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+/*
+ * 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 {
+
+/*
+ * generates a sine wave at equal steps.
+ *
+ * As most of our functions use sine or cosine at equal steps,
+ * it is very efficient to compute them that way (single multiply and subtract),
+ * rather than invoking the math library sin() or cos() each time.
+ *
+ * SineGen uses Goertzel's Algorithm (as a generator not a filter)
+ * to calculate sine(wstart + n * wstep) or cosine(wstart + n * wstep)
+ * by stepping through 0, 1, ... n.
+ *
+ * e^i(wstart+wstep) = 2cos(wstep) * e^i(wstart) - e^i(wstart-wstep)
+ *
+ * or looking at just the imaginary sine term, as the cosine follows identically:
+ *
+ * sin(wstart+wstep) = 2cos(wstep) * sin(wstart) - sin(wstart-wstep)
+ *
+ * Goertzel's algorithm is more efficient than the angle addition formula,
+ * e^i(wstart+wstep) = e^i(wstart) * e^i(wstep), which takes up to
+ * 4 multiplies and 2 adds (or 3* and 3+) and requires both sine and
+ * cosine generation due to the complex * complex multiply (full rotation).
+ *
+ * See: http://en.wikipedia.org/wiki/Goertzel_algorithm
+ *
+ */
+
+class SineGen {
+public:
+ SineGen(double wstart, double wstep, bool cosine = false) {
+ if (cosine) {
+ mCurrent = cos(wstart);
+ mPrevious = cos(wstart - wstep);
+ } else {
+ mCurrent = sin(wstart);
+ mPrevious = sin(wstart - wstep);
+ }
+ mTwoCos = 2.*cos(wstep);
+ }
+ SineGen(double expNow, double expPrev, double twoCosStep) {
+ mCurrent = expNow;
+ mPrevious = expPrev;
+ mTwoCos = twoCosStep;
+ }
+ inline double value() const {
+ return mCurrent;
+ }
+ inline void advance() {
+ double tmp = mCurrent;
+ mCurrent = mCurrent*mTwoCos - mPrevious;
+ mPrevious = tmp;
+ }
+ inline double valueAdvance() {
+ double tmp = mCurrent;
+ mCurrent = mCurrent*mTwoCos - mPrevious;
+ mPrevious = tmp;
+ return tmp;
+ }
+
+private:
+ double mCurrent; // current value of sine/cosine
+ double mPrevious; // previous value of sine/cosine
+ double mTwoCos; // stepping factor
+};
+
+/*
+ * generates a series of sine generators, phase offset by fixed steps.
+ *
+ * This is used to generate polyphase sine generators, one per polyphase
+ * in the filter code below.
+ *
+ * The SineGen returned by value() starts at innerStart = outerStart + n*outerStep;
+ * increments by innerStep.
+ *
+ */
+
+class SineGenGen {
+public:
+ SineGenGen(double outerStart, double outerStep, double innerStep, bool cosine = false)
+ : mSineInnerCur(outerStart, outerStep, cosine),
+ mSineInnerPrev(outerStart-innerStep, outerStep, cosine)
+ {
+ mTwoCos = 2.*cos(innerStep);
+ }
+ inline SineGen value() {
+ return SineGen(mSineInnerCur.value(), mSineInnerPrev.value(), mTwoCos);
+ }
+ inline void advance() {
+ mSineInnerCur.advance();
+ mSineInnerPrev.advance();
+ }
+ inline SineGen valueAdvance() {
+ return SineGen(mSineInnerCur.valueAdvance(), mSineInnerPrev.valueAdvance(), mTwoCos);
+ }
+
+private:
+ SineGen mSineInnerCur; // generate the inner sine values (stepped by outerStep).
+ SineGen mSineInnerPrev; // generate the inner sine previous values
+ // (behind by innerStep, stepped by outerStep).
+ double mTwoCos; // the inner stepping factor for the returned SineGen.
+};
+
+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.
+ * For 16b coefficients this can improve stopband dB performance by up to 2dB.
+ *
+ * Many variants exist for the noise shaping: http://en.wikipedia.org/wiki/Noise_shaping
+ *
+ */
+
+static inline int64_t toint(double x, int64_t maxval, double& err) {
+ double val = x * maxval;
+ double ival = floor(val + 0.5 + err*0.2);
+ 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,
+ * _Handbook of Mathematical Functions_ (links below):
+ *
+ * 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.
+ *
+ * For the intermediate range 3.75 < x < 15, we use minimax polynomial fit.
+ *
+ */
+
+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;
+};
+
+#if USE_HORNERS_METHOD
+/* Polynomial evaluation of A + Bx + Cx^2 + Dx^3 + ...
+ * using Horner's Method: http://en.wikipedia.org/wiki/Horner's_method
+ *
+ * This has fewer multiplications than Estrin's method below, but has back to back
+ * floating point dependencies.
+ *
+ * On ARM this appears to work slower, so USE_HORNERS_METHOD is not default enabled.
+ */
+
+inline double Poly2(double A, double B, double x) {
+ return A + x * B;
+}
+
+inline double Poly4(double A, double B, double C, double D, double x) {
+ return A + x * (B + x * (C + x * (D)));
+}
+
+inline double Poly7(double A, double B, double C, double D, double E, double F, double G,
+ double x) {
+ return A + x * (B + x * (C + x * (D + x * (E + x * (F + x * (G))))));
+}
+
+inline double Poly9(double A, double B, double C, double D, double E, double F, double G,
+ double H, double I, double x) {
+ return A + x * (B + x * (C + x * (D + x * (E + x * (F + x * (G + x * (H + x * (I))))))));
+}
+
+#else
+/* Polynomial evaluation of A + Bx + Cx^2 + Dx^3 + ...
+ * using Estrin's Method: http://en.wikipedia.org/wiki/Estrin's_scheme
+ *
+ * This is typically faster, perhaps gains about 5-10% overall on ARM processors
+ * over Horner's method above.
+ */
+
+inline double Poly2(double A, double B, double x) {
+ return A + B * x;
+}
+
+inline double Poly3(double A, double B, double C, double x, double x2) {
+ return Poly2(A, B, x) + C * x2;
+}
+
+inline double Poly3(double A, double B, double C, double x) {
+ return Poly2(A, B, x) + C * x * x;
+}
+
+inline double Poly4(double A, double B, double C, double D, double x, double x2) {
+ return Poly2(A, B, x) + Poly2(C, D, x) * x2; // same as poly2(poly2, poly2, x2);
+}
+
+inline double Poly4(double A, double B, double C, double D, double x) {
+ return Poly4(A, B, C, D, x, x * x);
+}
+
+inline double Poly7(double A, double B, double C, double D, double E, double F, double G,
+ double x) {
+ double x2 = x * x;
+ return Poly4(A, B, C, D, x, x2) + Poly3(E, F, G, x, x2) * (x2 * x2);
+}
+
+inline double Poly8(double A, double B, double C, double D, double E, double F, double G,
+ double H, double x, double x2, double x4) {
+ return Poly4(A, B, C, D, x, x2) + Poly4(E, F, G, H, x, x2) * x4;
+}
+
+inline double Poly9(double A, double B, double C, double D, double E, double F, double G,
+ double H, double I, double x) {
+ double x2 = x * x;
+#if 1
+ // It does not seem faster to explicitly decompose Poly8 into Poly4, but
+ // could depend on compiler floating point scheduling.
+ double x4 = x2 * x2;
+ return Poly8(A, B, C, D, E, F, G, H, x, x2, x4) + I * (x4 * x4);
+#else
+ double val = Poly4(A, B, C, D, x, x2);
+ double x4 = x2 * x2;
+ return val + Poly4(E, F, G, H, x, x2) * x4 + I * (x4 * x4);
+#endif
+}
+#endif
+
+static inline double I0(double x) {
+ if (x < 3.75) {
+ x *= x;
+ return Poly7(I0Term<0>::value, I0Term<1>::value,
+ I0Term<2>::value, I0Term<3>::value,
+ I0Term<4>::value, I0Term<5>::value,
+ I0Term<6>::value, x); // e < 1.6e-7
+ }
+ if (1) {
+ /*
+ * Series expansion coefs are easy to calculate, but are expanded around 0,
+ * so error is unequal over the interval 0 < x < 3.75, the error being
+ * significantly better near 0.
+ *
+ * A better solution is to use precise minimax polynomial fits.
+ *
+ * We use a slightly more complicated solution for 3.75 < x < 15, based on
+ * the tables in Blair and Edwards, "Stable Rational Minimax Approximations
+ * to the Modified Bessel Functions I0(x) and I1(x)", Chalk Hill Nuclear Laboratory,
+ * AECL-4928.
+ *
+ * http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/06/178/6178667.pdf
+ *
+ * See Table 11 for 0 < x < 15; e < 10^(-7.13).
+ *
+ * Note: Beta cannot exceed 15 (hence Stopband cannot exceed 144dB = 24b).
+ *
+ * This speeds up overall computation by about 40% over using the else clause below,
+ * which requires sqrt and exp.
+ *
+ */
+
+ x *= x;
+ double num = Poly9(-0.13544938430e9, -0.33153754512e8,
+ -0.19406631946e7, -0.48058318783e5,
+ -0.63269783360e3, -0.49520779070e1,
+ -0.24970910370e-1, -0.74741159550e-4,
+ -0.18257612460e-6, x);
+ double y = x - 225.; // reflection around 15 (squared)
+ double den = Poly4(-0.34598737196e8, 0.23852643181e6,
+ -0.70699387620e3, 0.10000000000e1, y);
+ return num / den;
+
+#if IO_EXTENDED_BETA
+ /* Table 42 for x > 15; e < 10^(-8.11).
+ * This is used for Beta>15, but is disabled here as
+ * we never use Beta that high.
+ *
+ * NOTE: This should be enabled only for x > 15.
+ */
+
+ double y = 1./x;
+ double z = y - (1./15);
+ double num = Poly2(0.415079861746e1, -0.5149092496e1, z);
+ double den = Poly3(0.103150763823e2, -0.14181687413e2,
+ 0.1000000000e1, z);
+ return exp(x) * sqrt(y) * num / den;
+#endif
+ } else {
+ /*
+ * NOT USED, but reference for large Beta.
+ *
+ * Abramowitz and Stegun asymptotic formula.
+ * works for x > 3.75.
+ */
+ double y = 1./x;
+ return exp(x) * sqrt(y) *
+ // note: reciprocal squareroot may be easier!
+ // http://en.wikipedia.org/wiki/Fast_inverse_square_root
+ Poly9(I0ATerm<0>::value, I0ATerm<1>::value,
+ I0ATerm<2>::value, I0ATerm<3>::value,
+ I0ATerm<4>::value, I0ATerm<5>::value,
+ I0ATerm<6>::value, I0ATerm<7>::value,
+ I0ATerm<8>::value, y); // (... e) < 1.9e-7
+ }
+}
+
+/* A speed optimized version of the Modified Bessel I0() which incorporates
+ * the sqrt and numerator multiply and denominator divide into the computation.
+ * This speeds up filter computation by about 10-15%.
+ */
+static inline double I0SqrRat(double x2, double num, double den) {
+ if (x2 < (3.75 * 3.75)) {
+ return Poly7(I0Term<0>::value, I0Term<1>::value,
+ I0Term<2>::value, I0Term<3>::value,
+ I0Term<4>::value, I0Term<5>::value,
+ I0Term<6>::value, x2) * num / den; // e < 1.6e-7
+ }
+ num *= Poly9(-0.13544938430e9, -0.33153754512e8,
+ -0.19406631946e7, -0.48058318783e5,
+ -0.63269783360e3, -0.49520779070e1,
+ -0.24970910370e-1, -0.74741159550e-4,
+ -0.18257612460e-6, x2); // e < 10^(-7.13).
+ double y = x2 - 225.; // reflection around 15 (squared)
+ den *= Poly4(-0.34598737196e8, 0.23852643181e6,
+ -0.70699387620e3, 0.10000000000e1, y);
+ return num / den;
+}
+
+/*
+ * calculates the transition bandwidth for a Kaiser filter
+ *
+ * Formula 3.2.8, Vaidyanathan, _Multirate Systems and Filter Banks_, p. 48
+ * Formula 7.76, Oppenheim and Schafer, _Discrete-time Signal Processing, 3e_, p. 542
+ *
+ * @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 of the overall polyphase filter at w.
+ *
+ * Calculates the DTFT transfer coefficient H(w) for 0 <= w <= PI, utilizing the
+ * fact that h[n] is symmetric (cosines only, no complex arithmetic).
+ *
+ * We use Goertzel's algorithm to accelerate the computation to essentially
+ * a single multiply and 2 adds per filter coefficient h[].
+ *
+ * Be careful be careful to consider that h[n] is the overall polyphase filter,
+ * with L phases, so rescaling H(w)/L is probably what you expect for "unity gain",
+ * as you only use one of the polyphases at a time.
+ */
+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; // "center coefficient" from first bank
+ coef += halfNumCoef; // skip first filterbank (picked up by the last filterbank).
+#if SLOW_FIRTRANSFER
+ /* Original code for reference. This is equivalent to the code below, but slower. */
+ 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++);
+ }
+ }
+#else
+ /*
+ * Our overall filter is stored striped by polyphases, not a contiguous h[n].
+ * We could fetch coefficients in a non-contiguous fashion
+ * but that will not scale to vector processing.
+ *
+ * We apply Goertzel's algorithm directly to each polyphase filter bank instead of
+ * using cosine generation/multiplication, thereby saving one multiply per inner loop.
+ *
+ * See: http://en.wikipedia.org/wiki/Goertzel_algorithm
+ * Also: Oppenheim and Schafer, _Discrete Time Signal Processing, 3e_, p. 720.
+ *
+ * We use the basic recursion to incorporate the cosine steps into real sequence x[n]:
+ * s[n] = x[n] + (2cosw)*s[n-1] + s[n-2]
+ *
+ * y[n] = s[n] - e^(iw)s[n-1]
+ * = sum_{k=-\infty}^{n} x[k]e^(-iw(n-k))
+ * = e^(-iwn) sum_{k=0}^{n} x[k]e^(iwk)
+ *
+ * The summation contains the frequency steps we want multiplied by the source
+ * (similar to a DTFT).
+ *
+ * Using symmetry, and just the real part (be careful, this must happen
+ * after any internal complex multiplications), the polyphase filterbank
+ * transfer function is:
+ *
+ * Hpp[n, w, w_0] = sum_{k=0}^{n} x[k] * cos(wk + w_0)
+ * = Re{ e^(iwn + iw_0) y[n]}
+ * = cos(wn+w_0) * s[n] - cos(w(n+1)+w_0) * s[n-1]
+ *
+ * using the fact that s[n] of real x[n] is real.
+ *
+ */
+ double dcos = 2. * cos(L*w);
+ int start = ((halfNumCoef)*L + 1);
+ SineGen cc((start - L) * w, w, true); // cosine
+ SineGen cp(start * w, w, true); // cosine
+ for (int i=1 ; i<=L ; ++i) {
+ double sc = 0;
+ double sp = 0;
+ for (int j=0 ; j<halfNumCoef ; ++j) {
+ double tmp = sc;
+ sc = static_cast<double>(*coef++) + dcos*sc - sp;
+ sp = tmp;
+ }
+ // If we are awfully clever, we can apply Goertzel's algorithm
+ // again on the sc and sp sequences returned here.
+ accum += cc.valueAdvance() * sc - cp.valueAdvance() * sp;
+ }
+#endif
+ return accum*2.;
+}
+
+/*
+ * evaluates the minimum and maximum |H(f)| bound in a band region.
+ *
+ * This is usually done with equally spaced increments in the target band in question.
+ * The passband is often very small, and sampled that way. The stopband is often much
+ * larger.
+ *
+ * We use the fact that the overall polyphase filter has an additional bank at the end
+ * for interpolation; hence it is overspecified for the H(f) computation. Thus the
+ * first polyphase is never actually checked, excepting its first term.
+ *
+ * In this code we use the firTransfer() evaluator above, which uses Goertzel's
+ * algorithm to calculate the transfer function at each point.
+ *
+ * TODO: An alternative with equal spacing is the FFT/DFT. An alternative with unequal
+ * spacing is a chirp transform.
+ *
+ * @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;
+}
+
+/*
+ * evaluates the |H(f)| lowpass band characteristics.
+ *
+ * This function tests the lowpass characteristics for the overall polyphase filter,
+ * and is used to verify the design. For this case, fp should be set to the
+ * passband normalized frequency from 0 to 0.5 for the overall filter (thus it
+ * is the designed polyphase bank value / L). Likewise for fs.
+ *
+ * @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 fp is the passband normalized frequency, 0 < fp < fs < 0.5.
+ *
+ * @param fs is the stopband normalized frequency, 0 < fp < fs < 0.5.
+ *
+ * @param passSteps is the number of passband sampling steps.
+ *
+ * @param stopSteps is the number of stopband sampling steps.
+ *
+ * @param passMin is the minimum value in the passband
+ *
+ * @param passMax is the maximum value in the passband (useful for scaling). This should
+ * be less than 1., to avoid sine wave test overflow.
+ *
+ * @param passRipple is the passband ripple. Typically this should be less than 0.1 for
+ * an audio filter. Generally speaker/headphone device characteristics will dominate
+ * the passband term.
+ *
+ * @param stopMax is the maximum value in the stopband.
+ *
+ * @param stopRipple is the stopband ripple, also known as stopband attenuation.
+ * Typically this should be greater than ~80dB for low quality, and greater than
+ * ~100dB for full 16b quality, otherwise aliasing may become noticeable.
+ *
+ */
+template <typename T>
+static void testFir(const T* coef, int L, int halfNumCoef,
+ double fp, double fs, int passSteps, int stopSteps,
+ double &passMin, double &passMax, double &passRipple,
+ double &stopMax, double &stopRipple) {
+ double fmin, fmax;
+ testFir(coef, L, halfNumCoef, 0., fp, passSteps, fmin, fmax);
+ double d1 = (fmax - fmin)/2.;
+ passMin = fmin;
+ passMax = fmax;
+ passRipple = -20.*log10(1. - d1); // passband ripple
+ testFir(coef, L, halfNumCoef, fs, 0.5, stopSteps, fmin, fmax);
+ // fmin is really not important for the stopband.
+ stopMax = fmax;
+ stopRipple = -20.*log10(fmax); // stopband ripple/attenuation
+}
+
+/*
+ * Calculates the overall polyphase filter 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.
+ *
+ * We use the last filterbank for some transfer function calculation purposes,
+ * so it needs to be generated anyways.
+ *
+ * @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, Vaidyanathan, _Multirate Systems and Filter Banks_, p. 48
+ // Formula 7.75, Oppenheim and Schafer, _Discrete-time Signal Processing, 3e_, p. 542
+ //
+ // 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 xstep = (2. * M_PI) * fcr / L;
+ const double xfrac = 1. / N;
+ const double yscale = atten * L / (I0(beta) * M_PI);
+ const double sqrbeta = sqr(beta);
+
+ // We use sine generators, which computes sines on regular step intervals.
+ // This speeds up overall computation about 40% from computing the sine directly.
+
+ SineGenGen sgg(0., xstep, L*xstep); // generates sine generators (one per polyphase)
+
+ for (int i=0 ; i<=L ; ++i) { // generate an extra set of coefs for interpolation
+
+ // computation for a single polyphase of the overall filter.
+ SineGen sg = sgg.valueAdvance(); // current sine generator for "j" inner loop.
+ double err = 0; // for noise shaping on int16_t coefficients (over each polyphase)
+
+ for (int j=0, ix=i ; j<halfNumCoef ; ++j, ix+=L) {
+ double y;
+ if (CC_LIKELY(ix)) {
+ double x = static_cast<double>(ix);
+
+ // sine generator: sg.valueAdvance() returns sin(ix*xstep);
+ // y = I0(beta * sqrt(1.0 - sqr(x * xfrac))) * yscale * sg.valueAdvance() / x;
+ y = I0SqrRat(sqrbeta * (1.0 - sqr(x * xfrac)), yscale * sg.valueAdvance(), x);
+ } else {
+ y = 2. * atten * fcr; // center of filter, sinc(0) = 1.
+ sg.advance();
+ }
+
+ 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 if (is_same<T, int32_t>::value) {
+ *coef++ = static_cast<T>(toint(y, 1ULL<<(sizeof(T)*8-1)));
+ } else { // assumed float or double
+ *coef++ = static_cast<T>(y);
+ }
+ }
+ }
+}
+
+}; // namespace android
+
+#endif /*ANDROID_AUDIO_RESAMPLER_FIR_GEN_H*/