AudioResamplerFirGen.h revision 86eae0e5931103e040ac2cdd023ef5db252e09f6 
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 * Sinc function is the traditional variant.
24 *
25 * TODO: Investigate optimizations (regular sampling grid, NEON vector accelerations)
26 * TODO: Remove comparison at 0 and trap at a higher level.
27 *
28 */
29
30static inline double sinc(double x) {
31    if (fabs(x) < FLT_MIN) {
32        return 1.;
33    }
34    return sin(x) / x;
35}
36
37static inline double sqr(double x) {
38    return x * x;
39}
40
41/*
42 * rounds a double to the nearest integer for FIR coefficients.
43 *
44 * One variant uses noise shaping, which must keep error history
45 * to work (the err parameter, initialized to 0).
46 * The other variant is a non-noise shaped version for
47 * S32 coefficients (noise shaping doesn't gain much).
48 *
49 * Caution: No bounds saturation is applied, but isn't needed in
50 * this case.
51 *
52 * @param x is the value to round.
53 *
54 * @param maxval is the maximum integer scale factor expressed as an int64 (for headroom).
55 * Typically this may be the maximum positive integer+1 (using the fact that double precision
56 * FIR coefficients generated here are never that close to 1.0 to pose an overflow condition).
57 *
58 * @param err is the previous error (actual - rounded) for the previous rounding op.
59 *
60 */
61
62static inline int64_t toint(double x, int64_t maxval, double& err) {
63    double val = x * maxval;
64    double ival = floor(val + 0.5 + err*0.17);
65    err = val - ival;
66    return static_cast<int64_t>(ival);
67}
68
69static inline int64_t toint(double x, int64_t maxval) {
70    return static_cast<int64_t>(floor(x * maxval + 0.5));
71}
72
73/*
74 * Modified Bessel function of the first kind
75 * http://en.wikipedia.org/wiki/Bessel_function
76 *
77 * The formulas are taken from Abramowitz and Stegun:
78 *
79 * http://people.math.sfu.ca/~cbm/aands/page_375.htm
80 * http://people.math.sfu.ca/~cbm/aands/page_378.htm
81 *
82 * http://dlmf.nist.gov/10.25
83 * http://dlmf.nist.gov/10.40
84 *
85 * Note we assume x is nonnegative (the function is symmetric,
86 * pass in the absolute value as needed).
87 *
88 * Constants are compile time derived with templates I0Term<> and
89 * I0ATerm<> to the precision of the compiler.  The series can be expanded
90 * to any precision needed, but currently set around 24b precision.
91 *
92 * We use a bit of template math here, constexpr would probably be
93 * more appropriate for a C++11 compiler.
94 *
95 */
96
97template <int N>
98struct I0Term {
99    static const double value = I0Term<N-1>::value/ (4. * N * N);
100};
101
102template <>
103struct I0Term<0> {
104    static const double value = 1.;
105};
106
107template <int N>
108struct I0ATerm {
109    static const double value = I0ATerm<N-1>::value * (2.*N-1.) * (2.*N-1.) / (8. * N);
110};
111
112template <>
113struct I0ATerm<0> { // 1/sqrt(2*PI);
114    static const double value = 0.398942280401432677939946059934381868475858631164934657665925;
115};
116
117static inline double I0(double x) {
118    if (x < 3.75) { // TODO: Estrin's method instead of Horner's method?
119        x *= x;
120        return I0Term<0>::value + x*(
121                I0Term<1>::value + x*(
122                I0Term<2>::value + x*(
123                I0Term<3>::value + x*(
124                I0Term<4>::value + x*(
125                I0Term<5>::value + x*(
126                I0Term<6>::value)))))); // e < 1.6e-7
127    }
128    // a bit ugly here - perhaps we expand the top series
129    // to permit computation to x < 20 (a reasonable range)
130    double y = 1./x;
131    return exp(x) * sqrt(y) * (
132            // note: reciprocal squareroot may be easier!
133            // http://en.wikipedia.org/wiki/Fast_inverse_square_root
134            I0ATerm<0>::value + y*(
135            I0ATerm<1>::value + y*(
136            I0ATerm<2>::value + y*(
137            I0ATerm<3>::value + y*(
138            I0ATerm<4>::value + y*(
139            I0ATerm<5>::value + y*(
140            I0ATerm<6>::value + y*(
141            I0ATerm<7>::value + y*(
142            I0ATerm<8>::value))))))))); // (... e) < 1.9e-7
143}
144
145/*
146 * calculates the transition bandwidth for a Kaiser filter
147 *
148 * Formula 3.2.8, Multirate Systems and Filter Banks, PP Vaidyanathan, pg. 48
149 *
150 * @param halfNumCoef is half the number of coefficients per filter phase.
151 * @param stopBandAtten is the stop band attenuation desired.
152 * @return the transition bandwidth in normalized frequency (0 <= f <= 0.5)
153 */
154static inline double firKaiserTbw(int halfNumCoef, double stopBandAtten) {
155    return (stopBandAtten - 7.95)/(2.*14.36*halfNumCoef);
156}
157
158/*
159 * calculates the fir transfer response.
160 *
161 * calculates the transfer coefficient H(w) for 0 <= w <= PI.
162 * Be careful be careful to consider the fact that this is an interpolated filter
163 * of length L, so normalizing H(w)/L is probably what you expect.
164 */
165template <typename T>
166static inline double firTransfer(const T* coef, int L, int halfNumCoef, double w) {
167    double accum = static_cast<double>(coef[0])*0.5;
168    coef += halfNumCoef;    // skip first row.
169    for (int i=1 ; i<=L ; ++i) {
170        for (int j=0, ix=i ; j<halfNumCoef ; ++j, ix+=L) {
171            accum += cos(ix*w)*static_cast<double>(*coef++);
172        }
173    }
174    return accum*2.;
175}
176
177/*
178 * returns the minimum and maximum |H(f)| bounds
179 *
180 * @param coef is the designed polyphase filter banks
181 *
182 * @param L is the number of phases (for interpolation)
183 *
184 * @param halfNumCoef should be half the number of coefficients for a single
185 * polyphase.
186 *
187 * @param fstart is the normalized frequency start.
188 *
189 * @param fend is the normalized frequency end.
190 *
191 * @param steps is the number of steps to take (sampling) between frequency start and end
192 *
193 * @param firMin returns the minimum transfer |H(f)| found
194 *
195 * @param firMax returns the maximum transfer |H(f)| found
196 *
197 * 0 <= f <= 0.5.
198 * This is used to test passband and stopband performance.
199 */
200template <typename T>
201static void testFir(const T* coef, int L, int halfNumCoef,
202        double fstart, double fend, int steps, double &firMin, double &firMax) {
203    double wstart = fstart*(2.*M_PI);
204    double wend = fend*(2.*M_PI);
205    double wstep = (wend - wstart)/steps;
206    double fmax, fmin;
207    double trf = firTransfer(coef, L, halfNumCoef, wstart);
208    if (trf<0) {
209        trf = -trf;
210    }
211    fmin = fmax = trf;
212    wstart += wstep;
213    for (int i=1; i<steps; ++i) {
214        trf = firTransfer(coef, L, halfNumCoef, wstart);
215        if (trf<0) {
216            trf = -trf;
217        }
218        if (trf>fmax) {
219            fmax = trf;
220        }
221        else if (trf<fmin) {
222            fmin = trf;
223        }
224        wstart += wstep;
225    }
226    // renormalize - this is only needed for integer filter types
227    double norm = 1./((1ULL<<(sizeof(T)*8-1))*L);
228
229    firMin = fmin * norm;
230    firMax = fmax * norm;
231}
232
233/*
234 * Calculates the polyphase filter banks based on a windowed sinc function.
235 *
236 * The windowed sinc is an odd length symmetric filter of exactly L*halfNumCoef*2+1
237 * taps for the entire kernel.  This is then decomposed into L+1 polyphase filterbanks.
238 * The last filterbank is used for interpolation purposes (and is mostly composed
239 * of the first bank shifted by one sample), and is unnecessary if one does
240 * not do interpolation.
241 *
242 * @param coef is the caller allocated space for coefficients.  This should be
243 * exactly (L+1)*halfNumCoef in size.
244 *
245 * @param L is the number of phases (for interpolation)
246 *
247 * @param halfNumCoef should be half the number of coefficients for a single
248 * polyphase.
249 *
250 * @param stopBandAtten is the stopband value, should be >50dB.
251 *
252 * @param fcr is cutoff frequency/sampling rate (<0.5).  At this point, the energy
253 * should be 6dB less. (fcr is where the amplitude drops by half).  Use the
254 * firKaiserTbw() to calculate the transition bandwidth.  fcr is the midpoint
255 * between the stop band and the pass band (fstop+fpass)/2.
256 *
257 * @param atten is the attenuation (generally slightly less than 1).
258 */
259
260template <typename T>
261static inline void firKaiserGen(T* coef, int L, int halfNumCoef,
262        double stopBandAtten, double fcr, double atten) {
263    //
264    // Formula 3.2.5, 3.2.7, Multirate Systems and Filter Banks, PP Vaidyanathan, pg. 48
265    //
266    // See also: http://melodi.ee.washington.edu/courses/ee518/notes/lec17.pdf
267    //
268    // Kaiser window and beta parameter
269    //
270    //         | 0.1102*(A - 8.7)                         A > 50
271    //  beta = | 0.5842*(A - 21)^0.4 + 0.07886*(A - 21)   21 <= A <= 50
272    //         | 0.                                       A < 21
273    //
274    // with A is the desired stop-band attenuation in dBFS
275    //
276    //    30 dB    2.210
277    //    40 dB    3.384
278    //    50 dB    4.538
279    //    60 dB    5.658
280    //    70 dB    6.764
281    //    80 dB    7.865
282    //    90 dB    8.960
283    //   100 dB   10.056
284
285    const int N = L * halfNumCoef; // non-negative half
286    const double beta = 0.1102 * (stopBandAtten - 8.7); // >= 50dB always
287    const double yscale = 2. * atten * fcr / I0(beta);
288    const double xstep = 2. * M_PI * fcr / L;
289    const double xfrac = 1. / N;
290    double err = 0; // for noise shaping on int16_t coefficients
291    for (int i=0 ; i<=L ; ++i) { // generate an extra set of coefs for interpolation
292        for (int j=0, ix=i ; j<halfNumCoef ; ++j, ix+=L) {
293            double y = I0(beta * sqrt(1.0 - sqr(ix * xfrac))) * sinc(ix * xstep) * yscale;
294
295            // (caution!) float version does not need rounding
296            if (is_same<T, int16_t>::value) { // int16_t needs noise shaping
297                *coef++ = static_cast<T>(toint(y, 1ULL<<(sizeof(T)*8-1), err));
298            } else {
299                *coef++ = static_cast<T>(toint(y, 1ULL<<(sizeof(T)*8-1)));
300            }
301        }
302    }
303}
304
305}; // namespace android
306
307#endif /*ANDROID_AUDIO_RESAMPLER_FIR_GEN_H*/
308