cos(wstart); 536582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mPrevious = cos(wstart - wstep); 546582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } else { 556582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mCurrent = sin(wstart); 566582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mPrevious = sin(wstart - wstep); 576582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 586582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mTwoCos = 2.*cos(wstep); 5986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 606582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung SineGen(double expNow, double expPrev, double twoCosStep) { 616582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mCurrent = expNow; 626582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mPrevious = expPrev; 636582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mTwoCos = twoCosStep; 646582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 656582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung inline double value() const { 666582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return mCurrent; 676582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 686582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung inline void advance() { 696582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double tmp = mCurrent; 706582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mCurrent = mCurrent*mTwoCos - mPrevious; 716582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mPrevious = tmp; 726582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 736582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung inline double valueAdvance() { 746582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double tmp = mCurrent; 756582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mCurrent = mCurrent*mTwoCos - mPrevious; 766582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mPrevious = tmp; 776582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return tmp; 786582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 796582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 806582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hungprivate: 816582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double mCurrent; // current value of sine/cosine 826582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double mPrevious; // previous value of sine/cosine 836582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double mTwoCos; // stepping factor 846582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung}; 856582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 866582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung/* 876582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * generates a series of sine generators, phase offset by fixed steps. 886582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 896582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * This is used to generate polyphase sine generators, one per polyphase 906582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * in the filter code below. 916582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 926582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * The SineGen returned by value() starts at innerStart = outerStart + n*outerStep; 936582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * increments by innerStep. 946582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 956582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung */ 966582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 976582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hungclass SineGenGen { 986582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hungpublic: 996582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung SineGenGen(double outerStart, double outerStep, double innerStep, bool cosine = false) 1006582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung : mSineInnerCur(outerStart, outerStep, cosine), 1016582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mSineInnerPrev(outerStart-innerStep, outerStep, cosine) 1026582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung { 1036582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mTwoCos = 2.*cos(innerStep); 1046582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 1056582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung inline SineGen value() { 1066582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return SineGen(mSineInnerCur.value(), mSineInnerPrev.value(), mTwoCos); 1076582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 1086582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung inline void advance() { 1096582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mSineInnerCur.advance(); 1106582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung mSineInnerPrev.advance(); 1116582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 1126582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung inline SineGen valueAdvance() { 1136582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return SineGen(mSineInnerCur.valueAdvance(), mSineInnerPrev.valueAdvance(), mTwoCos); 1146582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 1156582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 1166582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hungprivate: 1176582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung SineGen mSineInnerCur; // generate the inner sine values (stepped by outerStep). 1186582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung SineGen mSineInnerPrev; // generate the inner sine previous values 1196582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // (behind by innerStep, stepped by outerStep). 1206582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double mTwoCos; // the inner stepping factor for the returned SineGen. 1216582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung}; 12286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 12386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstatic inline double sqr(double x) { 12486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung return x * x; 12586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung} 12686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 12786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung/* 12886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * rounds a double to the nearest integer for FIR coefficients. 12986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 13086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * One variant uses noise shaping, which must keep error history 13186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * to work (the err parameter, initialized to 0). 13286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * The other variant is a non-noise shaped version for 13386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * S32 coefficients (noise shaping doesn't gain much). 13486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 1356582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Caution: No bounds saturation is applied, but isn't needed in this case. 13686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 13786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param x is the value to round. 13886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 13986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param maxval is the maximum integer scale factor expressed as an int64 (for headroom). 14086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * Typically this may be the maximum positive integer+1 (using the fact that double precision 14186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * FIR coefficients generated here are never that close to 1.0 to pose an overflow condition). 14286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 14386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param err is the previous error (actual - rounded) for the previous rounding op. 1446582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * For 16b coefficients this can improve stopband dB performance by up to 2dB. 1456582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 1466582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Many variants exist for the noise shaping: http://en.wikipedia.org/wiki/Noise_shaping 14786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 14886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung */ 14986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 15086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstatic inline int64_t toint(double x, int64_t maxval, double& err) { 15186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung double val = x * maxval; 1526582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double ival = floor(val + 0.5 + err*0.2); 15386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung err = val - ival; 15486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung return static_cast<int64_t>(ival); 15586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung} 15686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 15786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstatic inline int64_t toint(double x, int64_t maxval) { 15886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung return static_cast<int64_t>(floor(x * maxval + 0.5)); 15986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung} 16086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 16186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung/* 16286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * Modified Bessel function of the first kind 16386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * http://en.wikipedia.org/wiki/Bessel_function 16486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 1656582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * The formulas are taken from Abramowitz and Stegun, 1666582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * _Handbook of Mathematical Functions_ (links below): 16786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 16886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * http://people.math.sfu.ca/~cbm/aands/page_375.htm 16986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * http://people.math.sfu.ca/~cbm/aands/page_378.htm 17086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 17186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * http://dlmf.nist.gov/10.25 17286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * http://dlmf.nist.gov/10.40 17386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 17486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * Note we assume x is nonnegative (the function is symmetric, 17586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * pass in the absolute value as needed). 17686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 17786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * Constants are compile time derived with templates I0Term<> and 17886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * I0ATerm<> to the precision of the compiler. The series can be expanded 17986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * to any precision needed, but currently set around 24b precision. 18086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 18186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * We use a bit of template math here, constexpr would probably be 18286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * more appropriate for a C++11 compiler. 18386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 1846582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * For the intermediate range 3.75 < x < 15, we use minimax polynomial fit. 1856582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 18686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung */ 18786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 18886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungtemplate <int N> 18986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstruct I0Term { 1906582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung static const double value = I0Term<N-1>::value / (4. * N * N); 19186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung}; 19286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 19386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungtemplate <> 19486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstruct I0Term<0> { 19586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung static const double value = 1.; 19686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung}; 19786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 19886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungtemplate <int N> 19986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstruct I0ATerm { 20086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung static const double value = I0ATerm<N-1>::value * (2.*N-1.) * (2.*N-1.) / (8. * N); 20186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung}; 20286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 20386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungtemplate <> 20486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstruct I0ATerm<0> { // 1/sqrt(2*PI); 20586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung static const double value = 0.398942280401432677939946059934381868475858631164934657665925; 20686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung}; 20786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 2086582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#if USE_HORNERS_METHOD 2096582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung/* Polynomial evaluation of A + Bx + Cx^2 + Dx^3 + ... 2106582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * using Horner's Method: http://en.wikipedia.org/wiki/Horner's_method 2116582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 2126582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * This has fewer multiplications than Estrin's method below, but has back to back 2136582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * floating point dependencies. 2146582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 2156582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * On ARM this appears to work slower, so USE_HORNERS_METHOD is not default enabled. 2166582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung */ 2176582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2186582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly2(double A, double B, double x) { 2196582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return A + x * B; 2206582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2216582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2226582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly4(double A, double B, double C, double D, double x) { 2236582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return A + x * (B + x * (C + x * (D))); 2246582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2256582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2266582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly7(double A, double B, double C, double D, double E, double F, double G, 2276582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double x) { 2286582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return A + x * (B + x * (C + x * (D + x * (E + x * (F + x * (G)))))); 2296582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2306582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2316582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly9(double A, double B, double C, double D, double E, double F, double G, 2326582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double H, double I, double x) { 2336582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return A + x * (B + x * (C + x * (D + x * (E + x * (F + x * (G + x * (H + x * (I)))))))); 2346582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2356582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2366582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#else 2376582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung/* Polynomial evaluation of A + Bx + Cx^2 + Dx^3 + ... 2386582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * using Estrin's Method: http://en.wikipedia.org/wiki/Estrin's_scheme 2396582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 2406582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * This is typically faster, perhaps gains about 5-10% overall on ARM processors 2416582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * over Horner's method above. 2426582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung */ 2436582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2446582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly2(double A, double B, double x) { 2456582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return A + B * x; 2466582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2476582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2486582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly3(double A, double B, double C, double x, double x2) { 2496582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return Poly2(A, B, x) + C * x2; 2506582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2516582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2526582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly3(double A, double B, double C, double x) { 2536582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return Poly2(A, B, x) + C * x * x; 2546582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2556582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2566582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly4(double A, double B, double C, double D, double x, double x2) { 2576582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return Poly2(A, B, x) + Poly2(C, D, x) * x2; // same as poly2(poly2, poly2, x2); 2586582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2596582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2606582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly4(double A, double B, double C, double D, double x) { 2616582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return Poly4(A, B, C, D, x, x * x); 2626582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2636582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2646582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly7(double A, double B, double C, double D, double E, double F, double G, 2656582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double x) { 2666582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double x2 = x * x; 2676582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return Poly4(A, B, C, D, x, x2) + Poly3(E, F, G, x, x2) * (x2 * x2); 2686582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2696582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2706582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly8(double A, double B, double C, double D, double E, double F, double G, 2716582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double H, double x, double x2, double x4) { 2726582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return Poly4(A, B, C, D, x, x2) + Poly4(E, F, G, H, x, x2) * x4; 2736582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2746582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 2756582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hunginline double Poly9(double A, double B, double C, double D, double E, double F, double G, 2766582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double H, double I, double x) { 2776582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double x2 = x * x; 2786582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#if 1 2796582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // It does not seem faster to explicitly decompose Poly8 into Poly4, but 2806582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // could depend on compiler floating point scheduling. 2816582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double x4 = x2 * x2; 2826582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return Poly8(A, B, C, D, E, F, G, H, x, x2, x4) + I * (x4 * x4); 2836582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#else 2846582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double val = Poly4(A, B, C, D, x, x2); 2856582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double x4 = x2 * x2; 2866582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return val + Poly4(E, F, G, H, x, x2) * x4 + I * (x4 * x4); 2876582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#endif 2886582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 2896582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#endif 2906582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 29186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstatic inline double I0(double x) { 2926582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung if (x < 3.75) { 2936582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung x *= x; 2946582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return Poly7(I0Term<0>::value, I0Term<1>::value, 2956582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung I0Term<2>::value, I0Term<3>::value, 2966582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung I0Term<4>::value, I0Term<5>::value, 2976582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung I0Term<6>::value, x); // e < 1.6e-7 2986582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 2996582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung if (1) { 3006582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung /* 3016582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Series expansion coefs are easy to calculate, but are expanded around 0, 3026582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * so error is unequal over the interval 0 < x < 3.75, the error being 3036582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * significantly better near 0. 3046582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 3056582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * A better solution is to use precise minimax polynomial fits. 3066582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 3076582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * We use a slightly more complicated solution for 3.75 < x < 15, based on 3086582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * the tables in Blair and Edwards, "Stable Rational Minimax Approximations 3096582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * to the Modified Bessel Functions I0(x) and I1(x)", Chalk Hill Nuclear Laboratory, 3106582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * AECL-4928. 3116582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 3126582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/06/178/6178667.pdf 3136582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 3146582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * See Table 11 for 0 < x < 15; e < 10^(-7.13). 3156582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 3166582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Note: Beta cannot exceed 15 (hence Stopband cannot exceed 144dB = 24b). 3176582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 3186582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * This speeds up overall computation by about 40% over using the else clause below, 3196582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * which requires sqrt and exp. 3206582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 3216582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung */ 3226582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 32386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung x *= x; 3246582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double num = Poly9(-0.13544938430e9, -0.33153754512e8, 3256582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung -0.19406631946e7, -0.48058318783e5, 3266582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung -0.63269783360e3, -0.49520779070e1, 3276582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung -0.24970910370e-1, -0.74741159550e-4, 3286582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung -0.18257612460e-6, x); 3296582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double y = x - 225.; // reflection around 15 (squared) 3306582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double den = Poly4(-0.34598737196e8, 0.23852643181e6, 3316582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung -0.70699387620e3, 0.10000000000e1, y); 3326582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return num / den; 3336582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 3346582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#if IO_EXTENDED_BETA 3356582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung /* Table 42 for x > 15; e < 10^(-8.11). 3366582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * This is used for Beta>15, but is disabled here as 3376582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * we never use Beta that high. 3386582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 3396582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * NOTE: This should be enabled only for x > 15. 3406582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung */ 3416582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 3426582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double y = 1./x; 3436582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double z = y - (1./15); 3446582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double num = Poly2(0.415079861746e1, -0.5149092496e1, z); 3456582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double den = Poly3(0.103150763823e2, -0.14181687413e2, 3466582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 0.1000000000e1, z); 3476582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return exp(x) * sqrt(y) * num / den; 3486582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#endif 3496582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } else { 3506582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung /* 3516582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * NOT USED, but reference for large Beta. 3526582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 3536582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Abramowitz and Stegun asymptotic formula. 3546582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * works for x > 3.75. 3556582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung */ 3566582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double y = 1./x; 3576582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return exp(x) * sqrt(y) * 3586582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // note: reciprocal squareroot may be easier! 3596582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // http://en.wikipedia.org/wiki/Fast_inverse_square_root 3606582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung Poly9(I0ATerm<0>::value, I0ATerm<1>::value, 3616582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung I0ATerm<2>::value, I0ATerm<3>::value, 3626582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung I0ATerm<4>::value, I0ATerm<5>::value, 3636582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung I0ATerm<6>::value, I0ATerm<7>::value, 3646582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung I0ATerm<8>::value, y); // (... e) < 1.9e-7 36586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 36686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung} 36786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 368bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung/* A speed optimized version of the Modified Bessel I0() which incorporates 369bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung * the sqrt and numerator multiply and denominator divide into the computation. 370bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung * This speeds up filter computation by about 10-15%. 371bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung */ 372bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hungstatic inline double I0SqrRat(double x2, double num, double den) { 373bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung if (x2 < (3.75 * 3.75)) { 374bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung return Poly7(I0Term<0>::value, I0Term<1>::value, 375bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung I0Term<2>::value, I0Term<3>::value, 376bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung I0Term<4>::value, I0Term<5>::value, 377bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung I0Term<6>::value, x2) * num / den; // e < 1.6e-7 378bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung } 379bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung num *= Poly9(-0.13544938430e9, -0.33153754512e8, 380bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung -0.19406631946e7, -0.48058318783e5, 381bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung -0.63269783360e3, -0.49520779070e1, 382bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung -0.24970910370e-1, -0.74741159550e-4, 383bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung -0.18257612460e-6, x2); // e < 10^(-7.13). 384bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung double y = x2 - 225.; // reflection around 15 (squared) 385bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung den *= Poly4(-0.34598737196e8, 0.23852643181e6, 386bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung -0.70699387620e3, 0.10000000000e1, y); 387bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung return num / den; 388bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung} 389bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung 39086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung/* 39186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * calculates the transition bandwidth for a Kaiser filter 39286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 3936582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Formula 3.2.8, Vaidyanathan, _Multirate Systems and Filter Banks_, p. 48 3946582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Formula 7.76, Oppenheim and Schafer, _Discrete-time Signal Processing, 3e_, p. 542 39586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 39686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param halfNumCoef is half the number of coefficients per filter phase. 3976582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 39886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param stopBandAtten is the stop band attenuation desired. 3996582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 40086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @return the transition bandwidth in normalized frequency (0 <= f <= 0.5) 40186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung */ 40286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstatic inline double firKaiserTbw(int halfNumCoef, double stopBandAtten) { 4036582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung return (stopBandAtten - 7.95)/((2.*14.36)*halfNumCoef); 40486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung} 40586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 40686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung/* 4076582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * calculates the fir transfer response of the overall polyphase filter at w. 4086582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4096582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Calculates the DTFT transfer coefficient H(w) for 0 <= w <= PI, utilizing the 4106582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * fact that h[n] is symmetric (cosines only, no complex arithmetic). 4116582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4126582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * We use Goertzel's algorithm to accelerate the computation to essentially 4136582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * a single multiply and 2 adds per filter coefficient h[]. 41486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 4156582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Be careful be careful to consider that h[n] is the overall polyphase filter, 4166582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * with L phases, so rescaling H(w)/L is probably what you expect for "unity gain", 4176582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * as you only use one of the polyphases at a time. 41886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung */ 41986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungtemplate <typename T> 42086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstatic inline double firTransfer(const T* coef, int L, int halfNumCoef, double w) { 4216582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double accum = static_cast<double>(coef[0])*0.5; // "center coefficient" from first bank 4226582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung coef += halfNumCoef; // skip first filterbank (picked up by the last filterbank). 4236582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#if SLOW_FIRTRANSFER 4246582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung /* Original code for reference. This is equivalent to the code below, but slower. */ 42586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung for (int i=1 ; i<=L ; ++i) { 42686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung for (int j=0, ix=i ; j<halfNumCoef ; ++j, ix+=L) { 42786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung accum += cos(ix*w)*static_cast<double>(*coef++); 42886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 42986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 4306582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#else 4316582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung /* 4326582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Our overall filter is stored striped by polyphases, not a contiguous h[n]. 4336582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * We could fetch coefficients in a non-contiguous fashion 4346582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * but that will not scale to vector processing. 4356582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4366582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * We apply Goertzel's algorithm directly to each polyphase filter bank instead of 4376582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * using cosine generation/multiplication, thereby saving one multiply per inner loop. 4386582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4396582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * See: http://en.wikipedia.org/wiki/Goertzel_algorithm 4406582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Also: Oppenheim and Schafer, _Discrete Time Signal Processing, 3e_, p. 720. 4416582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4426582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * We use the basic recursion to incorporate the cosine steps into real sequence x[n]: 4436582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * s[n] = x[n] + (2cosw)*s[n-1] + s[n-2] 4446582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4456582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * y[n] = s[n] - e^(iw)s[n-1] 4466582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * = sum_{k=-\infty}^{n} x[k]e^(-iw(n-k)) 4476582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * = e^(-iwn) sum_{k=0}^{n} x[k]e^(iwk) 4486582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4496582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * The summation contains the frequency steps we want multiplied by the source 4506582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * (similar to a DTFT). 4516582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4526582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Using symmetry, and just the real part (be careful, this must happen 4536582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * after any internal complex multiplications), the polyphase filterbank 4546582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * transfer function is: 4556582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4566582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Hpp[n, w, w_0] = sum_{k=0}^{n} x[k] * cos(wk + w_0) 4576582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * = Re{ e^(iwn + iw_0) y[n]} 4586582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * = cos(wn+w_0) * s[n] - cos(w(n+1)+w_0) * s[n-1] 4596582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4606582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * using the fact that s[n] of real x[n] is real. 4616582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4626582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung */ 4636582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double dcos = 2. * cos(L*w); 4646582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung int start = ((halfNumCoef)*L + 1); 4656582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung SineGen cc((start - L) * w, w, true); // cosine 4666582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung SineGen cp(start * w, w, true); // cosine 4676582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung for (int i=1 ; i<=L ; ++i) { 4686582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double sc = 0; 4696582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double sp = 0; 4706582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung for (int j=0 ; j<halfNumCoef ; ++j) { 4716582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double tmp = sc; 4726582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung sc = static_cast<double>(*coef++) + dcos*sc - sp; 4736582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung sp = tmp; 4746582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 4756582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // If we are awfully clever, we can apply Goertzel's algorithm 4766582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // again on the sc and sp sequences returned here. 4776582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung accum += cc.valueAdvance() * sc - cp.valueAdvance() * sp; 4786582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 4796582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung#endif 48086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung return accum*2.; 48186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung} 48286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 48386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung/* 4846582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * evaluates the minimum and maximum |H(f)| bound in a band region. 4856582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4866582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * This is usually done with equally spaced increments in the target band in question. 4876582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * The passband is often very small, and sampled that way. The stopband is often much 4886582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * larger. 4896582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4906582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * We use the fact that the overall polyphase filter has an additional bank at the end 4916582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * for interpolation; hence it is overspecified for the H(f) computation. Thus the 4926582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * first polyphase is never actually checked, excepting its first term. 4936582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4946582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * In this code we use the firTransfer() evaluator above, which uses Goertzel's 4956582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * algorithm to calculate the transfer function at each point. 4966582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 4976582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * TODO: An alternative with equal spacing is the FFT/DFT. An alternative with unequal 4986582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * spacing is a chirp transform. 49986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 50086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param coef is the designed polyphase filter banks 50186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 50286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param L is the number of phases (for interpolation) 50386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 50486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param halfNumCoef should be half the number of coefficients for a single 50586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * polyphase. 50686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 50786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param fstart is the normalized frequency start. 50886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 50986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param fend is the normalized frequency end. 51086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 51186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param steps is the number of steps to take (sampling) between frequency start and end 51286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 51386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param firMin returns the minimum transfer |H(f)| found 51486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 51586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param firMax returns the maximum transfer |H(f)| found 51686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 51786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 0 <= f <= 0.5. 51886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * This is used to test passband and stopband performance. 51986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung */ 52086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungtemplate <typename T> 52186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstatic void testFir(const T* coef, int L, int halfNumCoef, 52286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung double fstart, double fend, int steps, double &firMin, double &firMax) { 52386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung double wstart = fstart*(2.*M_PI); 52486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung double wend = fend*(2.*M_PI); 52586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung double wstep = (wend - wstart)/steps; 52686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung double fmax, fmin; 52786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung double trf = firTransfer(coef, L, halfNumCoef, wstart); 52886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung if (trf<0) { 52986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung trf = -trf; 53086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 53186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung fmin = fmax = trf; 53286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung wstart += wstep; 53386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung for (int i=1; i<steps; ++i) { 53486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung trf = firTransfer(coef, L, halfNumCoef, wstart); 53586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung if (trf<0) { 53686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung trf = -trf; 53786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 53886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung if (trf>fmax) { 53986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung fmax = trf; 54086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 54186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung else if (trf<fmin) { 54286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung fmin = trf; 54386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 54486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung wstart += wstep; 54586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 54686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // renormalize - this is only needed for integer filter types 54786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung double norm = 1./((1ULL<<(sizeof(T)*8-1))*L); 54886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 54986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung firMin = fmin * norm; 55086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung firMax = fmax * norm; 55186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung} 55286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 55386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung/* 5546582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * evaluates the |H(f)| lowpass band characteristics. 5556582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5566582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * This function tests the lowpass characteristics for the overall polyphase filter, 5576582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * and is used to verify the design. For this case, fp should be set to the 5586582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * passband normalized frequency from 0 to 0.5 for the overall filter (thus it 5596582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * is the designed polyphase bank value / L). Likewise for fs. 5606582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5616582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param coef is the designed polyphase filter banks 5626582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5636582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param L is the number of phases (for interpolation) 5646582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5656582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param halfNumCoef should be half the number of coefficients for a single 5666582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * polyphase. 5676582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5686582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param fp is the passband normalized frequency, 0 < fp < fs < 0.5. 5696582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5706582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param fs is the stopband normalized frequency, 0 < fp < fs < 0.5. 5716582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5726582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param passSteps is the number of passband sampling steps. 5736582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5746582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param stopSteps is the number of stopband sampling steps. 5756582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5766582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param passMin is the minimum value in the passband 5776582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5786582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param passMax is the maximum value in the passband (useful for scaling). This should 5796582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * be less than 1., to avoid sine wave test overflow. 5806582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5816582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param passRipple is the passband ripple. Typically this should be less than 0.1 for 5826582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * an audio filter. Generally speaker/headphone device characteristics will dominate 5836582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * the passband term. 5846582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5856582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param stopMax is the maximum value in the stopband. 5866582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5876582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * @param stopRipple is the stopband ripple, also known as stopband attenuation. 5886582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Typically this should be greater than ~80dB for low quality, and greater than 5896582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * ~100dB for full 16b quality, otherwise aliasing may become noticeable. 5906582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 5916582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung */ 5926582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hungtemplate <typename T> 5936582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hungstatic void testFir(const T* coef, int L, int halfNumCoef, 5946582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double fp, double fs, int passSteps, int stopSteps, 5956582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double &passMin, double &passMax, double &passRipple, 5966582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double &stopMax, double &stopRipple) { 5976582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double fmin, fmax; 5986582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung testFir(coef, L, halfNumCoef, 0., fp, passSteps, fmin, fmax); 5996582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double d1 = (fmax - fmin)/2.; 6006582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung passMin = fmin; 6016582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung passMax = fmax; 6026582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung passRipple = -20.*log10(1. - d1); // passband ripple 6036582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung testFir(coef, L, halfNumCoef, fs, 0.5, stopSteps, fmin, fmax); 6046582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // fmin is really not important for the stopband. 6056582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung stopMax = fmax; 6066582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung stopRipple = -20.*log10(fmax); // stopband ripple/attenuation 6076582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung} 6086582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 6096582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung/* 6106582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * Calculates the overall polyphase filter based on a windowed sinc function. 61186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 61286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * The windowed sinc is an odd length symmetric filter of exactly L*halfNumCoef*2+1 61386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * taps for the entire kernel. This is then decomposed into L+1 polyphase filterbanks. 61486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * The last filterbank is used for interpolation purposes (and is mostly composed 61586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * of the first bank shifted by one sample), and is unnecessary if one does 61686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * not do interpolation. 61786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 6186582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * We use the last filterbank for some transfer function calculation purposes, 6196582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * so it needs to be generated anyways. 6206582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung * 62186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param coef is the caller allocated space for coefficients. This should be 62286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * exactly (L+1)*halfNumCoef in size. 62386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 62486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param L is the number of phases (for interpolation) 62586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 62686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param halfNumCoef should be half the number of coefficients for a single 62786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * polyphase. 62886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 62986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param stopBandAtten is the stopband value, should be >50dB. 63086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 63186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param fcr is cutoff frequency/sampling rate (<0.5). At this point, the energy 63286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * should be 6dB less. (fcr is where the amplitude drops by half). Use the 63386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * firKaiserTbw() to calculate the transition bandwidth. fcr is the midpoint 63486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * between the stop band and the pass band (fstop+fpass)/2. 63586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * 63686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung * @param atten is the attenuation (generally slightly less than 1). 63786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung */ 63886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 63986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungtemplate <typename T> 64086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hungstatic inline void firKaiserGen(T* coef, int L, int halfNumCoef, 64186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung double stopBandAtten, double fcr, double atten) { 64286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 6436582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // Formula 3.2.5, 3.2.7, Vaidyanathan, _Multirate Systems and Filter Banks_, p. 48 6446582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // Formula 7.75, Oppenheim and Schafer, _Discrete-time Signal Processing, 3e_, p. 542 64586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 64686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // See also: http://melodi.ee.washington.edu/courses/ee518/notes/lec17.pdf 64786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 64886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // Kaiser window and beta parameter 64986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 65086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // | 0.1102*(A - 8.7) A > 50 65186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // beta = | 0.5842*(A - 21)^0.4 + 0.07886*(A - 21) 21 <= A <= 50 65286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // | 0. A < 21 65386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 65486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // with A is the desired stop-band attenuation in dBFS 65586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 65686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 30 dB 2.210 65786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 40 dB 3.384 65886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 50 dB 4.538 65986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 60 dB 5.658 66086eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 70 dB 6.764 66186eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 80 dB 7.865 66286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 90 dB 8.960 66386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung // 100 dB 10.056 66486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 66586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung const int N = L * halfNumCoef; // non-negative half 66686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung const double beta = 0.1102 * (stopBandAtten - 8.7); // >= 50dB always 6676582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung const double xstep = (2. * M_PI) * fcr / L; 66886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung const double xfrac = 1. / N; 6696582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung const double yscale = atten * L / (I0(beta) * M_PI); 670bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung const double sqrbeta = sqr(beta); 6716582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 6726582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // We use sine generators, which computes sines on regular step intervals. 6736582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // This speeds up overall computation about 40% from computing the sine directly. 6746582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 6756582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung SineGenGen sgg(0., xstep, L*xstep); // generates sine generators (one per polyphase) 6766582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 67786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung for (int i=0 ; i<=L ; ++i) { // generate an extra set of coefs for interpolation 6786582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 6796582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // computation for a single polyphase of the overall filter. 6806582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung SineGen sg = sgg.valueAdvance(); // current sine generator for "j" inner loop. 6816582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double err = 0; // for noise shaping on int16_t coefficients (over each polyphase) 6826582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 68386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung for (int j=0, ix=i ; j<halfNumCoef ; ++j, ix+=L) { 6846582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double y; 6856582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung if (CC_LIKELY(ix)) { 6866582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung double x = static_cast<double>(ix); 6876582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung 6886582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung // sine generator: sg.valueAdvance() returns sin(ix*xstep); 689bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung // y = I0(beta * sqrt(1.0 - sqr(x * xfrac))) * yscale * sg.valueAdvance() / x; 690bafa561d0c9363c5307b6b1daa498bd3ae36089dAndy Hung y = I0SqrRat(sqrbeta * (1.0 - sqr(x * xfrac)), yscale * sg.valueAdvance(), x); 6916582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } else { 6926582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung y = 2. * atten * fcr; // center of filter, sinc(0) = 1. 6936582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung sg.advance(); 6946582f2b14a21e630654c5522ef9ad64e80d5058dAndy Hung } 69586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 69686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung if (is_same<T, int16_t>::value) { // int16_t needs noise shaping 69786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung *coef++ = static_cast<T>(toint(y, 1ULL<<(sizeof(T)*8-1), err)); 698430b61c72094882bc48693dfc10c256a6ae36ee9Andy Hung } else if (is_same<T, int32_t>::value) { 69986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung *coef++ = static_cast<T>(toint(y, 1ULL<<(sizeof(T)*8-1))); 700430b61c72094882bc48693dfc10c256a6ae36ee9Andy Hung } else { // assumed float or double 701430b61c72094882bc48693dfc10c256a6ae36ee9Andy Hung *coef++ = static_cast<T>(y); 70286eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 70386eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 70486eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung } 70586eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung} 70686eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 70786eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung}; // namespace android 70886eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung 70986eae0e5931103e040ac2cdd023ef5db252e09f6Andy Hung#endif /*ANDROID_AUDIO_RESAMPLER_FIR_GEN_H*/ 710