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+const dctSize = 512; // Default DCT size, read from header
+
+// --- Utility Functions for Audio Processing ---
+// Fast O(N log N) IDCT using FFT
+// JavaScript equivalent of C++ idct_512
+function javascript_idct_512(input) {
+ return javascript_idct_512_fft(input);
+}
+
+// Hanning window for smooth audio transitions (JavaScript equivalent)
+function hanningWindow(size) {
+ const window = new Float32Array(size);
+ const PI = Math.PI;
+ for (let i = 0; i < size; i++) {
+ window[i] = 0.5 * (1 - Math.cos((2 * PI * i) / (size - 1)));
+ }
+ return window;
+}
+
+const hanningWindowArray = hanningWindow(dctSize); // Pre-calculate window
+
+// ============================================================================
+// FFT-based DCT/IDCT Implementation
+// ============================================================================
+// Fast Fourier Transform using Radix-2 Cooley-Tukey algorithm
+// This implementation MUST match the C++ version in src/audio/fft.cc exactly
+
+// Bit-reversal permutation (in-place)
+// Reorders array elements by reversing their binary indices
+function bitReversePermute(real, imag, N) {
+ // Calculate number of bits needed
+ let temp_bits = N;
+ let num_bits = 0;
+ while (temp_bits > 1) {
+ temp_bits >>= 1;
+ num_bits++;
+ }
+
+ for (let i = 0; i < N; i++) {
+ // Compute bit-reversed index
+ let j = 0;
+ let temp = i;
+ for (let b = 0; b < num_bits; b++) {
+ j = (j << 1) | (temp & 1);
+ temp >>= 1;
+ }
+
+ // Swap if j > i (to avoid swapping twice)
+ if (j > i) {
+ const tmp_real = real[i];
+ const tmp_imag = imag[i];
+ real[i] = real[j];
+ imag[i] = imag[j];
+ real[j] = tmp_real;
+ imag[j] = tmp_imag;
+ }
+ }
+}
+
+// In-place radix-2 FFT (after bit-reversal)
+// direction: +1 for forward FFT, -1 for inverse FFT
+function fftRadix2(real, imag, N, direction) {
+ const PI = Math.PI;
+
+ // Butterfly operations
+ for (let stage_size = 2; stage_size <= N; stage_size *= 2) {
+ const half_stage = stage_size / 2;
+ const angle = direction * 2.0 * PI / stage_size;
+
+ // Precompute twiddle factors for this stage
+ let wr = 1.0;
+ let wi = 0.0;
+ const wr_delta = Math.cos(angle);
+ const wi_delta = Math.sin(angle);
+
+ for (let k = 0; k < half_stage; k++) {
+ // Apply butterfly to all groups at this stage
+ for (let group_start = k; group_start < N; group_start += stage_size) {
+ const i = group_start;
+ const j = group_start + half_stage;
+
+ // Complex multiplication: (real[j] + i*imag[j]) * (wr + i*wi)
+ const temp_real = real[j] * wr - imag[j] * wi;
+ const temp_imag = real[j] * wi + imag[j] * wr;
+
+ // Butterfly operation
+ real[j] = real[i] - temp_real;
+ imag[j] = imag[i] - temp_imag;
+ real[i] = real[i] + temp_real;
+ imag[i] = imag[i] + temp_imag;
+ }
+
+ // Update twiddle factor for next k (rotation)
+ const wr_old = wr;
+ wr = wr_old * wr_delta - wi * wi_delta;
+ wi = wr_old * wi_delta + wi * wr_delta;
+ }
+ }
+}
+
+// Forward FFT: Time domain → Frequency domain
+function fftForward(real, imag, N) {
+ bitReversePermute(real, imag, N);
+ fftRadix2(real, imag, N, +1);
+}
+
+// Inverse FFT: Frequency domain → Time domain
+function fftInverse(real, imag, N) {
+ bitReversePermute(real, imag, N);
+ fftRadix2(real, imag, N, -1);
+
+ // Scale by 1/N
+ const scale = 1.0 / N;
+ for (let i = 0; i < N; i++) {
+ real[i] *= scale;
+ imag[i] *= scale;
+ }
+}
+
+// DCT-II via FFT using reordering method (matches C++ dct_fft)
+// Reference: Numerical Recipes Chapter 12.3
+function javascript_dct_fft(input, N) {
+ const PI = Math.PI;
+
+ // Allocate arrays for N-point FFT
+ const real = new Float32Array(N);
+ const imag = new Float32Array(N);
+
+ // Reorder input: even indices first, then odd indices reversed
+ // [x[0], x[2], x[4], ...] followed by [x[N-1], x[N-3], x[N-5], ...]
+ for (let i = 0; i < N / 2; i++) {
+ real[i] = input[2 * i]; // Even indices: 0, 2, 4, ...
+ real[N - 1 - i] = input[2 * i + 1]; // Odd indices reversed: N-1, N-3, ...
+ }
+ // imag is already zeros (Float32Array default)
+
+ // Apply N-point FFT
+ fftForward(real, imag, N);
+
+ // Extract DCT coefficients with phase correction
+ // DCT[k] = Re{FFT[k] * exp(-j*pi*k/(2*N))} * normalization
+ const output = new Float32Array(N);
+ for (let k = 0; k < N; k++) {
+ const angle = -PI * k / (2.0 * N);
+ const wr = Math.cos(angle);
+ const wi = Math.sin(angle);
+
+ // Complex multiplication: (real[k] + j*imag[k]) * (wr + j*wi)
+ // Real part: real*wr - imag*wi
+ const dct_value = real[k] * wr - imag[k] * wi;
+
+ // Apply DCT-II normalization
+ if (k === 0) {
+ output[k] = dct_value * Math.sqrt(1.0 / N);
+ } else {
+ output[k] = dct_value * Math.sqrt(2.0 / N);
+ }
+ }
+
+ return output;
+}
+
+// IDCT (DCT-III) via FFT using reordering method (matches C++ idct_fft)
+// Reference: Numerical Recipes Chapter 12.3
+function javascript_idct_fft(input, N) {
+ const PI = Math.PI;
+
+ // Allocate arrays for N-point FFT
+ const real = new Float32Array(N);
+ const imag = new Float32Array(N);
+
+ // Prepare FFT input with inverse phase correction
+ // FFT[k] = DCT[k] * exp(+j*pi*k/(2*N)) / normalization
+ // Note: DCT-III needs factor of 2 for AC terms
+ for (let k = 0; k < N; k++) {
+ const angle = PI * k / (2.0 * N); // Positive angle for inverse
+ const wr = Math.cos(angle);
+ const wi = Math.sin(angle);
+
+ // Inverse of DCT-II normalization with correct DCT-III scaling
+ let scaled;
+ if (k === 0) {
+ scaled = input[k] / Math.sqrt(1.0 / N);
+ } else {
+ // DCT-III needs factor of 2 for AC terms
+ scaled = input[k] / Math.sqrt(2.0 / N) * 2.0;
+ }
+
+ // Complex multiplication: scaled * (wr + j*wi)
+ real[k] = scaled * wr;
+ imag[k] = scaled * wi;
+ }
+
+ // Apply inverse FFT
+ fftInverse(real, imag, N);
+
+ // Unpack: reverse the reordering from DCT
+ // Even output indices come from first half of FFT output
+ // Odd output indices come from second half (reversed)
+ const output = new Float32Array(N);
+ for (let i = 0; i < N / 2; i++) {
+ output[2 * i] = real[i]; // Even positions
+ output[2 * i + 1] = real[N - 1 - i]; // Odd positions (reversed)
+ }
+
+ return output;
+}
+
+// Convenience wrappers for dctSize = 512 (backward compatible)
+function javascript_dct_512_fft(input) {
+ return javascript_dct_fft(input, dctSize);
+}
+
+function javascript_idct_512_fft(input) {
+ return javascript_idct_fft(input, dctSize);
+}
+