| /* |
| * Copyright (C) 2013 The Android Open Source Project |
| * |
| * Licensed under the Apache License, Version 2.0 (the "License"); |
| * you may not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| #ifndef ANDROID_AUDIO_RESAMPLER_FIR_GEN_H |
| #define ANDROID_AUDIO_RESAMPLER_FIR_GEN_H |
| |
| namespace android { |
| |
| /* |
| * Sinc function is the traditional variant. |
| * |
| * TODO: Investigate optimizations (regular sampling grid, NEON vector accelerations) |
| * TODO: Remove comparison at 0 and trap at a higher level. |
| * |
| */ |
| |
| static inline double sinc(double x) { |
| if (fabs(x) < FLT_MIN) { |
| return 1.; |
| } |
| return sin(x) / x; |
| } |
| |
| static inline double sqr(double x) { |
| return x * x; |
| } |
| |
| /* |
| * rounds a double to the nearest integer for FIR coefficients. |
| * |
| * One variant uses noise shaping, which must keep error history |
| * to work (the err parameter, initialized to 0). |
| * The other variant is a non-noise shaped version for |
| * S32 coefficients (noise shaping doesn't gain much). |
| * |
| * Caution: No bounds saturation is applied, but isn't needed in |
| * this case. |
| * |
| * @param x is the value to round. |
| * |
| * @param maxval is the maximum integer scale factor expressed as an int64 (for headroom). |
| * Typically this may be the maximum positive integer+1 (using the fact that double precision |
| * FIR coefficients generated here are never that close to 1.0 to pose an overflow condition). |
| * |
| * @param err is the previous error (actual - rounded) for the previous rounding op. |
| * |
| */ |
| |
| static inline int64_t toint(double x, int64_t maxval, double& err) { |
| double val = x * maxval; |
| double ival = floor(val + 0.5 + err*0.17); |
| err = val - ival; |
| return static_cast<int64_t>(ival); |
| } |
| |
| static inline int64_t toint(double x, int64_t maxval) { |
| return static_cast<int64_t>(floor(x * maxval + 0.5)); |
| } |
| |
| /* |
| * Modified Bessel function of the first kind |
| * http://en.wikipedia.org/wiki/Bessel_function |
| * |
| * The formulas are taken from Abramowitz and Stegun: |
| * |
| * http://people.math.sfu.ca/~cbm/aands/page_375.htm |
| * http://people.math.sfu.ca/~cbm/aands/page_378.htm |
| * |
| * http://dlmf.nist.gov/10.25 |
| * http://dlmf.nist.gov/10.40 |
| * |
| * Note we assume x is nonnegative (the function is symmetric, |
| * pass in the absolute value as needed). |
| * |
| * Constants are compile time derived with templates I0Term<> and |
| * I0ATerm<> to the precision of the compiler. The series can be expanded |
| * to any precision needed, but currently set around 24b precision. |
| * |
| * We use a bit of template math here, constexpr would probably be |
| * more appropriate for a C++11 compiler. |
| * |
| */ |
| |
| template <int N> |
| struct I0Term { |
| static const double value = I0Term<N-1>::value/ (4. * N * N); |
| }; |
| |
| template <> |
| struct I0Term<0> { |
| static const double value = 1.; |
| }; |
| |
| template <int N> |
| struct I0ATerm { |
| static const double value = I0ATerm<N-1>::value * (2.*N-1.) * (2.*N-1.) / (8. * N); |
| }; |
| |
| template <> |
| struct I0ATerm<0> { // 1/sqrt(2*PI); |
| static const double value = 0.398942280401432677939946059934381868475858631164934657665925; |
| }; |
| |
| static inline double I0(double x) { |
| if (x < 3.75) { // TODO: Estrin's method instead of Horner's method? |
| x *= x; |
| return I0Term<0>::value + x*( |
| I0Term<1>::value + x*( |
| I0Term<2>::value + x*( |
| I0Term<3>::value + x*( |
| I0Term<4>::value + x*( |
| I0Term<5>::value + x*( |
| I0Term<6>::value)))))); // e < 1.6e-7 |
| } |
| // a bit ugly here - perhaps we expand the top series |
| // to permit computation to x < 20 (a reasonable range) |
| double y = 1./x; |
| return exp(x) * sqrt(y) * ( |
| // note: reciprocal squareroot may be easier! |
| // http://en.wikipedia.org/wiki/Fast_inverse_square_root |
| I0ATerm<0>::value + y*( |
| I0ATerm<1>::value + y*( |
| I0ATerm<2>::value + y*( |
| I0ATerm<3>::value + y*( |
| I0ATerm<4>::value + y*( |
| I0ATerm<5>::value + y*( |
| I0ATerm<6>::value + y*( |
| I0ATerm<7>::value + y*( |
| I0ATerm<8>::value))))))))); // (... e) < 1.9e-7 |
| } |
| |
| /* |
| * calculates the transition bandwidth for a Kaiser filter |
| * |
| * Formula 3.2.8, Multirate Systems and Filter Banks, PP Vaidyanathan, pg. 48 |
| * |
| * @param halfNumCoef is half the number of coefficients per filter phase. |
| * @param stopBandAtten is the stop band attenuation desired. |
| * @return the transition bandwidth in normalized frequency (0 <= f <= 0.5) |
| */ |
| static inline double firKaiserTbw(int halfNumCoef, double stopBandAtten) { |
| return (stopBandAtten - 7.95)/(2.*14.36*halfNumCoef); |
| } |
| |
| /* |
| * calculates the fir transfer response. |
| * |
| * calculates the transfer coefficient H(w) for 0 <= w <= PI. |
| * Be careful be careful to consider the fact that this is an interpolated filter |
| * of length L, so normalizing H(w)/L is probably what you expect. |
| */ |
| template <typename T> |
| static inline double firTransfer(const T* coef, int L, int halfNumCoef, double w) { |
| double accum = static_cast<double>(coef[0])*0.5; |
| coef += halfNumCoef; // skip first row. |
| for (int i=1 ; i<=L ; ++i) { |
| for (int j=0, ix=i ; j<halfNumCoef ; ++j, ix+=L) { |
| accum += cos(ix*w)*static_cast<double>(*coef++); |
| } |
| } |
| return accum*2.; |
| } |
| |
| /* |
| * returns the minimum and maximum |H(f)| bounds |
| * |
| * @param coef is the designed polyphase filter banks |
| * |
| * @param L is the number of phases (for interpolation) |
| * |
| * @param halfNumCoef should be half the number of coefficients for a single |
| * polyphase. |
| * |
| * @param fstart is the normalized frequency start. |
| * |
| * @param fend is the normalized frequency end. |
| * |
| * @param steps is the number of steps to take (sampling) between frequency start and end |
| * |
| * @param firMin returns the minimum transfer |H(f)| found |
| * |
| * @param firMax returns the maximum transfer |H(f)| found |
| * |
| * 0 <= f <= 0.5. |
| * This is used to test passband and stopband performance. |
| */ |
| template <typename T> |
| static void testFir(const T* coef, int L, int halfNumCoef, |
| double fstart, double fend, int steps, double &firMin, double &firMax) { |
| double wstart = fstart*(2.*M_PI); |
| double wend = fend*(2.*M_PI); |
| double wstep = (wend - wstart)/steps; |
| double fmax, fmin; |
| double trf = firTransfer(coef, L, halfNumCoef, wstart); |
| if (trf<0) { |
| trf = -trf; |
| } |
| fmin = fmax = trf; |
| wstart += wstep; |
| for (int i=1; i<steps; ++i) { |
| trf = firTransfer(coef, L, halfNumCoef, wstart); |
| if (trf<0) { |
| trf = -trf; |
| } |
| if (trf>fmax) { |
| fmax = trf; |
| } |
| else if (trf<fmin) { |
| fmin = trf; |
| } |
| wstart += wstep; |
| } |
| // renormalize - this is only needed for integer filter types |
| double norm = 1./((1ULL<<(sizeof(T)*8-1))*L); |
| |
| firMin = fmin * norm; |
| firMax = fmax * norm; |
| } |
| |
| /* |
| * Calculates the polyphase filter banks based on a windowed sinc function. |
| * |
| * The windowed sinc is an odd length symmetric filter of exactly L*halfNumCoef*2+1 |
| * taps for the entire kernel. This is then decomposed into L+1 polyphase filterbanks. |
| * The last filterbank is used for interpolation purposes (and is mostly composed |
| * of the first bank shifted by one sample), and is unnecessary if one does |
| * not do interpolation. |
| * |
| * @param coef is the caller allocated space for coefficients. This should be |
| * exactly (L+1)*halfNumCoef in size. |
| * |
| * @param L is the number of phases (for interpolation) |
| * |
| * @param halfNumCoef should be half the number of coefficients for a single |
| * polyphase. |
| * |
| * @param stopBandAtten is the stopband value, should be >50dB. |
| * |
| * @param fcr is cutoff frequency/sampling rate (<0.5). At this point, the energy |
| * should be 6dB less. (fcr is where the amplitude drops by half). Use the |
| * firKaiserTbw() to calculate the transition bandwidth. fcr is the midpoint |
| * between the stop band and the pass band (fstop+fpass)/2. |
| * |
| * @param atten is the attenuation (generally slightly less than 1). |
| */ |
| |
| template <typename T> |
| static inline void firKaiserGen(T* coef, int L, int halfNumCoef, |
| double stopBandAtten, double fcr, double atten) { |
| // |
| // Formula 3.2.5, 3.2.7, Multirate Systems and Filter Banks, PP Vaidyanathan, pg. 48 |
| // |
| // See also: http://melodi.ee.washington.edu/courses/ee518/notes/lec17.pdf |
| // |
| // Kaiser window and beta parameter |
| // |
| // | 0.1102*(A - 8.7) A > 50 |
| // beta = | 0.5842*(A - 21)^0.4 + 0.07886*(A - 21) 21 <= A <= 50 |
| // | 0. A < 21 |
| // |
| // with A is the desired stop-band attenuation in dBFS |
| // |
| // 30 dB 2.210 |
| // 40 dB 3.384 |
| // 50 dB 4.538 |
| // 60 dB 5.658 |
| // 70 dB 6.764 |
| // 80 dB 7.865 |
| // 90 dB 8.960 |
| // 100 dB 10.056 |
| |
| const int N = L * halfNumCoef; // non-negative half |
| const double beta = 0.1102 * (stopBandAtten - 8.7); // >= 50dB always |
| const double yscale = 2. * atten * fcr / I0(beta); |
| const double xstep = 2. * M_PI * fcr / L; |
| const double xfrac = 1. / N; |
| double err = 0; // for noise shaping on int16_t coefficients |
| for (int i=0 ; i<=L ; ++i) { // generate an extra set of coefs for interpolation |
| for (int j=0, ix=i ; j<halfNumCoef ; ++j, ix+=L) { |
| double y = I0(beta * sqrt(1.0 - sqr(ix * xfrac))) * sinc(ix * xstep) * yscale; |
| |
| // (caution!) float version does not need rounding |
| if (is_same<T, int16_t>::value) { // int16_t needs noise shaping |
| *coef++ = static_cast<T>(toint(y, 1ULL<<(sizeof(T)*8-1), err)); |
| } else { |
| *coef++ = static_cast<T>(toint(y, 1ULL<<(sizeof(T)*8-1))); |
| } |
| } |
| } |
| } |
| |
| }; // namespace android |
| |
| #endif /*ANDROID_AUDIO_RESAMPLER_FIR_GEN_H*/ |