Test code and output plots comparing two very-close BLAMPs vs a single BLEP, with single-precision float

main.cpp

#include "elliptic-blep.h"
#include "plot.h"
#include "simple-fft.h"

#include <vector>

void generateWaveform(float freq, float shape, std::vector<float> &result, bool sawtooth) {
	float phase = 0;
	
	float gradUp = freq*2/shape;
	float gradDown = freq*-2/(1 - shape);
	float corner1 = 0.5*shape, corner2 = 1 - corner1;
	signalsmith::blep::EllipticBlep<float> blepper;
	
	// Initial gradient change to kick us off
	blepper.add(gradUp, 2);
	
	for (auto &v : result) {
		// Move the oscillator forwards
		float prevPhase = phase;
		phase += freq;
		// And the blepper
		blepper.step();

		if (sawtooth) {
			if (phase >= corner1 && prevPhase < corner1) {
				float samplesInPast = (phase - corner1)/freq;
				// -2 step jump
				blepper.add(-2, 1, samplesInPast);
			}
			if (phase >= 1) {
				phase -= 1;
			}
		} else {
			if (phase >= corner2 && prevPhase < corner2) {
				float samplesInPast = (phase - corner2)/freq;
				blepper.add(gradUp - gradDown, 2, samplesInPast);
			}
			if (phase >= 1) {
				phase -= 1;
				prevPhase -= 1;
			}
			// Discontinuities
			if (phase >= corner1 && prevPhase < corner1) {
				float samplesInPast = (phase - corner1)/freq;
				blepper.add(gradDown - gradUp, 2, samplesInPast);
			}
		}

		// Naive waveform
		if (phase < corner1) {
			v = 2*phase/shape;
		} else if (phase < corner2) {
			v = (2*phase - 1)/(shape - 1);
		} else {
			v = 2*(phase - 1)/shape;
		}
		// Add BLEP
		v += blepper.get();
	}
}

int main() {
	size_t length = 16384;
	float freq = 0.02373020996; // C6 at 44.1kHz

	signalsmith::plot::Figure figure;
	auto &timePlot = figure(0, 0).plot(600, 150);
	timePlot.x.linear(9.9/freq, 14.6/freq);
	timePlot.y.major(0).linear(-1.1, 1.1).minors(-1, 1);
	auto &freqPlot = figure(0, 1).plot(600, 200);
	freqPlot.x.linear(0, 0.5).major(0).minor(0.5, "Nyquist").label("frequency");
	freqPlot.y.linear(-130, 0).major(0).minors(-30, -60, -90, -120).label("dB");
	
	auto &timeLine = timePlot.line();
	auto &freqLine = freqPlot.line();
	
	std::vector<float> signal(length);
	signalsmith::linear::SimpleFFT<float> fft(length);

	using Complex = std::complex<float>;
	std::vector<Complex> fftTime(length), fftFreq(length);
	
	auto plotWaveform = [&](float shape, bool sawtooth){
		generateWaveform(freq, shape, signal, sawtooth);

		// Spectrum analysis
		for (size_t i = 0; i < length; ++i) {
			float r = (i + 0.5f)/length;
			fftTime[i] = signal[i]*(1 - std::cos(2*M_PI*r));
		}
		fft.fft(length, fftTime.data(), fftFreq.data());

		// Plot waveform and spectrum
		for (size_t i = 0; i < length; ++i) {
			timeLine.add(i, signal[i]);
			
			float db = 10*std::log10(std::norm(fftFreq[i]/float(length)) + 1e-30f);
			freqLine.add(i/float(length), db);
		}
	};
	
	for (double r = 0; r <= 1; r += 0.01) {
		float shape = 0.5 + 0.499*std::sin(r*2*M_PI);
		plotWaveform(shape, false);
		figure.toFrame(r*10);
	}
	figure.loopFrame(10);
	
	figure.write("animation.svg");

	figure.toFrame(0);
	figure.clearFrames();
	timePlot.title("shape = 0.5");
	plotWaveform(0.5, false);
	figure.write("shape-5.svg");

	figure.toFrame(0);
	figure.clearFrames();
	timePlot.title("shape = 0.9");
	plotWaveform(0.9, false);
	figure.write("shape-9.svg");

	figure.toFrame(0);
	figure.clearFrames();
	timePlot.title("shape = 0.999");
	plotWaveform(0.999, false);
	figure.write("shape-999.svg");
	
	figure.toFrame(0);
	figure.clearFrames();
	timePlot.title("shape = 0.9999");
	plotWaveform(0.9999, false);
	figure.write("shape-9999.svg");
	
	figure.toFrame(0);
	figure.clearFrames();
	timePlot.title("shape = 0.99999");
	plotWaveform(0.99999, false);
	figure.write("shape-99999.svg");

	figure.toFrame(0);
	figure.clearFrames();
	timePlot.title("shape = sawtooth");
	plotWaveform(1, true);
	figure.write("shape-sawtooth.svg");
}

shape-5.svg

shape-9.svg

shape-999.svg

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192.37 116.09 193.87 116.16 193.28 116.24 197.31 116.31 196.7 116.38 198.78 116.46 198.64 116.53 201.86 116.6 201.53 116.6 201.53 116.67 202.43 117.7 203.61 117.77 194.26 117.85 161.37 117.92 156.72 117.99 171.32 117.99 171.32 118.07 204.54 118.65 217.41 118.8 172.16 118.87 170.7 118.95 190.26 118.95 190.26 119.02 219.34 121.73 226.17 121.8 193.86 121.88 176.97 121.95 180.35 121.95 180.35 122.02 208.55 123.63 232.77 123.71 197.31 123.78 189.5 123.85 200.19 123.85 200.19 123.93 238.07 125.76 228.6 125.83 194.64 125.9 187.51 125.98 199.2 125.98 199.2 126.05 260.24 126.27 233.45 126.34 199.85 126.42 196.65 126.42 196.65 126.49 212.27 129.79 219.47 129.86 197.25 129.93 197.69 129.93 197.69 130 217.66 130.3 204.11 130.37 189.27 130.44 193.41 130.44 193.41 130.52 225.21 132.42 202.39 132.5 189.44 132.57 194.35 132.57 194.35 132.64 222.7 133.81 211.34 133.89 202.03 133.89 202.03 133.96 210.28 134.25 221.46 134.33 184.45 134.4 178.56 134.47 191.54 134.47 191.54 134.55 227.38 137.26 221.94 137.4 172.42 137.48 170.74 137.55 189.5 137.55 189.5 137.62 221.86 138.21 210.13 138.28 182.14 138.35 163.42 138.43 165.14 138.5 189.64 138.57 214.71 141.14 202.51 141.28 196.74 141.36 195.32 141.43 190.26 141.5 188.63 141.65 180.75 141.87 166.47 142.02 152.39 142.09 143.08 142.16 130.74 142.24 112.01 142.31 45.64 142.38 36.79 142.46 46.47 142.53 113.02 142.6 131.34 142.68 143.5 142.82 160.4 142.97 172.08 143.19 184.65 143.26 188.41 143.33 190.96 143.41 194.45 143.55 199.47 143.55 199.47 143.63 202.96 146.12 226.09 146.34 158.15 146.41 157.23 146.48 177.16 146.48 177.16 146.56 203.41 147.14 220.11 147.22 187.78 147.29 170.27 147.36 172.61 147.44 198.28 147.51 223.17 150.22 228.97 150.29 187.59 150.37 175.86 150.44 182.83 150.44 182.83 150.51 228.3 150.81 209.51 150.88 201.83 150.88 201.83 150.95 212.98 152.12 222.69 152.2 194.13 152.27 190.19 152.27 190.19 152.34 205.22 154.25 218.29 154.32 191.19 154.39 187.94 154.39 187.94 154.47 204.09 154.76 218.96 154.83 197.65 154.91 197.79 154.91 197.79 154.98 218.94 158.28 210.58 158.35 195.25 158.42 199.47 158.42 199.47 158.5 225.16 158.72 240.03 158.79 199.03 158.86 188.73 158.94 196.88 158.94 196.88 159.01 251.21 160.84 233.41 160.91 197.96 160.99 189.07 161.06 197.53 161.06 197.53 161.13 242.26 162.3 206.97 162.38 202.06 162.38 202.06 162.45 213.17 162.74 207.01 162.82 182.05 162.89 179.73 162.96 198.14 162.96 198.14 163.04 227.53 165.75 215.81 165.82 188.47 165.89 170.64 165.97 172.49 166.04 198.66 166.11 224.42 166.7 209.81 166.77 176.27 166.85 162.96 166.92 168.22 166.92 168.22 166.99 203.15 168.31 203.84 168.38 200.97 168.53 198.65 168.6 198.26 168.68 196.17 168.75 194.7 168.82 193.62 168.97 190.56 169.12 187.43 169.26 183.55 169.41 179.89 169.63 173.29 169.85 165.49 170.07 155.4 170.21 147.15 170.36 136.67 170.51 122.33 170.58 112.54 170.65 99.31 170.73 78.16 170.8 44.58 170.87 39.62 170.95 53.71 171.02 89.3 171.09 105.84 171.24 126.04 171.39 139.21 171.53 149.18 171.75 160.56 171.97 169.34 172.19 176.62 172.34 180.88 172.49 184.63 172.71 189.73 172.78 190.83 172.85 192.92 173 195.49 173.07 196.07 173.14 199.93 173.22 198.33 173.29 201.25 173.36 201.47 173.36 201.47 173.44 203.51 174.61 215.45 174.68 201.6 174.76 173.35 174.83 155.68 174.9 158.57 174.98 185.08 174.98 185.08 175.05 204.5 175.63 225.01 175.71 182.01 175.78 169.19 175.85 175.36 175.85 175.36 175.93 210.12 178.71 232.18 178.78 182.95 178.86 175.41 178.93 186.39 178.93 186.39 179 228.42 179.3 206.37 179.37 202.02 179.37 202.02 179.44 219.63 180.62 214.14 180.69 191.85 180.76 191.58 180.76 191.58 180.83 211.91 182.74 209.3 182.81 188.63 182.89 189.07 182.89 189.07 182.96 210.65 183.25 211.17 183.33 196.16 183.4 199.53 183.4 199.53 183.47 228.19 186.77 204.61 186.84 194.11 186.91 202.21 186.91 202.21 186.99 234.66 187.21 232.26 187.28 195.18 187.35 188.97 187.43 201.26 187.43 201.26 187.5 239 189.33 225.99 189.4 194.62 189.48 189.34 189.55 201.96 189.55 201.96 189.62 239.53 191.16 225.31 191.24 198.77 191.31 180.42 191.38 181.7 191.38 181.7 191.46 207.06 194.24 217.29 194.31 182.43 194.38 169.61 194.46 175.16 194.46 175.16 194.53 213.5 195.19 219.15 195.26 171.97 195.34 163.26 195.41 172.14 195.41 172.14 195.48 208.3 196.58 202.26 196.66 201.48 196.73 199.27 196.8 199.51 196.88 197.69 197.02 195.06 197.09 194.37 197.17 192.55 197.39 188.35 197.53 185.08 197.68 181.84 197.75 179.79 197.83 178.25 198.05 171.69 198.19 166.88 198.34 161.48 198.56 151.27 198.71 142.83 198.85 132.04 199 117.15 199.07 106.82 199.15 92.54 199.29 44.12 199.37 42.86 199.44 62.2 199.51 89.98 199.58 105.09 199.73 124.24 199.88 136.99 200.02 146.69 200.24 157.85 200.46 166.52 200.68 173.71 200.98 181.63 201.2 186.76 201.27 187.71 201.34 190.04 201.42 190.95 201.49 192.51 201.56 193.13 201.64 196.23 201.71 195.64 201.78 197.99 201.86 198.54 201.93 199.96 202 200.63 202 200.63 202.08 202.42 203.17 208.11 203.25 166.73 203.32 153.98 203.39 160.74 203.47 197.84 203.47 197.84 203.54 209.77 204.13 220.04 204.2 177.56 204.27 168.94 204.35 179.14 204.35 179.14 204.42 228.49 207.2 209.52 207.28 179.43 207.35 175.64 207.42 191.31 207.42 191.31 207.5 221.82 209.11 207.37 209.18 190.4 209.25 193.78 209.25 193.78 209.33 221.08 211.23 202.35 211.3 186.93 211.38 191.01 211.38 191.01 211.45 220.08 211.74 205.92 211.82 195.34 211.89 202.22 211.89 202.22 211.96 241.79 215.19 237.61 215.26 200.28 215.33 193.86 215.33 193.86 215.41 205.96 215.7 218.31 215.77 192.39 215.84 189.97 215.84 189.97 215.92 206.8 217.82 217.62 217.9 192.1 217.97 190.39 217.97 190.39 218.04 207.99 219.21 220.88 219.29 202.01 219.29 202.01 219.36 203.5 219.65 228.79 219.73 193.03 219.8 179.54 219.87 184.59 219.87 184.59 219.95 220.45 222.73 231.95 222.8 177.99 222.88 169.37 222.95 178.89 222.95 178.89 223.02 226.88 223.68 208.17 223.75 169 223.83 164.19 223.9 177.3 223.9 177.3 223.97 202.73 225.15 204 225.22 201.88 225.29 201.58 225.51 197.51 225.59 196.81 225.66 194.84 225.73 193.91 225.81 192.05 225.95 189.26 226.1 185.99 226.25 182.04 226.32 180.69 226.46 176.34 226.68 169.09 226.83 163.61 227.05 153.21 227.2 144.57 227.34 133.46 227.49 117.98 227.56 107.04 227.64 91.52 227.71 61.9 227.78 44.28 227.86 46.66 228 96.34 228.08 110.28 228.22 128.48 228.37 140.83 228.52 150.28 228.74 161.25 228.96 169.78 229.17 176.87 229.47 184.73 229.61 187.93 229.69 189.9 229.76 190.49 229.83 193.41 229.91 193.84 229.98 195.55 230.05 196.05 230.13 199.18 230.2 198.64 230.27 201 230.35 201.74 230.42 202.62 231.67 211.15 231.74 161.41 231.81 153.05 231.88 163.81 231.88 163.81 231.96 227.58 232.62 204.61 232.69 174.23 232.76 169.53 232.84 184.19 232.84 184.19 232.91 221.13 235.62 223.07 235.77 176.8 235.84 176.59 235.91 198.13 235.99 223.38 236.21 217.17 236.28 202.19 236.28 202.19 236.35 205.27 237.52 246.45 237.6 202.03 237.67 189.75 237.74 196.78 237.74 196.78 237.82 234.36 239.65 250.56 239.72 196.91 239.79 185.98 239.87 193.81 239.87 193.81 239.94 237.59 240.16 255.8 240.23 202.04 240.31 195.25 240.31 195.25 240.38 205.98 243.68 223.37 243.75 197.18 243.82 194.45 243.82 194.45 243.9 210.84 244.19 209.52 244.26 190.54 244.34 191.76 244.34 191.76 244.41 214.96 246.31 209.85 246.39 190.41 246.46 192.22 246.46 192.22 246.53 216.59 247.71 213.56 247.78 200.67 247.78 200.67 247.85 205.43 248.14 246.67 248.22 188.73 248.29 179.41 248.36 188.46 248.36 188.46 248.44 248.33 251.22 208.34 251.29 174.71 251.37 169.87 251.44 183.89 251.44 183.89 251.51 217.67 252.1 220.96 252.25 167.08 252.32 165.75 252.39 184.45 252.47 203.45 254.22 204.26 254.3 201.44 254.37 200.62 254.52 197.07 254.66 194.06 254.74 191.25 254.81 190.76 254.88 187.65 254.96 185.97 255.18 178.63 255.32 173.09 255.54 162.42 255.69 153.57 255.83 142.13 255.98 126.02 256.05 114.39 256.13 97.35 256.2 57.69 256.27 45.01 256.35 51.13 256.42 89.33 256.49 109.68 256.57 122.61 256.71 139.97 256.86 151.95 257.01 161.17 257.23 171.98 257.45 180.35 257.74 189.47 257.96 195.09 258.03 196.95 258.11 198.08 258.18 200.67 258.25 199.79 258.25 199.79 258.33 204.9 260.08 202.37 260.16 188.4 260.23 157.19 260.3 152.85 260.38 168.02 260.38 168.02 260.45 202.4 261.04 216.72 261.18 171.84 261.25 170.92 261.33 190.93 261.33 190.93 261.4 219.2 264.11 222.01 264.18 190.89 264.26 174.94 264.33 178.38 264.33 178.38 264.4 208.03 264.7 212.1 264.77 201.41 264.77 201.41 264.84 208.6 266.02 242.96 266.09 197.87 266.16 189.8 266.24 200.6 266.24 200.6 266.31 248.42 268.14 230.31 268.21 192.68 268.29 185.79 268.36 197.69 268.36 197.69 268.43 243.6 268.65 228.36 268.73 199.27 268.8 196 268.8 196 268.87 211.16 272.17 214.85 272.24 195.07 272.31 195.88 272.31 195.88 272.39 217.13 272.68 203.32 272.75 189.57 272.83 194.42 272.83 194.42 272.9 226.45 274.8 203.53 274.88 189.41 274.95 194.88 274.95 194.88 275.02 230.6 276.2 208.89 276.27 199.98 276.27 199.98 276.34 208.62 276.64 219.46 276.71 185.5 276.78 180.06 276.86 193.48 276.86 193.48 276.93 229.87 279.64 220.31 279.79 172.34 279.86 171.08 279.93 190.51 279.93 190.51 280 217.93 280.59 212.42 280.66 183.98 280.74 165.98 280.81 168.02 280.88 195.15 280.88 195.15 280.96 208.54 283.45 204.28 283.59 199.79 283.67 196.83 283.74 195.18 283.81 191 283.96 184.58 284.11 176.53 284.18 172.04 284.33 160.19 284.47 143.07 284.55 130.66 284.62 111.71 284.69 54.7 284.77 46.26 284.84 56.36 284.91 113.74 284.99 131.86 285.13 153.13 285.28 166.86 285.42 176.9 285.57 185.11 285.72 191.25 285.79 195.27 285.86 197.23 285.94 199.82 286.01 202.38 288.5 216.09 288.57 200.39 288.72 153.93 288.79 153.36 288.94 200.2 288.94 200.2 289.01 215.83 289.53 217.16 289.6 187.2 289.67 170.23 289.75 173.1 289.82 200.32 289.89 222.7 292.6 231.9 292.68 185.21 292.75 173.81 292.82 181.1 292.82 181.1 292.9 227.02 293.19 208.2 293.26 201.59 293.26 201.59 293.33 212.91 294.51 226.63 294.58 194.6 294.65 190.44 294.65 190.44 294.73 205.22 296.63 216.83 296.7 189.49 296.78 186.33 296.78 186.33 296.85 202.98 297.14 217.9 297.22 197.41 297.29 197.6 297.29 197.6 297.36 218.28 300.66 208.62 300.73 193.75 300.81 198.12 300.81 198.12 300.88 225.42 301.1 243.75 301.17 198.76 301.25 189.37 301.32 197.99 301.32 197.99 301.39 258.68 303.22 232.79 303.3 198.49 303.37 189.03 303.44 198.5 303.44 198.5 303.52 249.51 304.69 205.57 304.76 199.93 304.76 199.93 304.83 213.34 305.13 207.89 305.2 183.2 305.27 181.49 305.35 199.84 305.35 199.84 305.42 227.6 308.13 216.51 308.2 188.03 308.28 170.68 308.35 172.95 308.42 199.66 308.5 222.05 309.08 213.25 309.16 178.36 309.23 165.54 309.3 171.18 309.3 171.18 309.38 213.07 311.13 203.17 311.21 200.18 311.28 199.56 311.5 194.46 311.65 190.83 311.72 189.77 311.79 186.64 311.87 185.22 312.16 175.36 312.3 169.55 312.52 158.77 312.67 149.55 312.82 137.36 312.96 119.63 313.04 106.31 313.11 84.86 313.18 52.56 313.26 47.99 313.33 62.57 313.4 97.06 313.48 113.44 313.62 133.53 313.77 146.78 313.92 156.58 314.06 164.5 314.28 174.09 314.5 181.65 314.65 186.25 314.87 191.85 314.94 193.9 315.01 194.99 315.09 197.31 315.16 197.87 315.23 201.7 315.31 200.38 315.31 200.38 315.38 203.01 316.99 208.87 317.07 200.19 317.14 168.16 317.21 151.53 317.29 154.61 317.36 182.56 317.43 204.51 318.02 223.67 318.09 181.57 318.16 169.32 318.24 176.09 318.24 176.09 318.31 216.14 321.09 223.81 321.17 180.8 321.24 173.43 321.31 184.9 321.31 184.9 321.39 230.35 323 215.36 323.07 192.13 323.14 191.65 323.14 191.65 323.22 210.99 325.12 207.62 325.2 187.19 325.27 187.64 325.27 187.64 325.34 210.32 325.63 211.43 325.71 196.47 325.78 200.38 325.78 200.38 325.85 227.96 329.15 203.93 329.22 193.27 329.3 201.21 329.3 201.21 329.37 236.87 329.59 228.04 329.66 195.47 329.74 189.91 329.74 189.91 329.81 202.75 331.71 242.19 331.79 194.57 331.86 189.32 331.86 189.32 331.93 203.25 333.18 203.14 333.25 200.74 333.25 200.74 333.33 220.22 333.54 234.85 333.62 200.28 333.69 181.73 333.76 183.72 333.76 183.72 333.84 208.24 336.62 219.34 336.69 182.25 336.77 169.72 336.84 175.63 336.84 175.63 336.91 214.48 337.57 224.81 337.65 174.45 337.72 165.72 337.79 175.47 337.79 175.47 337.87 211.85 339.33 203.75 339.4 202.21 339.48 201.25 339.55 199.29 339.62 198.94 339.7 196.66 339.77 195.5 339.92 192.4 340.06 188.89 340.14 186.97 340.21 185.53 340.28 182.89 340.43 178.87 340.65 171.29 340.87 161.97 341.02 154.34 341.16 144.88 341.31 132.29 341.46 113.7 341.53 99.31 341.67 51.21 341.75 50.31 341.82 70.27 341.89 97.49 341.97 112.48 342.11 131.53 342.26 144.34 342.41 153.89 342.55 161.64 342.77 171.03 342.99 178.56 343.14 183.08 343.29 186.92 343.43 190.71 343.51 191.86 343.58 193.95 343.65 194.94 343.73 197.54 343.8 197.67 343.87 199.57 343.95 200.81 343.95 200.81 344.02 202.45 345.56 207.2 345.63 161.65 345.7 149.89 345.78 156.68 345.85 199.22 345.85 199.22 345.92 218.17 346.51 224.61 346.58 177.15 346.66 169.15 346.73 180.12 346.73 180.12 346.8 230.2 349.58 205.96 349.66 177.39 349.73 173.81 349.8 190.04 349.8 190.04 349.88 221.8 351.49 207.41 351.56 190.54 351.64 193.58 351.64 193.58 351.71 218.36 353.54 235.43 353.61 200.8 353.69 185.71 353.76 189.77 353.76 189.77 353.83 221.48 354.13 206.84 354.2 196.44 354.2 196.44 354.27 204.41 357.57 241.44 357.64 200.31 357.71 193.49 357.71 193.49 357.79 205.32 358.08 217.16 358.15 193.17 358.23 191.21 358.23 191.21 358.3 209.04 360.21 218.26 360.28 191.77 360.35 190.4 360.35 190.4 360.42 209.68 361.6 219.11 361.67 201.29 361.67 201.29 361.74 202.53 362.04 237.89 362.11 194.55 362.18 181.06 362.26 186.73 362.26 186.73 362.33 221.24 365.11 244.13 365.19 177.97 365.26 169.55 365.33 179.36 365.33 179.36 365.41 227.95 366.06 204.03 366.14 171.63 366.21 166.57 366.28 181.02 366.28 181.02 366.36 210.68 367.97 203.57 368.04 201.6 368.12 200.99 368.33 196.01 368.41 194.75 368.48 192.62 368.7 187.5 368.92 180.96 369.14 173.35 369.36 163.79 369.51 156 369.65 146.28 369.8 133.28 369.95 113.71 370.02 98.05 370.09 67.73 370.17 50.66 370.24 53.41 370.39 103.63 370.46 117.45 370.61 135.59 370.75 147.98 370.9 157.28 371.04 164.88 371.26 174.11 371.48 181.59 371.63 186.02 371.78 189.9 371.85 191.39 371.92 193.65 372 194.74 372.07 196.66 372.22 199.82 372.29 200.89 372.29 200.89 372.36 202.41 374.05 203.11 374.12 156.54 374.19 148.94 374.27 159.74 374.27 159.74 374.34 206.35 375 204.4 375.07 173.96 375.15 169.84 375.22 185.51 375.22 185.51 375.29 218.33 378 222.01 378.15 174.87 378.22 174.98 378.3 197.02 378.37 222.29 379.91 246.23 379.98 201.6 380.05 189.79 380.13 196.47 380.13 196.47 380.2 229.73 382.03 244.41 382.1 195.6 382.18 184.97 382.25 192.86 382.25 192.86 382.32 247.59 382.62 203.54 382.69 197.32 382.69 197.32 382.76 209.85 386.06 227.5 386.13 197.44 386.21 194.4 386.21 194.4 386.28 210.68 386.57 209.84 386.65 191.68 386.72 193.22 386.72 193.22 386.79 217.65 388.7 207.87 388.77 190.01 388.84 192.4 388.84 192.4 388.92 218.86 390.09 213.72 390.16 200.09 390.16 200.09 390.23 205.24 390.53 247.56 390.6 190.19 390.67 181.11 390.75 190.63 390.75 190.63 390.82 275.23 393.6 208.42 393.68 174.85 393.75 170.15 393.82 184.38 393.82 184.38 393.9 218.25 394.48 215.98 394.63 169.57 394.7 168.23 394.78 187.74 394.78 187.74 394.85 217.51 396.97 202.82 397.12 199.84 397.19 197.41 397.27 195.61 397.41 191.21 397.63 183.76 397.71 180.07 397.85 173.74 398 165.81 398.14 155.74 398.29 142.37 398.44 121.71 398.51 104.49 398.58 63.1 398.66 50.87 398.73 57.38 398.8 97.51 398.88 117.59 398.95 130.44 399.1 147.77 399.24 159.76 399.46 172.81 399.68 182.76 399.9 190.6 400.05 194.69 400.27 201.1 400.34 202.19 400.34 202.19 400.42 204.88 402.47 213.89 402.61 152.51 402.69 148.67 402.76 164.1 402.83 196.28 402.83 196.28 402.91 211.46 403.42 218.13 403.56 171.69 403.64 171.29 403.71 192.57 403.78 219.11 406.49 221.53 406.57 188.76 406.64 173.15 406.71 176.96 406.71 176.96 406.79 207.35 408.4 241.47 408.47 197.31 408.54 189.82 408.62 200.53 408.62 200.53 408.69 243.71 410.52 232.86 410.6 191.58 410.67 184.93 410.74 197.04 410.74 197.04 410.82 238.64 411.04 228.07 411.11 201.35 411.18 198.99 411.18 198.99 411.25 216.86 414.55 216.62 414.62 195.27 414.7 195.89 414.7 195.89 414.77 217.94 415.06 204.34 415.14 190.89 415.21 196.06 415.21 196.06 415.28 230.38 417.11 236.38 417.19 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shape-9999.svg

shape-99999.svg

shape-sawtooth.svg

simple-fft.h

#ifndef SIGNALSMITH_DSP_LINEAR_SIMPLEFFT_H
#define SIGNALSMITH_DSP_LINEAR_SIMPLEFFT_H

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif

#include <complex>
#include <vector>

namespace signalsmith { namespace linear {

/// A self-contained, reasonably fast power-of-2 FFT template
template<typename Sample>
struct SimpleFFT {
	using Complex = std::complex<Sample>;
	
	SimpleFFT(int maxSize=0) {
		resize(maxSize);
	}
	
	void resize(int maxSize) {
		twiddles.resize(maxSize/2);
		for (int i = 0; i < maxSize/2; ++i) {
			double twiddlePhase = -2*M_PI*i/maxSize;
			twiddles[i] = {
				Sample(std::cos(twiddlePhase)),
				Sample(std::sin(twiddlePhase))
			};
		}
		working.resize(maxSize);
	}
	
	void fft(int size, const Complex *time, Complex *freq) {
		if (size <= 1) {
			*freq = *time;
			return;
		}
		fftPass<false>(size, 1, time, freq, working.data());
	}

	void ifft(int size, const Complex *freq, Complex *time) {
		if (size <= 1) {
			*time = *freq;
			return;
		}
		fftPass<true>(size, 1, freq, time, working.data());
	}
private:
	std::vector<Complex> twiddles;
	std::vector<Complex> working;

	// Calculate a [size]-point FFT, where each element is a block of [stride] values
	template<bool inverse>
	void fftPass(int size, int stride, const Complex *input, Complex *output, Complex *working) const {
		if (size > 2) {
			// Calculate the two half-size FFTs (odd and even) by doubling the stride
			fftPass<inverse>(size/2, stride*2, input, working, output);
			combine2<inverse>(size, stride, working, output);
		} else {
			// The input can already be considered a 1-point FFT
			combine2<inverse>(size, stride, input, output);
		}
	}
	
	// Combine interleaved even/odd results into a single spectrum
	template<bool inverse>
	void combine2(int size, int stride, const Complex *input, Complex *output) const {
		auto twiddleStep = twiddles.size()*2/size;
		for (int i = 0; i < size/2; ++i) {
			Complex twiddle = twiddles[i*twiddleStep];
			
			const Complex *inputA = input + 2*i*stride;
			const Complex *inputB = input + (2*i + 1)*stride;
			Complex *outputA = output + i*stride;
			Complex *outputB = output + (i + size/2)*stride;
			for (int s = 0; s < stride; ++s) {
				Complex a = inputA[s];
				Complex b = inputB[s]*(inverse ? std::conj(twiddle) : twiddle);
				outputA[s] = a + b;
				outputB[s] = a - b;
			}
		}
	}
};

}} // namespace
#endif // include guard