334 lines
9.2 KiB
C++
334 lines
9.2 KiB
C++
/*
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* Paula.cpp
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* ---------
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* Purpose: Emulating the Amiga's sound chip, Paula, by implementing resampling using band-limited steps (BLEPs)
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* Notes : The BLEP table generator code is a translation of Antti S. Lankila's original Python code.
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* Authors: OpenMPT Devs
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* Antti S. Lankila
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* The OpenMPT source code is released under the BSD license. Read LICENSE for more details.
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*/
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#include "stdafx.h"
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#include "Paula.h"
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#include "TinyFFT.h"
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#include <complex>
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#include <numeric>
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OPENMPT_NAMESPACE_BEGIN
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// Compute Bessel function Izero(y) using a series approximation
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double Izero(double y);
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namespace Paula
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{
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namespace
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{
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MPT_NOINLINE std::vector<double> KaiserFIR(int numTaps, double cutoff, double beta)
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{
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const double izeroBeta = Izero(beta);
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const double kPi = 4.0 * std::atan(1.0) * cutoff;
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const double xDiv = 1.0 / ((numTaps / 2) * (numTaps / 2));
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const int numTapsDiv2 = numTaps / 2;
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std::vector<double> result(numTaps);
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for(int i = 0; i < numTaps; i++)
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{
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double fsinc;
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if(i == numTapsDiv2)
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{
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fsinc = 1.0;
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} else
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{
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const double x = i - numTapsDiv2;
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const double xPi = x * kPi;
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// - sinc - - Kaiser window - -sinc-
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fsinc = std::sin(xPi) * Izero(beta * std::sqrt(1 - x * x * xDiv)) / (izeroBeta * xPi);
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}
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result[i] = fsinc * cutoff;
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}
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return result;
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}
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MPT_NOINLINE void FIR_MinPhase(std::vector<double> &table, const TinyFFT &fft)
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{
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std::vector<std::complex<double>> cepstrum(fft.Size());
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MPT_ASSERT(cepstrum.size() >= table.size());
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for(size_t i = 0; i < table.size(); i++)
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cepstrum[i] = table[i];
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// Compute the real cepstrum: fft -> abs + ln -> ifft -> real
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fft.FFT(cepstrum);
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for(auto &v : cepstrum)
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v = std::log(std::abs(v));
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fft.IFFT(cepstrum);
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fft.Normalize(cepstrum);
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// Window the cepstrum in such a way that anticausal components become rejected
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for(size_t i = 1; i < cepstrum.size() / 2; i++)
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{
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cepstrum[i] *= 2;
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cepstrum[i + cepstrum.size() / 2] *= 0;
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}
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// Now cancel the previous steps: fft -> exp -> ifft -> real
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fft.FFT(cepstrum);
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for(auto &v : cepstrum)
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v = std::exp(v);
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fft.IFFT(cepstrum);
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fft.Normalize(cepstrum);
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for(size_t i = 0; i < table.size(); i++)
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table[i] = cepstrum[i].real();
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}
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class BiquadFilter
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{
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double b0, b1, b2, a1, a2, x1 = 0.0, x2 = 0.0, y1 = 0.0, y2 = 0.0;
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double Filter(double x0)
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{
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double y0 = b0 * x0 + b1 * x1 + b2 * x2 - a1 * y1 - a2 * y2;
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x2 = x1;
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x1 = x0;
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y2 = y1;
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y1 = y0;
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return y0;
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}
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public:
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BiquadFilter(double b0_, double b1_, double b2_, double a1_, double a2_)
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: b0(b0_), b1(b1_), b2(b2_), a1(a1_), a2(a2_)
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{ }
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std::vector<double> Run(std::vector<double> table)
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{
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x1 = 0.0;
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x2 = 0.0;
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y1 = 0.0;
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y2 = 0.0;
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// Initialize filter to stable state
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for(int i = 0; i < 10000; i++)
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Filter(table[0]);
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// Now run the filter
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for(auto &v : table)
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v = Filter(v);
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return table;
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}
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};
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// Observe: a and b are reversed here. To be absolutely clear:
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// a is the nominator and b is the denominator. :-/
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BiquadFilter ZTransform(double a0, double a1, double a2, double b0, double b1, double b2, double fc, double fs)
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{
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// Prewarp s - domain coefficients
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const double wp = 2.0 * fs * std::tan(M_PI * fc / fs);
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a2 /= wp * wp;
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a1 /= wp;
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b2 /= wp * wp;
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b1 /= wp;
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// Compute bilinear transform and return it
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const double bd = 4 * b2 * fs * fs + 2 * b1 * fs + b0;
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return BiquadFilter(
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(4 * a2 * fs * fs + 2 * a1 * fs + a0) / bd,
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(2 * a0 - 8 * a2 * fs * fs) / bd,
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(4 * a2 * fs * fs - 2 * a1 * fs + a0) / bd,
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(2 * b0 - 8 * b2 * fs * fs) / bd,
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(4 * b2 * fs * fs - 2 * b1 * fs + b0) / bd);
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}
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BiquadFilter MakeRCLowpass(double sampleRate, double freq)
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{
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const double omega = 2 * M_PI * freq / sampleRate;
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const double term = 1 + 1 / omega;
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return BiquadFilter(1 / term, 0.0, 0.0, -1.0 + 1.0 / term, 0.0);
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}
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BiquadFilter MakeButterworth(double fs, double fc, double res_dB = 0)
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{
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// 2nd-order Butterworth s-domain coefficients are:
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//
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// b0 = 1.0 b1 = 0 b2 = 0
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// a0 = 1 a1 = sqrt(2) a2 = 1
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//
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// by tweaking the a1 parameter, some resonance can be produced.
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const double res = std::pow(10.0, (-res_dB / 10.0 / 2.0));
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return ZTransform(1, 0, 0, 1, std::sqrt(2) * res, 1, fc, fs);
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}
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MPT_NOINLINE void Integrate(std::vector<double> &table)
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{
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const double total = std::accumulate(table.begin(), table.end(), 0.0);
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double startVal = -total;
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for(auto &v : table)
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{
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startVal += v;
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v = startVal;
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}
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}
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MPT_NOINLINE void Quantize(const std::vector<double> &in, Paula::BlepArray &quantized)
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{
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MPT_ASSERT(in.size() == Paula::BLEP_SIZE);
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constexpr int fact = 1 << Paula::BLEP_SCALE;
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const double cv = fact / (in.back() - in.front());
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for(int i = 0; i < Paula::BLEP_SIZE; i++)
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{
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double val = in[i] * cv;
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#ifdef MPT_INTMIXER
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val = mpt::round(val);
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#endif
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quantized[i] = static_cast<mixsample_t>(-val);
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}
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}
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} // namespace
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void BlepTables::InitTables()
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{
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constexpr double sampleRate = Paula::PAULA_HZ;
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// Because Amiga only has 84 dB SNR, the noise floor is low enough with -90 dB.
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// A500 model uses slightly lower-quality kaiser window to obtain slightly
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// steeper stopband attenuation. The fixed filters attenuates the sidelobes by
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// 12 dB, compensating for the worse performance of the kaiser window.
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// 21 kHz stopband is not fully attenuated by 22 kHz. If the sampling frequency
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// is 44.1 kHz, all frequencies above 22 kHz will alias over 20 kHz, thus inaudible.
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// The output should be aliasingless for 48 kHz sampling frequency.
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auto unfilteredA500 = KaiserFIR(Paula::BLEP_SIZE, 21000.0 / sampleRate * 2.0, 8.0);
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auto unfilteredA1200 = KaiserFIR(Paula::BLEP_SIZE, 21000.0 / sampleRate * 2.0, 9.0);
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// Move filtering effects to start to allow IIRs more time to settle
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constexpr size_t padSize = 8;
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constexpr int fftSize = static_cast<int>(mpt::bit_width(size_t(Paula::BLEP_SIZE)) + mpt::bit_width(padSize) - 2);
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const TinyFFT fft(fftSize);
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FIR_MinPhase(unfilteredA500, fft);
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FIR_MinPhase(unfilteredA1200, fft);
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// Make digital models for the filters on Amiga 500 and 1200.
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auto filterFixed5kHz = MakeRCLowpass(sampleRate, 4900.0);
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// The leakage filter seems to reduce treble in both models a bit
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// The A500 filter seems to be well modelled only with a 4.9 kHz
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// filter although the component values would suggest 5 kHz filter.
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auto filterLeakage = MakeRCLowpass(sampleRate, 32000.0);
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auto filterLED = MakeButterworth(sampleRate, 3275.0, -0.70);
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// Apply fixed filter to A500
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auto amiga500Off = filterFixed5kHz.Run(unfilteredA500);
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// Produce the filtered outputs
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auto amiga1200Off = filterLeakage.Run(unfilteredA1200);
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// Produce LED filters
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auto amiga500On = filterLED.Run(amiga500Off);
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auto amiga1200On = filterLED.Run(amiga1200Off);
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// Integrate to produce blep
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Integrate(amiga500Off);
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Integrate(amiga500On);
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Integrate(amiga1200Off);
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Integrate(amiga1200On);
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Integrate(unfilteredA1200);
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// Quantize and scale
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Quantize(amiga500Off, WinSincIntegral[A500Off]);
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Quantize(amiga500On, WinSincIntegral[A500On]);
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Quantize(amiga1200Off, WinSincIntegral[A1200Off]);
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Quantize(amiga1200On, WinSincIntegral[A1200On]);
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Quantize(unfilteredA1200, WinSincIntegral[Unfiltered]);
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}
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const Paula::BlepArray &BlepTables::GetAmigaTable(Resampling::AmigaFilter amigaType, bool enableFilter) const
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{
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if(amigaType == Resampling::AmigaFilter::A500)
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return enableFilter ? WinSincIntegral[A500On] : WinSincIntegral[A500Off];
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if(amigaType == Resampling::AmigaFilter::A1200)
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return enableFilter ? WinSincIntegral[A1200On] : WinSincIntegral[A1200Off];
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return WinSincIntegral[Unfiltered];
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}
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// we do not initialize blepState here
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// cppcheck-suppress uninitMemberVar
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State::State(uint32 sampleRate)
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{
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double amigaClocksPerSample = static_cast<double>(PAULA_HZ) / sampleRate;
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numSteps = static_cast<int>(amigaClocksPerSample / MINIMUM_INTERVAL);
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stepRemainder = SamplePosition::FromDouble(amigaClocksPerSample - numSteps * MINIMUM_INTERVAL);
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remainder = SamplePosition(0);
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}
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void State::Reset()
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{
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remainder = SamplePosition(0);
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activeBleps = 0;
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firstBlep = MAX_BLEPS / 2u;
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globalOutputLevel = 0;
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}
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void State::InputSample(int16 sample)
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{
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if(sample != globalOutputLevel)
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{
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// Start a new blep: level is the difference, age (or phase) is 0 clocks.
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firstBlep = (firstBlep - 1u) % MAX_BLEPS;
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if(activeBleps < std::size(blepState))
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activeBleps++;
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blepState[firstBlep].age = 0;
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blepState[firstBlep].level = sample - globalOutputLevel;
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globalOutputLevel = sample;
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}
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}
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// Return output simulated as series of bleps
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int State::OutputSample(const BlepArray &WinSincIntegral)
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{
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int output = globalOutputLevel * (1 << Paula::BLEP_SCALE);
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uint32 lastBlep = firstBlep + activeBleps;
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for(uint32 i = firstBlep; i != lastBlep; i++)
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{
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const auto &blep = blepState[i % MAX_BLEPS];
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output -= WinSincIntegral[blep.age] * blep.level;
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}
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output /= (1 << (Paula::BLEP_SCALE - 2)); // - 2 to compensate for the fact that we reduced the input sample bit depth
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return output;
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}
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// Advance the simulation by given number of clock ticks
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void State::Clock(int cycles)
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{
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uint32 lastBlep = firstBlep + activeBleps;
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for(uint32 i = firstBlep; i != lastBlep; i++)
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{
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auto &blep = blepState[i % MAX_BLEPS];
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blep.age += static_cast<uint16>(cycles);
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if(blep.age >= Paula::BLEP_SIZE)
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{
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activeBleps = static_cast<uint16>(i - firstBlep);
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return;
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}
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}
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}
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}
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OPENMPT_NAMESPACE_END
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