`dct` — type-II discrete cosine transform

Purpose

The DCT-II module is the cepstral projection step of the MFCC pipeline: it takes the log mel-spectrum of one frame and produces a compact vector of cepstral coefficients. The same routine is reusable anywhere a closed-form orthonormal-with-scale DCT is needed.

This implementation is unscaled (no sqrt(2/N) orthonormality factor) because downstream MFCC analysis is unit-agnostic: every coefficient is later compared to peers, not to an external reference. Callers that need an orthonormal form can post-multiply by the standard scaling factor.

Features

Closed-form X_k = Σ x_n · cos((π/N)(n + ½)k) for 0 ≤ k < coefficients.
Cached per (inputSize, coefficients) so repeated frames reuse the kernel matrix.
Pure portable TypeScript over Float32Array inputs and outputs.

Usage: Basic

import { dctII } from "@suaveplan/audio-analysis-spectrum/algorithms/dct";

const logMel = new Float32Array(40); // log mel-spectrum
const mfcc = dctII(logMel, 13);

Usage: Advanced

import {
  clearDctCache,
  dctII,
} from "@suaveplan/audio-analysis-spectrum/algorithms/dct";

const coeffs = dctII(logMel, 20);
// later, before a benchmark sweep
clearDctCache();

API Reference

dctII(input, coefficients): Float32Array — first coefficients cepstral values.
clearDctCache(): void — evict every cached kernel.

Implementation Notes

The kernel is stored as a flat Float64Array of coefficients * inputSize doubles so the per-frame inner loop is a single linear pass with no nested allocation. Kernel construction is O(coefficients · inputSize) and is cached on the (inputSize, coefficients) pair; runtime cost is then a single matrix-vector multiply per frame. Boundary checks on coefficients (positive, ≤ melBands) are enforced at the analyzer layer before this routine is called, so this module assumes a validated input.

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dct — type-II discrete cosine transform