# `window` — discrete window functions

## Purpose

Window functions taper the endpoints of each analysis frame so the FFT sees a periodic-looking signal rather than the abrupt discontinuities created by a rectangular slice. Tapering reduces spectral leakage at the cost of a small main-lobe widening, which is the standard trade-off used by every spectral analyzer in this package.

The module exposes three closed-form windows — Hann, Hamming, and Blackman — selectable by the `window` option of `SpectrumAnalyzerOptions`. Vectors are cached per `(name, size)` so the spectrum, spectrogram, and MFCC analyzers share a single allocation across every frame of the same shape.

## Features

- Hann, Hamming, Blackman generators producing `Float32Array` vectors.
- Cached per `(name, size)` to avoid re-allocation on every frame.
- `applyWindow` for in-place multiplication into a caller-provided buffer.
- `clearWindowCache` for benchmarks measuring cold-start cost.

## Usage: Basic

```ts
import {
  applyWindow,
  getWindow,
} from "@suaveplan/audio-analysis-spectrum/algorithms/window";

const w = getWindow("hann", 2048);
const frame = new Float32Array(2048);
const out = new Float32Array(2048);
applyWindow(frame, w, out);
```

## Usage: Advanced

```ts
import {
  clearWindowCache,
  getWindow,
} from "@suaveplan/audio-analysis-spectrum/algorithms/window";

// Pre-warm the cache for the working set.
for (const name of ["hann", "hamming", "blackman"] as const) {
  for (const size of [1024, 2048, 4096]) getWindow(name, size);
}

// Later, before a benchmark, evict every vector.
clearWindowCache();
```

## API Reference

- `getWindow(name, size): Float32Array` — cached window vector.
- `applyWindow(frame, window, out): void` — element-wise multiply.
- `clearWindowCache(): void` — drop every cached vector.
- `WindowName = "hann" | "hamming" | "blackman"`.

## Implementation Notes

Each closed form is the standard periodic definition with `N - 1` in the denominator, so the endpoints of Hann and Blackman are exact zeros and the centre is exactly `1`. Hamming uses the `(0.54, 0.46)` coefficients from Hamming's 1989 paper. The cache key is `${name}:${size}`; since both inputs are tightly constrained by the analyzer layer the key set is small.