AudioResamplerFirGen.h revision 6582f2b14a21e630654c5522ef9ad64e80d5058d
1/* 2 * Copyright (C) 2013 The Android Open Source Project 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 17#ifndef ANDROID_AUDIO_RESAMPLER_FIR_GEN_H 18#define ANDROID_AUDIO_RESAMPLER_FIR_GEN_H 19 20namespace android { 21 22/* 23 * generates a sine wave at equal steps. 24 * 25 * As most of our functions use sine or cosine at equal steps, 26 * it is very efficient to compute them that way (single multiply and subtract), 27 * rather than invoking the math library sin() or cos() each time. 28 * 29 * SineGen uses Goertzel's Algorithm (as a generator not a filter) 30 * to calculate sine(wstart + n * wstep) or cosine(wstart + n * wstep) 31 * by stepping through 0, 1, ... n. 32 * 33 * e^i(wstart+wstep) = 2cos(wstep) * e^i(wstart) - e^i(wstart-wstep) 34 * 35 * or looking at just the imaginary sine term, as the cosine follows identically: 36 * 37 * sin(wstart+wstep) = 2cos(wstep) * sin(wstart) - sin(wstart-wstep) 38 * 39 * Goertzel's algorithm is more efficient than the angle addition formula, 40 * e^i(wstart+wstep) = e^i(wstart) * e^i(wstep), which takes up to 41 * 4 multiplies and 2 adds (or 3* and 3+) and requires both sine and 42 * cosine generation due to the complex * complex multiply (full rotation). 43 * 44 * See: http://en.wikipedia.org/wiki/Goertzel_algorithm 45 * 46 */ 47 48class SineGen { 49public: 50 SineGen(double wstart, double wstep, bool cosine = false) { 51 if (cosine) { 52 mCurrent = cos(wstart); 53 mPrevious = cos(wstart - wstep); 54 } else { 55 mCurrent = sin(wstart); 56 mPrevious = sin(wstart - wstep); 57 } 58 mTwoCos = 2.*cos(wstep); 59 } 60 SineGen(double expNow, double expPrev, double twoCosStep) { 61 mCurrent = expNow; 62 mPrevious = expPrev; 63 mTwoCos = twoCosStep; 64 } 65 inline double value() const { 66 return mCurrent; 67 } 68 inline void advance() { 69 double tmp = mCurrent; 70 mCurrent = mCurrent*mTwoCos - mPrevious; 71 mPrevious = tmp; 72 } 73 inline double valueAdvance() { 74 double tmp = mCurrent; 75 mCurrent = mCurrent*mTwoCos - mPrevious; 76 mPrevious = tmp; 77 return tmp; 78 } 79 80private: 81 double mCurrent; // current value of sine/cosine 82 double mPrevious; // previous value of sine/cosine 83 double mTwoCos; // stepping factor 84}; 85 86/* 87 * generates a series of sine generators, phase offset by fixed steps. 88 * 89 * This is used to generate polyphase sine generators, one per polyphase 90 * in the filter code below. 91 * 92 * The SineGen returned by value() starts at innerStart = outerStart + n*outerStep; 93 * increments by innerStep. 94 * 95 */ 96 97class SineGenGen { 98public: 99 SineGenGen(double outerStart, double outerStep, double innerStep, bool cosine = false) 100 : mSineInnerCur(outerStart, outerStep, cosine), 101 mSineInnerPrev(outerStart-innerStep, outerStep, cosine) 102 { 103 mTwoCos = 2.*cos(innerStep); 104 } 105 inline SineGen value() { 106 return SineGen(mSineInnerCur.value(), mSineInnerPrev.value(), mTwoCos); 107 } 108 inline void advance() { 109 mSineInnerCur.advance(); 110 mSineInnerPrev.advance(); 111 } 112 inline SineGen valueAdvance() { 113 return SineGen(mSineInnerCur.valueAdvance(), mSineInnerPrev.valueAdvance(), mTwoCos); 114 } 115 116private: 117 SineGen mSineInnerCur; // generate the inner sine values (stepped by outerStep). 118 SineGen mSineInnerPrev; // generate the inner sine previous values 119 // (behind by innerStep, stepped by outerStep). 120 double mTwoCos; // the inner stepping factor for the returned SineGen. 121}; 122 123static inline double sqr(double x) { 124 return x * x; 125} 126 127/* 128 * rounds a double to the nearest integer for FIR coefficients. 129 * 130 * One variant uses noise shaping, which must keep error history 131 * to work (the err parameter, initialized to 0). 132 * The other variant is a non-noise shaped version for 133 * S32 coefficients (noise shaping doesn't gain much). 134 * 135 * Caution: No bounds saturation is applied, but isn't needed in this case. 136 * 137 * @param x is the value to round. 138 * 139 * @param maxval is the maximum integer scale factor expressed as an int64 (for headroom). 140 * Typically this may be the maximum positive integer+1 (using the fact that double precision 141 * FIR coefficients generated here are never that close to 1.0 to pose an overflow condition). 142 * 143 * @param err is the previous error (actual - rounded) for the previous rounding op. 144 * For 16b coefficients this can improve stopband dB performance by up to 2dB. 145 * 146 * Many variants exist for the noise shaping: http://en.wikipedia.org/wiki/Noise_shaping 147 * 148 */ 149 150static inline int64_t toint(double x, int64_t maxval, double& err) { 151 double val = x * maxval; 152 double ival = floor(val + 0.5 + err*0.2); 153 err = val - ival; 154 return static_cast<int64_t>(ival); 155} 156 157static inline int64_t toint(double x, int64_t maxval) { 158 return static_cast<int64_t>(floor(x * maxval + 0.5)); 159} 160 161/* 162 * Modified Bessel function of the first kind 163 * http://en.wikipedia.org/wiki/Bessel_function 164 * 165 * The formulas are taken from Abramowitz and Stegun, 166 * _Handbook of Mathematical Functions_ (links below): 167 * 168 * http://people.math.sfu.ca/~cbm/aands/page_375.htm 169 * http://people.math.sfu.ca/~cbm/aands/page_378.htm 170 * 171 * http://dlmf.nist.gov/10.25 172 * http://dlmf.nist.gov/10.40 173 * 174 * Note we assume x is nonnegative (the function is symmetric, 175 * pass in the absolute value as needed). 176 * 177 * Constants are compile time derived with templates I0Term<> and 178 * I0ATerm<> to the precision of the compiler. The series can be expanded 179 * to any precision needed, but currently set around 24b precision. 180 * 181 * We use a bit of template math here, constexpr would probably be 182 * more appropriate for a C++11 compiler. 183 * 184 * For the intermediate range 3.75 < x < 15, we use minimax polynomial fit. 185 * 186 */ 187 188template <int N> 189struct I0Term { 190 static const double value = I0Term<N-1>::value / (4. * N * N); 191}; 192 193template <> 194struct I0Term<0> { 195 static const double value = 1.; 196}; 197 198template <int N> 199struct I0ATerm { 200 static const double value = I0ATerm<N-1>::value * (2.*N-1.) * (2.*N-1.) / (8. * N); 201}; 202 203template <> 204struct I0ATerm<0> { // 1/sqrt(2*PI); 205 static const double value = 0.398942280401432677939946059934381868475858631164934657665925; 206}; 207 208#if USE_HORNERS_METHOD 209/* Polynomial evaluation of A + Bx + Cx^2 + Dx^3 + ... 210 * using Horner's Method: http://en.wikipedia.org/wiki/Horner's_method 211 * 212 * This has fewer multiplications than Estrin's method below, but has back to back 213 * floating point dependencies. 214 * 215 * On ARM this appears to work slower, so USE_HORNERS_METHOD is not default enabled. 216 */ 217 218inline double Poly2(double A, double B, double x) { 219 return A + x * B; 220} 221 222inline double Poly4(double A, double B, double C, double D, double x) { 223 return A + x * (B + x * (C + x * (D))); 224} 225 226inline double Poly7(double A, double B, double C, double D, double E, double F, double G, 227 double x) { 228 return A + x * (B + x * (C + x * (D + x * (E + x * (F + x * (G)))))); 229} 230 231inline double Poly9(double A, double B, double C, double D, double E, double F, double G, 232 double H, double I, double x) { 233 return A + x * (B + x * (C + x * (D + x * (E + x * (F + x * (G + x * (H + x * (I)))))))); 234} 235 236#else 237/* Polynomial evaluation of A + Bx + Cx^2 + Dx^3 + ... 238 * using Estrin's Method: http://en.wikipedia.org/wiki/Estrin's_scheme 239 * 240 * This is typically faster, perhaps gains about 5-10% overall on ARM processors 241 * over Horner's method above. 242 */ 243 244inline double Poly2(double A, double B, double x) { 245 return A + B * x; 246} 247 248inline double Poly3(double A, double B, double C, double x, double x2) { 249 return Poly2(A, B, x) + C * x2; 250} 251 252inline double Poly3(double A, double B, double C, double x) { 253 return Poly2(A, B, x) + C * x * x; 254} 255 256inline double Poly4(double A, double B, double C, double D, double x, double x2) { 257 return Poly2(A, B, x) + Poly2(C, D, x) * x2; // same as poly2(poly2, poly2, x2); 258} 259 260inline double Poly4(double A, double B, double C, double D, double x) { 261 return Poly4(A, B, C, D, x, x * x); 262} 263 264inline double Poly7(double A, double B, double C, double D, double E, double F, double G, 265 double x) { 266 double x2 = x * x; 267 return Poly4(A, B, C, D, x, x2) + Poly3(E, F, G, x, x2) * (x2 * x2); 268} 269 270inline double Poly8(double A, double B, double C, double D, double E, double F, double G, 271 double H, double x, double x2, double x4) { 272 return Poly4(A, B, C, D, x, x2) + Poly4(E, F, G, H, x, x2) * x4; 273} 274 275inline double Poly9(double A, double B, double C, double D, double E, double F, double G, 276 double H, double I, double x) { 277 double x2 = x * x; 278#if 1 279 // It does not seem faster to explicitly decompose Poly8 into Poly4, but 280 // could depend on compiler floating point scheduling. 281 double x4 = x2 * x2; 282 return Poly8(A, B, C, D, E, F, G, H, x, x2, x4) + I * (x4 * x4); 283#else 284 double val = Poly4(A, B, C, D, x, x2); 285 double x4 = x2 * x2; 286 return val + Poly4(E, F, G, H, x, x2) * x4 + I * (x4 * x4); 287#endif 288} 289#endif 290 291static inline double I0(double x) { 292 if (x < 3.75) { 293 x *= x; 294 return Poly7(I0Term<0>::value, I0Term<1>::value, 295 I0Term<2>::value, I0Term<3>::value, 296 I0Term<4>::value, I0Term<5>::value, 297 I0Term<6>::value, x); // e < 1.6e-7 298 } 299 if (1) { 300 /* 301 * Series expansion coefs are easy to calculate, but are expanded around 0, 302 * so error is unequal over the interval 0 < x < 3.75, the error being 303 * significantly better near 0. 304 * 305 * A better solution is to use precise minimax polynomial fits. 306 * 307 * We use a slightly more complicated solution for 3.75 < x < 15, based on 308 * the tables in Blair and Edwards, "Stable Rational Minimax Approximations 309 * to the Modified Bessel Functions I0(x) and I1(x)", Chalk Hill Nuclear Laboratory, 310 * AECL-4928. 311 * 312 * http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/06/178/6178667.pdf 313 * 314 * See Table 11 for 0 < x < 15; e < 10^(-7.13). 315 * 316 * Note: Beta cannot exceed 15 (hence Stopband cannot exceed 144dB = 24b). 317 * 318 * This speeds up overall computation by about 40% over using the else clause below, 319 * which requires sqrt and exp. 320 * 321 */ 322 323 x *= x; 324 double num = Poly9(-0.13544938430e9, -0.33153754512e8, 325 -0.19406631946e7, -0.48058318783e5, 326 -0.63269783360e3, -0.49520779070e1, 327 -0.24970910370e-1, -0.74741159550e-4, 328 -0.18257612460e-6, x); 329 double y = x - 225.; // reflection around 15 (squared) 330 double den = Poly4(-0.34598737196e8, 0.23852643181e6, 331 -0.70699387620e3, 0.10000000000e1, y); 332 return num / den; 333 334#if IO_EXTENDED_BETA 335 /* Table 42 for x > 15; e < 10^(-8.11). 336 * This is used for Beta>15, but is disabled here as 337 * we never use Beta that high. 338 * 339 * NOTE: This should be enabled only for x > 15. 340 */ 341 342 double y = 1./x; 343 double z = y - (1./15); 344 double num = Poly2(0.415079861746e1, -0.5149092496e1, z); 345 double den = Poly3(0.103150763823e2, -0.14181687413e2, 346 0.1000000000e1, z); 347 return exp(x) * sqrt(y) * num / den; 348#endif 349 } else { 350 /* 351 * NOT USED, but reference for large Beta. 352 * 353 * Abramowitz and Stegun asymptotic formula. 354 * works for x > 3.75. 355 */ 356 double y = 1./x; 357 return exp(x) * sqrt(y) * 358 // note: reciprocal squareroot may be easier! 359 // http://en.wikipedia.org/wiki/Fast_inverse_square_root 360 Poly9(I0ATerm<0>::value, I0ATerm<1>::value, 361 I0ATerm<2>::value, I0ATerm<3>::value, 362 I0ATerm<4>::value, I0ATerm<5>::value, 363 I0ATerm<6>::value, I0ATerm<7>::value, 364 I0ATerm<8>::value, y); // (... e) < 1.9e-7 365 } 366} 367 368/* 369 * calculates the transition bandwidth for a Kaiser filter 370 * 371 * Formula 3.2.8, Vaidyanathan, _Multirate Systems and Filter Banks_, p. 48 372 * Formula 7.76, Oppenheim and Schafer, _Discrete-time Signal Processing, 3e_, p. 542 373 * 374 * @param halfNumCoef is half the number of coefficients per filter phase. 375 * 376 * @param stopBandAtten is the stop band attenuation desired. 377 * 378 * @return the transition bandwidth in normalized frequency (0 <= f <= 0.5) 379 */ 380static inline double firKaiserTbw(int halfNumCoef, double stopBandAtten) { 381 return (stopBandAtten - 7.95)/((2.*14.36)*halfNumCoef); 382} 383 384/* 385 * calculates the fir transfer response of the overall polyphase filter at w. 386 * 387 * Calculates the DTFT transfer coefficient H(w) for 0 <= w <= PI, utilizing the 388 * fact that h[n] is symmetric (cosines only, no complex arithmetic). 389 * 390 * We use Goertzel's algorithm to accelerate the computation to essentially 391 * a single multiply and 2 adds per filter coefficient h[]. 392 * 393 * Be careful be careful to consider that h[n] is the overall polyphase filter, 394 * with L phases, so rescaling H(w)/L is probably what you expect for "unity gain", 395 * as you only use one of the polyphases at a time. 396 */ 397template <typename T> 398static inline double firTransfer(const T* coef, int L, int halfNumCoef, double w) { 399 double accum = static_cast<double>(coef[0])*0.5; // "center coefficient" from first bank 400 coef += halfNumCoef; // skip first filterbank (picked up by the last filterbank). 401#if SLOW_FIRTRANSFER 402 /* Original code for reference. This is equivalent to the code below, but slower. */ 403 for (int i=1 ; i<=L ; ++i) { 404 for (int j=0, ix=i ; j<halfNumCoef ; ++j, ix+=L) { 405 accum += cos(ix*w)*static_cast<double>(*coef++); 406 } 407 } 408#else 409 /* 410 * Our overall filter is stored striped by polyphases, not a contiguous h[n]. 411 * We could fetch coefficients in a non-contiguous fashion 412 * but that will not scale to vector processing. 413 * 414 * We apply Goertzel's algorithm directly to each polyphase filter bank instead of 415 * using cosine generation/multiplication, thereby saving one multiply per inner loop. 416 * 417 * See: http://en.wikipedia.org/wiki/Goertzel_algorithm 418 * Also: Oppenheim and Schafer, _Discrete Time Signal Processing, 3e_, p. 720. 419 * 420 * We use the basic recursion to incorporate the cosine steps into real sequence x[n]: 421 * s[n] = x[n] + (2cosw)*s[n-1] + s[n-2] 422 * 423 * y[n] = s[n] - e^(iw)s[n-1] 424 * = sum_{k=-\infty}^{n} x[k]e^(-iw(n-k)) 425 * = e^(-iwn) sum_{k=0}^{n} x[k]e^(iwk) 426 * 427 * The summation contains the frequency steps we want multiplied by the source 428 * (similar to a DTFT). 429 * 430 * Using symmetry, and just the real part (be careful, this must happen 431 * after any internal complex multiplications), the polyphase filterbank 432 * transfer function is: 433 * 434 * Hpp[n, w, w_0] = sum_{k=0}^{n} x[k] * cos(wk + w_0) 435 * = Re{ e^(iwn + iw_0) y[n]} 436 * = cos(wn+w_0) * s[n] - cos(w(n+1)+w_0) * s[n-1] 437 * 438 * using the fact that s[n] of real x[n] is real. 439 * 440 */ 441 double dcos = 2. * cos(L*w); 442 int start = ((halfNumCoef)*L + 1); 443 SineGen cc((start - L) * w, w, true); // cosine 444 SineGen cp(start * w, w, true); // cosine 445 for (int i=1 ; i<=L ; ++i) { 446 double sc = 0; 447 double sp = 0; 448 for (int j=0 ; j<halfNumCoef ; ++j) { 449 double tmp = sc; 450 sc = static_cast<double>(*coef++) + dcos*sc - sp; 451 sp = tmp; 452 } 453 // If we are awfully clever, we can apply Goertzel's algorithm 454 // again on the sc and sp sequences returned here. 455 accum += cc.valueAdvance() * sc - cp.valueAdvance() * sp; 456 } 457#endif 458 return accum*2.; 459} 460 461/* 462 * evaluates the minimum and maximum |H(f)| bound in a band region. 463 * 464 * This is usually done with equally spaced increments in the target band in question. 465 * The passband is often very small, and sampled that way. The stopband is often much 466 * larger. 467 * 468 * We use the fact that the overall polyphase filter has an additional bank at the end 469 * for interpolation; hence it is overspecified for the H(f) computation. Thus the 470 * first polyphase is never actually checked, excepting its first term. 471 * 472 * In this code we use the firTransfer() evaluator above, which uses Goertzel's 473 * algorithm to calculate the transfer function at each point. 474 * 475 * TODO: An alternative with equal spacing is the FFT/DFT. An alternative with unequal 476 * spacing is a chirp transform. 477 * 478 * @param coef is the designed polyphase filter banks 479 * 480 * @param L is the number of phases (for interpolation) 481 * 482 * @param halfNumCoef should be half the number of coefficients for a single 483 * polyphase. 484 * 485 * @param fstart is the normalized frequency start. 486 * 487 * @param fend is the normalized frequency end. 488 * 489 * @param steps is the number of steps to take (sampling) between frequency start and end 490 * 491 * @param firMin returns the minimum transfer |H(f)| found 492 * 493 * @param firMax returns the maximum transfer |H(f)| found 494 * 495 * 0 <= f <= 0.5. 496 * This is used to test passband and stopband performance. 497 */ 498template <typename T> 499static void testFir(const T* coef, int L, int halfNumCoef, 500 double fstart, double fend, int steps, double &firMin, double &firMax) { 501 double wstart = fstart*(2.*M_PI); 502 double wend = fend*(2.*M_PI); 503 double wstep = (wend - wstart)/steps; 504 double fmax, fmin; 505 double trf = firTransfer(coef, L, halfNumCoef, wstart); 506 if (trf<0) { 507 trf = -trf; 508 } 509 fmin = fmax = trf; 510 wstart += wstep; 511 for (int i=1; i<steps; ++i) { 512 trf = firTransfer(coef, L, halfNumCoef, wstart); 513 if (trf<0) { 514 trf = -trf; 515 } 516 if (trf>fmax) { 517 fmax = trf; 518 } 519 else if (trf<fmin) { 520 fmin = trf; 521 } 522 wstart += wstep; 523 } 524 // renormalize - this is only needed for integer filter types 525 double norm = 1./((1ULL<<(sizeof(T)*8-1))*L); 526 527 firMin = fmin * norm; 528 firMax = fmax * norm; 529} 530 531/* 532 * evaluates the |H(f)| lowpass band characteristics. 533 * 534 * This function tests the lowpass characteristics for the overall polyphase filter, 535 * and is used to verify the design. For this case, fp should be set to the 536 * passband normalized frequency from 0 to 0.5 for the overall filter (thus it 537 * is the designed polyphase bank value / L). Likewise for fs. 538 * 539 * @param coef is the designed polyphase filter banks 540 * 541 * @param L is the number of phases (for interpolation) 542 * 543 * @param halfNumCoef should be half the number of coefficients for a single 544 * polyphase. 545 * 546 * @param fp is the passband normalized frequency, 0 < fp < fs < 0.5. 547 * 548 * @param fs is the stopband normalized frequency, 0 < fp < fs < 0.5. 549 * 550 * @param passSteps is the number of passband sampling steps. 551 * 552 * @param stopSteps is the number of stopband sampling steps. 553 * 554 * @param passMin is the minimum value in the passband 555 * 556 * @param passMax is the maximum value in the passband (useful for scaling). This should 557 * be less than 1., to avoid sine wave test overflow. 558 * 559 * @param passRipple is the passband ripple. Typically this should be less than 0.1 for 560 * an audio filter. Generally speaker/headphone device characteristics will dominate 561 * the passband term. 562 * 563 * @param stopMax is the maximum value in the stopband. 564 * 565 * @param stopRipple is the stopband ripple, also known as stopband attenuation. 566 * Typically this should be greater than ~80dB for low quality, and greater than 567 * ~100dB for full 16b quality, otherwise aliasing may become noticeable. 568 * 569 */ 570template <typename T> 571static void testFir(const T* coef, int L, int halfNumCoef, 572 double fp, double fs, int passSteps, int stopSteps, 573 double &passMin, double &passMax, double &passRipple, 574 double &stopMax, double &stopRipple) { 575 double fmin, fmax; 576 testFir(coef, L, halfNumCoef, 0., fp, passSteps, fmin, fmax); 577 double d1 = (fmax - fmin)/2.; 578 passMin = fmin; 579 passMax = fmax; 580 passRipple = -20.*log10(1. - d1); // passband ripple 581 testFir(coef, L, halfNumCoef, fs, 0.5, stopSteps, fmin, fmax); 582 // fmin is really not important for the stopband. 583 stopMax = fmax; 584 stopRipple = -20.*log10(fmax); // stopband ripple/attenuation 585} 586 587/* 588 * Calculates the overall polyphase filter based on a windowed sinc function. 589 * 590 * The windowed sinc is an odd length symmetric filter of exactly L*halfNumCoef*2+1 591 * taps for the entire kernel. This is then decomposed into L+1 polyphase filterbanks. 592 * The last filterbank is used for interpolation purposes (and is mostly composed 593 * of the first bank shifted by one sample), and is unnecessary if one does 594 * not do interpolation. 595 * 596 * We use the last filterbank for some transfer function calculation purposes, 597 * so it needs to be generated anyways. 598 * 599 * @param coef is the caller allocated space for coefficients. This should be 600 * exactly (L+1)*halfNumCoef in size. 601 * 602 * @param L is the number of phases (for interpolation) 603 * 604 * @param halfNumCoef should be half the number of coefficients for a single 605 * polyphase. 606 * 607 * @param stopBandAtten is the stopband value, should be >50dB. 608 * 609 * @param fcr is cutoff frequency/sampling rate (<0.5). At this point, the energy 610 * should be 6dB less. (fcr is where the amplitude drops by half). Use the 611 * firKaiserTbw() to calculate the transition bandwidth. fcr is the midpoint 612 * between the stop band and the pass band (fstop+fpass)/2. 613 * 614 * @param atten is the attenuation (generally slightly less than 1). 615 */ 616 617template <typename T> 618static inline void firKaiserGen(T* coef, int L, int halfNumCoef, 619 double stopBandAtten, double fcr, double atten) { 620 // 621 // Formula 3.2.5, 3.2.7, Vaidyanathan, _Multirate Systems and Filter Banks_, p. 48 622 // Formula 7.75, Oppenheim and Schafer, _Discrete-time Signal Processing, 3e_, p. 542 623 // 624 // See also: http://melodi.ee.washington.edu/courses/ee518/notes/lec17.pdf 625 // 626 // Kaiser window and beta parameter 627 // 628 // | 0.1102*(A - 8.7) A > 50 629 // beta = | 0.5842*(A - 21)^0.4 + 0.07886*(A - 21) 21 <= A <= 50 630 // | 0. A < 21 631 // 632 // with A is the desired stop-band attenuation in dBFS 633 // 634 // 30 dB 2.210 635 // 40 dB 3.384 636 // 50 dB 4.538 637 // 60 dB 5.658 638 // 70 dB 6.764 639 // 80 dB 7.865 640 // 90 dB 8.960 641 // 100 dB 10.056 642 643 const int N = L * halfNumCoef; // non-negative half 644 const double beta = 0.1102 * (stopBandAtten - 8.7); // >= 50dB always 645 const double xstep = (2. * M_PI) * fcr / L; 646 const double xfrac = 1. / N; 647 const double yscale = atten * L / (I0(beta) * M_PI); 648 649 // We use sine generators, which computes sines on regular step intervals. 650 // This speeds up overall computation about 40% from computing the sine directly. 651 652 SineGenGen sgg(0., xstep, L*xstep); // generates sine generators (one per polyphase) 653 654 for (int i=0 ; i<=L ; ++i) { // generate an extra set of coefs for interpolation 655 656 // computation for a single polyphase of the overall filter. 657 SineGen sg = sgg.valueAdvance(); // current sine generator for "j" inner loop. 658 double err = 0; // for noise shaping on int16_t coefficients (over each polyphase) 659 660 for (int j=0, ix=i ; j<halfNumCoef ; ++j, ix+=L) { 661 double y; 662 if (CC_LIKELY(ix)) { 663 double x = static_cast<double>(ix); 664 665 // sine generator: sg.valueAdvance() returns sin(ix*xstep); 666 y = I0(beta * sqrt(1.0 - sqr(x * xfrac))) * yscale * sg.valueAdvance() / x; 667 } else { 668 y = 2. * atten * fcr; // center of filter, sinc(0) = 1. 669 sg.advance(); 670 } 671 672 // (caution!) float version does not need rounding 673 if (is_same<T, int16_t>::value) { // int16_t needs noise shaping 674 *coef++ = static_cast<T>(toint(y, 1ULL<<(sizeof(T)*8-1), err)); 675 } else { 676 *coef++ = static_cast<T>(toint(y, 1ULL<<(sizeof(T)*8-1))); 677 } 678 } 679 } 680} 681 682}; // namespace android 683 684#endif /*ANDROID_AUDIO_RESAMPLER_FIR_GEN_H*/ 685