From 0bc30832be2c7de3e1797876c4efc936cce3d43b Mon Sep 17 00:00:00 2001 From: Tyler Date: Fri, 10 Apr 2026 23:27:56 -0700 Subject: [PATCH] Implement synchrosqueezing transform for sharp spectrogram display Co-authored-by: Qwen-Coder --- src/spectrogram.c | 127 ++++++++++++++-- synchrosqueezing_for_programmers.aux | 5 + synchrosqueezing_for_programmers.out | 0 synchrosqueezing_for_programmers.pdf | Bin 0 -> 151314 bytes synchrosqueezing_for_programmers.tex | 219 +++++++++++++++++++++++++++ 5 files changed, 341 insertions(+), 10 deletions(-) create mode 100644 synchrosqueezing_for_programmers.aux create mode 100644 synchrosqueezing_for_programmers.out create mode 100644 synchrosqueezing_for_programmers.pdf create mode 100644 synchrosqueezing_for_programmers.tex diff --git a/src/spectrogram.c b/src/spectrogram.c index 79f122d..d9f7545 100644 --- a/src/spectrogram.c +++ b/src/spectrogram.c @@ -65,6 +65,7 @@ typedef struct { typedef struct { FrequencyData* spectrum; + FrequencyData* derivativeSpectrum; // STFT with derivative window (for synchrosqueezing) int numBins; int sampleOffset; int sampleCount; @@ -116,6 +117,7 @@ typedef struct { ColormapType colormap; bool showGrid; int fftSize; // Current FFT size (128-2048) + bool useSynchrosqueezing; // Enable synchrosqueezing for sharper display // File browser state bool showFileBrowser; @@ -280,6 +282,7 @@ static void ComputeSTFT(AudioSignal* signal, StftResult* result, int fftSize) int numBins = fftSize / 2 + 1; float* windowedSamples = (float*)malloc(fftSize * sizeof(float)); + float* derivWindowedSamples = (float*)malloc(fftSize * sizeof(float)); float complex *complexInput = (float complex*)malloc(fftSize * sizeof(float complex)); float complex* fftOutput = (float complex*)malloc(fftSize * sizeof(float complex)); @@ -289,18 +292,23 @@ static void ComputeSTFT(AudioSignal* signal, StftResult* result, int fftSize) if (offset + samplesToCopy > signal->numSamples) { samplesToCopy = signal->numSamples - offset; memset(windowedSamples, 0, fftSize * sizeof(float)); + memset(derivWindowedSamples, 0, fftSize * sizeof(float)); } else { memcpy(windowedSamples, signal->samples + offset, fftSize * sizeof(float)); + memcpy(derivWindowedSamples, signal->samples + offset, fftSize * sizeof(float)); } // Apply Hann window: h(t) = 0.5 * (1 - cos(2πt)) + // And derivative window: h'(t) = π * sin(2πt) for (int i = 0; i < fftSize; i++) { float t = (float)i / (fftSize - 1); float hann = 0.5f * (1.0f - cosf(2.0f * M_PI * t)); + float derivHann = M_PI * sinf(2.0f * M_PI * t); windowedSamples[i] *= hann; + derivWindowedSamples[i] *= derivHann; } - // Compute STFT + // Compute normal STFT (V_f) for (int i = 0; i < fftSize; i++) complexInput[i] = windowedSamples[i] + 0.0f * I; FFT(complexInput, fftOutput, fftSize, false); @@ -314,14 +322,26 @@ static void ComputeSTFT(AudioSignal* signal, StftResult* result, int fftSize) result->segments[seg].spectrum[bin].amplitude = (bin == 0) ? cabsf(fftOutput[bin]) / fftSize : 2.0f * cabsf(fftOutput[bin]) / fftSize; result->segments[seg].spectrum[bin].phase = cargf(fftOutput[bin]); } + + // Compute derivative-window STFT (V_fd) for synchrosqueezing + result->segments[seg].derivativeSpectrum = (FrequencyData*)malloc(numBins * sizeof(FrequencyData)); + for (int i = 0; i < fftSize; i++) complexInput[i] = derivWindowedSamples[i] + 0.0f * I; + FFT(complexInput, fftOutput, fftSize, false); + + for (int bin = 0; bin < numBins; bin++) { + result->segments[seg].derivativeSpectrum[bin].frequency = (float)bin * signal->sampleRate / fftSize; + result->segments[seg].derivativeSpectrum[bin].amplitude = cabsf(fftOutput[bin]) / fftSize; + result->segments[seg].derivativeSpectrum[bin].phase = cargf(fftOutput[bin]); + } } - free(windowedSamples); free(complexInput); free(fftOutput); + free(windowedSamples); free(derivWindowedSamples); free(complexInput); free(fftOutput); } static void FreeSTFT(StftResult* result) { for (int i = 0; i < result->numSegments; i++) { free(result->segments[i].spectrum); + if (result->segments[i].derivativeSpectrum) free(result->segments[i].derivativeSpectrum); } free(result->segments); result->segments = NULL; @@ -433,6 +453,9 @@ static void GenerateSpectrogramTexture(StftResult* stft, Image* image, Texture2D if (stft->numSegments == 0) return; int width = stft->numSegments; int height = stft->segments[0].numBins; + int fftSize = (height - 1) * 2; + float freqPerBin = (float)stft->sampleRate / fftSize; + *image = GenImageColor(width, height, BLACK); Color* pixels = (Color*)image->data; @@ -443,16 +466,89 @@ static void GenerateSpectrogramTexture(StftResult* stft, Image* image, Texture2D if (stft->segments[seg].spectrum[bin].amplitude > maxAmplitude) maxAmplitude = stft->segments[seg].spectrum[bin].amplitude; - for (int seg = 0; seg < width; seg++) { - for (int bin = 0; bin < height; bin++) { - float amplitude = stft->segments[seg].spectrum[bin].amplitude; - float db = AmplitudeToDecibels(amplitude); - float normalized = (db - app.amplitudeFloorDb) / (app.amplitudeCeilingDb - app.amplitudeFloorDb); - normalized = Clamp(normalized, 0.0f, 1.0f); - int pixelIndex = (height - 1 - bin) * width + seg; - pixels[pixelIndex] = GetColormapColor(normalized, app.colormap); + if (app.useSynchrosqueezing) { + // ===== SYNCHROSQUEEZING ===== + // Reassign energy to true frequencies using derivative STFT + + // Accumulation buffer for reassigned energy + float* accumBuffer = (float*)calloc(width * height, sizeof(float)); + + for (int seg = 0; seg < width; seg++) { + for (int bin = 0; bin < height; bin++) { + FrequencyData* V_f = &stft->segments[seg].spectrum[bin]; + FrequencyData* V_fd = &stft->segments[seg].derivativeSpectrum[bin]; + + float amplitude = V_f->amplitude; + if (amplitude < 0.0001f) continue; + + // Compute instantaneous frequency using synchrosqueezing formula: + // ω̂ = bin_freq + Re[V_fd / (i * V_f)] + // Complex division: (a+bi)/(c+di) = ((ac+bd) + (bc-ad)i) / (c²+d²) + // We need Re[(a+bi) / (i*(c+di))] = Re[(a+bi) / (-d+ci)] = (ad+bc)/(c²+d²) + + float V_f_real = amplitude * cosf(V_f->phase); + float V_f_imag = amplitude * sinf(V_f->phase); + float V_fd_real = V_fd->amplitude * cosf(V_fd->phase); + float V_fd_imag = V_fd->amplitude * sinf(V_fd->phase); + + float denom = V_f_real * V_f_real + V_f_imag * V_f_imag; + + float trueFreq = V_f->frequency; // Default to bin frequency + + if (denom > 1e-10f) { + // Re[V_fd / (i * V_f)] = (V_fd_real * V_f_imag + V_fd_imag * V_f_real) / denom + float correction = (V_fd_real * V_f_imag + V_fd_imag * V_f_real) / denom; + trueFreq = V_f->frequency + correction; + } + + // Clamp to valid range + if (trueFreq < 0) trueFreq = 0; + if (trueFreq >= stft->sampleRate / 2.0f) trueFreq = stft->sampleRate / 2.0f - 1; + + // Map to bin coordinate + float targetBinF = trueFreq / freqPerBin; + if (targetBinF < 0) targetBinF = 0; + if (targetBinF >= height) targetBinF = height - 0.001f; + + // Bilinear splatting to neighboring bins + int bin0 = (int)targetBinF; + int bin1 = bin0 + 1; + if (bin1 >= height) bin1 = height - 1; + + float frac = targetBinF - bin0; + int idx0 = (height - 1 - bin0) * width + seg; + int idx1 = (height - 1 - bin1) * width + seg; + + accumBuffer[idx0] += amplitude * (1 - frac); + accumBuffer[idx1] += amplitude * frac; + } + } + + // Convert accumulation buffer to colors + for (int i = 0; i < width * height; i++) { + if (accumBuffer[i] > 0.0001f) { + float db = AmplitudeToDecibels(accumBuffer[i]); + float normalized = (db - app.amplitudeFloorDb) / (app.amplitudeCeilingDb - app.amplitudeFloorDb); + normalized = Clamp(normalized, 0.0f, 1.0f); + pixels[i] = GetColormapColor(normalized, app.colormap); + } + } + + free(accumBuffer); + } else { + // ===== STANDARD STFT (no synchrosqueezing) ===== + for (int seg = 0; seg < width; seg++) { + for (int bin = 0; bin < height; bin++) { + float amplitude = stft->segments[seg].spectrum[bin].amplitude; + float db = AmplitudeToDecibels(amplitude); + float normalized = (db - app.amplitudeFloorDb) / (app.amplitudeCeilingDb - app.amplitudeFloorDb); + normalized = Clamp(normalized, 0.0f, 1.0f); + int pixelIndex = (height - 1 - bin) * width + seg; + pixels[pixelIndex] = GetColormapColor(normalized, app.colormap); + } } } + if (texture->id != 0) UnloadTexture(*texture); *texture = LoadTextureFromImage(*image); SetTextureFilter(*texture, TEXTURE_FILTER_BILINEAR); @@ -940,6 +1036,16 @@ static void DrawSidebar(void) DrawRectangleLinesEx(gridCheck, 1, WHITE); DrawText("Show Grid", x + 25, y + 2, fontSize, LIGHTGRAY); y += 25; + // Synchrosqueezing toggle + Rectangle sqCheck = { x, y, 18, 18 }; + if (CheckCollisionPointRec(GetMousePosition(), sqCheck) && IsMouseButtonPressed(MOUSE_LEFT_BUTTON)) { + app.useSynchrosqueezing = !app.useSynchrosqueezing; + needsRegen = true; + } + DrawRectangleRec(sqCheck, app.useSynchrosqueezing ? BLUE : DARKGRAY); + DrawRectangleLinesEx(sqCheck, 1, WHITE); + DrawText("Synchrosqueezing (sharp)", x + 25, y + 2, fontSize, LIGHTGRAY); y += 25; + // File loading DrawText("File:", x, y, fontSize, LIGHTGRAY); y += 18; Rectangle fileButton = { x, y, sidebarWidth - 10, 25 }; @@ -1067,6 +1173,7 @@ int main(int argc, char* argv[]) app.fftSize = FFT_SIZE_DEFAULT; app.isPlaying = false; app.playbackFinished = false; + app.useSynchrosqueezing = true; // Enabled by default GenerateColormapTexture(); ScanDirectory(GetWorkingDirectory()); diff --git a/synchrosqueezing_for_programmers.aux b/synchrosqueezing_for_programmers.aux new file mode 100644 index 0000000..79d49a5 --- /dev/null +++ b/synchrosqueezing_for_programmers.aux @@ -0,0 +1,5 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\gdef \@abspage@last{5} diff --git a/synchrosqueezing_for_programmers.out b/synchrosqueezing_for_programmers.out new 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