# window-function

> Window functions for signal processing and spectral analysis

Latest version **3.0.2** (published 2026-07-11) · MIT license · 0 weekly downloads

## Install

```sh
npm install window-function
pnpm add window-function
yarn add window-function
bun add window-function
```

## Health

**Score 70/100 (B)** — status: active.

Positive: has types; esm support; no vulnerabilities; recently updated; high maintenance score; high quality score.

Warnings: low downloads.

## Facts

| | |
|---|---|
| Version | 3.0.2 |
| Published | 2026-07-11 |
| First published | 2017-06-23 |
| Weekly downloads | 0 |
| License | MIT |
| TypeScript types | bundled |
| Module format | ESM |
| Node | >=18 |
| Dependencies | 0 |
| Unpacked size | 47.3 KB |
| Known vulnerabilities | 0 |
| Install scripts | no |
| GitHub stars | 62 |
| Author | Ricky Reusser |
| Maintainers | mikolalysenko, rreusser, dy |
| Keywords | window-function, window, apodization, hann, hamming, blackman, kaiser, dpss, spectral-analysis, fft, fft-window, dsp, signal-processing, stft |

## Links

- npm: https://www.npmjs.com/package/window-function
- Repository: https://github.com/audiojs/window-function
- Issues: https://github.com/audiojs/window-function/issues
- Funding: https://github.com/sponsors/audiojs
- npm.io page: https://npm.io/package/window-function

## Recent versions

- 3.0.2 (latest) — 2026-07-11
- 3.0.1 — 2026-04-07
- 3.0.0 — 2026-03-26
- 2.1.0 — 2018-12-10
- 2.0.2 — 2017-06-23

## README

# window-function [![test](https://github.com/audiojs/window-function/actions/workflows/test.yml/badge.svg)](https://github.com/audiojs/window-function/actions/workflows/test.yml) [![npm](https://img.shields.io/npm/v/window-function)](https://www.npmjs.com/package/window-function) [![MIT](https://img.shields.io/badge/MIT-%E0%A5%90-white)](https://github.com/krishnized/license)

Collection of window functions for signal processing and spectral analysis.

```sh
npm install window-function
```

```js
import { hann, kaiser, generate, apply } from 'window-function'

// Every window: fn(i, N, ...params) → number
hann(50, 101)                    // single sample → 1.0

// Generate full window as Float64Array
let w = generate(hann, 1024)

// Apply window to a signal in-place
let signal = new Float64Array(1024).fill(1)
apply(signal, hann)              // signal *= hann

// Parameterized windows pass extra args
generate(kaiser, 1024, 8.6)     // Kaiser with β = 8.6
```

Or import individual windows directly:

```js
import hann from 'window-function/hann'
import kaiser from 'window-function/kaiser'
```


## Reference

<dl>
<dt>Simple</dt>
  <dd>

[rectangular](#rectangulari-n) ·
[triangular](#triangulari-n) ·
[bartlett](#bartletti-n) ·
[welch](#welchi-n) ·
[connes](#connesi-n) ·
[hann](#hanni-n) ·
[hamming](#hammingi-n) ·
[cosine](#cosinei-n) ·
[blackman](#blackmani-n) ·
[exactBlackman](#exactblackmani-n) ·
[nuttall](#nuttalli-n) ·
[blackmanNuttall](#blackmannuttalli-n) ·
[blackmanHarris](#blackmanharrisi-n) ·
[flatTop](#flattopi-n) ·
[bartlettHann](#bartletthanni-n) ·
[lanczos](#lanczosi-n) ·
[parzen](#parzeni-n) ·
[bohman](#bohmani-n)

</dd>

<dt>Parameterized</dt>
<dd>

[kaiser](#kaiseri-n-beta) ·
[gaussian](#gaussiani-n-sigma) ·
[generalizedNormal](#generalizednormali-n-sigma-p) ·
[tukey](#tukeyi-n-alpha) ·
[planckTaper](#plancktaperi-n-epsilon) ·
[powerOfSine](#powerofsinei-n-alpha) ·
[exponential](#exponentiali-n-tau) ·
[hannPoisson](#hannpoissoni-n-alpha) ·
[cauchy](#cauchyi-n-alpha) ·
[rifeVincent](#rifevincenti-n-order) ·
[confinedGaussian](#confinedgaussiani-n-sigmat)

</dd>

<dt>Array-computed</dt>
<dd>

[dolphChebyshev](#dolphchebyshevi-n-db) ·
[taylor](#taylori-n-nbar-sll) ·
[kaiserBesselDerived](#kaiserbesselderivedi-n-beta) ·
[dpss](#dpssi-n-w) ·
[ultraspherical](#ultrasphericali-n-mu-xmu)

</dd>
</dl>

## Simple — no parameters

### `rectangular(i, N)`

$w(n) = 1$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/rectangular.svg">

No windowing. Best frequency resolution, worst spectral leakage. Use for transient signals already zero at edges, or harmonic analysis with integer cycles.
**-13 dB** sidelobe · **-6 dB/oct** rolloff

### `triangular(i, N)`

$w(n) = 1 - \left|\frac{2n - N + 1}{N}\right|$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/triangular.svg">

Linear taper, nonzero endpoints. Simple smoothing, 2nd-order B-spline.
**-27 dB** sidelobe · **-12 dB/oct** rolloff

### `bartlett(i, N)`

$w(n) = 1 - \left|\frac{2n - N + 1}{N - 1}\right|$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/bartlett.svg">

Linear taper, zero endpoints. Bartlett's method PSD estimation.[^bartlett1950]
**-27 dB** sidelobe · **-12 dB/oct** rolloff

### `welch(i, N)`

$w(n) = 1 - \left(\frac{2n - N + 1}{N - 1}\right)^2$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/welch.svg">

Parabolic taper. Welch's method PSD estimation.[^welch1967]
**-21 dB** sidelobe · **-12 dB/oct** rolloff

### `connes(i, N)`

$w(n) = \left[1 - \left(\frac{2n - N + 1}{N - 1}\right)^2\right]^2$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/connes.svg">

Welch squared (4th power parabolic). FTIR spectroscopy, interferogram apodization.[^connes1961]
**-24 dB/oct** rolloff

### `hann(i, N)`

$w(n) = 0.5 - 0.5\cos\!\left(\frac{2\pi n}{N-1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/hann.svg">

Raised cosine, zero endpoints. The default general-purpose choice. STFT with 50% overlap (COLA). Also called "Hanning" (misnomer).[^blackman1958]
**-32 dB** sidelobe · **-18 dB/oct** rolloff

### `hamming(i, N)`

$w(n) = 0.54 - 0.46\cos\!\left(\frac{2\pi n}{N-1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/hamming.svg">

Raised cosine, nonzero endpoints. Optimized for first sidelobe cancellation. FIR filter design, speech processing.[^hamming1977]
**-43 dB** sidelobe · **-6 dB/oct** rolloff

### `cosine(i, N)`

$w(n) = \sin\!\left(\frac{\pi n}{N-1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/cosine.svg">

Half-period sine. MDCT audio codecs: MP3, AAC, Vorbis.[^princen1987]
**-23 dB** sidelobe · **-12 dB/oct** rolloff

### `blackman(i, N)`

$w(n) = 0.42 - 0.5\cos\!\left(\frac{2\pi n}{N-1}\right) + 0.08\cos\!\left(\frac{4\pi n}{N-1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/blackman.svg">

3-term cosine sum. Better leakage than Hann at the cost of wider main lobe.[^blackman1958]
**-58 dB** sidelobe · **-18 dB/oct** rolloff

### `exactBlackman(i, N)`

$w(n) = 0.42659 - 0.49656\cos\!\left(\frac{2\pi n}{N-1}\right) + 0.076849\cos\!\left(\frac{4\pi n}{N-1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/exactBlackman.svg">

Blackman with exact zero placement at 3rd and 4th sidelobes.[^harris1978]
**-69 dB** sidelobe · **-6 dB/oct** rolloff

### `nuttall(i, N)`

$w(n) = 0.355768 - 0.487396\cos\!\left(\frac{2\pi n}{N\!-\!1}\right) + 0.144232\cos\!\left(\frac{4\pi n}{N\!-\!1}\right) - 0.012604\cos\!\left(\frac{6\pi n}{N\!-\!1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/nuttall.svg">

4-term cosine sum, continuous 1st derivative. High-dynamic-range analysis without edge discontinuity.[^nuttall1981]
**-93 dB** sidelobe · **-18 dB/oct** rolloff

### `blackmanNuttall(i, N)`

$w(n) = 0.3635819 - 0.4891775\cos\!\left(\frac{2\pi n}{N\!-\!1}\right) + 0.1365995\cos\!\left(\frac{4\pi n}{N\!-\!1}\right) - 0.0106411\cos\!\left(\frac{6\pi n}{N\!-\!1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/blackmanNuttall.svg">

4-term cosine sum, lowest sidelobes among 4-term windows.[^nuttall1981]
**-98 dB** sidelobe · **-6 dB/oct** rolloff

### `blackmanHarris(i, N)`

$w(n) = 0.35875 - 0.48829\cos\!\left(\frac{2\pi n}{N\!-\!1}\right) + 0.14128\cos\!\left(\frac{4\pi n}{N\!-\!1}\right) - 0.01168\cos\!\left(\frac{6\pi n}{N\!-\!1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/blackmanHarris.svg">

4-term minimum sidelobe. ADC testing, measurement instrumentation, >80 dB dynamic range.[^harris1978]
**-92 dB** sidelobe · **-6 dB/oct** rolloff

### `flatTop(i, N)`

$w(n) = 1 - 1.93\cos\!\left(\frac{2\pi n}{N\!-\!1}\right) + 1.29\cos\!\left(\frac{4\pi n}{N\!-\!1}\right) - 0.388\cos\!\left(\frac{6\pi n}{N\!-\!1}\right) + 0.028\cos\!\left(\frac{8\pi n}{N\!-\!1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/flatTop.svg">

5-term cosine sum, near-zero scalloping. Peak ~4.64 (by design). Amplitude calibration, transducer calibration (~0.01 dB accuracy). ISO 18431.[^heinzel2002]
**-93 dB** sidelobe · **-6 dB/oct** rolloff

### `bartlettHann(i, N)`

$w(n) = 0.62 - 0.48\left|\frac{n}{N\!-\!1} - 0.5\right| - 0.38\cos\!\left(\frac{2\pi n}{N-1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/bartlettHann.svg">

Bartlett-Hann hybrid. Balanced near/far sidelobe levels.[^ha1989]
**-36 dB** sidelobe

### `lanczos(i, N)`

$w(n) = \text{sinc}\!\left(\frac{2n}{N-1} - 1\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/lanczos.svg">

Sinc main lobe. Image resampling, interpolation (FFmpeg, ImageMagick).[^duchon1979]
**-26 dB** sidelobe

### `parzen(i, N)`

$w(n) = 1 - 6a^2(1-a)$ for $|a| \le 0.5$, &ensp; $w(n) = 2(1-a)^3$ for $|a| > 0.5$, &ensp; $a = |(2n-N+1)/(N-1)|$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/parzen.svg">

4th-order B-spline. Always-positive spectrum. Kernel density estimation.[^parzen1961]
**-53 dB** sidelobe · **-24 dB/oct** rolloff

### `bohman(i, N)`

$w(n) = (1-|a|)\cos(\pi|a|) + \frac{\sin(\pi|a|)}{\pi}$, &ensp; $a = \frac{2n-N+1}{N-1}$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/bohman.svg">

Autocorrelation of cosine window. Fast sidelobe decay, spectral estimation.
**-46 dB** sidelobe · **-24 dB/oct** rolloff



## Parameterized — adjustable tradeoff

### `kaiser(i, N, beta)`

`beta`: shape — 0 = rectangular, 5.4 = Hamming, **8.6** (default) = Blackman.

$w(n) = \frac{I_0\!\left(\beta\sqrt{1 - \left(\frac{2n-N+1}{N-1}\right)^2}\right)}{I_0(\beta)}$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/kaiser.svg">

Near-optimal DPSS approximation via Bessel I₀. The standard parameterized window for FIR filter design.[^kaiser1974]

### `gaussian(i, N, sigma)`

`sigma`: width, default **0.4**.

$w(n) = \exp\!\left[-\frac{1}{2}\left(\frac{2n-N+1}{\sigma(N-1)}\right)^2\right]$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/gaussian.svg">

Gaussian bell, minimum time-bandwidth product. STFT/Gabor transform, frequency estimation via parabolic interpolation.[^gabor1946]

### `generalizedNormal(i, N, sigma, p)`

`sigma`: width (default **0.4**), `p`: shape — 2 = Gaussian, large = rectangular.

$w(n) = \exp\!\left[-\frac{1}{2}\left|\frac{2n-N+1}{\sigma(N-1)}\right|^p\right]$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/generalizedNormal.svg">

Continuous family between Gaussian and rectangular. Adjustable time-frequency tradeoff.

### `tukey(i, N, alpha)`

`alpha`: taper fraction — 0 = rectangular, **0.5** (default), 1 = Hann.

$w(n) = \tfrac{1}{2}[1+\cos(\pi(n/(\alpha(N\!-\!1)/2)-1))]$ in tapered edges, &ensp; $w(n) = 1$ in flat center.

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/tukey.svg">

Flat center with cosine-tapered edges. Preserves signal amplitude while tapering. Vibration analysis, LIGO.

### `planckTaper(i, N, epsilon)`

`epsilon`: taper fraction, default **0.1**.

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/planckTaper.svg">

C∞-smooth bump function (infinitely differentiable). Gravitational wave analysis (LIGO/Virgo).[^mckechan2010]

### `powerOfSine(i, N, alpha)`

`alpha`: exponent — 0 = rectangular, 1 = cosine, **2** (default) = Hann.

$w(n) = \sin^\alpha\!\left(\frac{\pi n}{N-1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/powerOfSine.svg">

$\sin^\alpha$ family. Codec design, parameterized spectral analysis.

### `exponential(i, N, tau)`

`tau`: time constant, default **1**.

$w(n) = \exp\!\left(\frac{-|2n-N+1|}{\tau(N-1)}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/exponential.svg">

Exponential decay from center. Modal analysis, impact testing.[^harris1978]

### `hannPoisson(i, N, alpha)`

`alpha`: decay, default **2**. At α ≥ 2 the transform has no sidelobes.

$w(n) = \frac{1}{2}\left(1-\cos\frac{2\pi n}{N\!-\!1}\right)\exp\!\left(\frac{-\alpha|2n\!-\!N\!+\!1|}{N-1}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/hannPoisson.svg">

Hann × exponential. Unique no-sidelobe property enables frequency estimators using convex optimization.

### `cauchy(i, N, alpha)`

`alpha`: width, default **3**.

$w(n) = \frac{1}{1+\left(\frac{\alpha(2n-N+1)}{N-1}\right)^2}$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/cauchy.svg">

Lorentzian shape. Matches spectral line shapes in spectroscopy.[^harris1978]

### `rifeVincent(i, N, order)`

`order`: **1** (default) = Hann, 2, 3. Throws for other values.

$w(n) = \frac{1}{Z}\sum_{k=0}^{K}(-1)^k a_k\cos\frac{2\pi kn}{N-1}$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/rifeVincent.svg">

Class I cosine-sum optimized for sidelobe fall-off. Power grid harmonic analysis, interpolated DFT.[^rife1970]

### `confinedGaussian(i, N, sigmaT)`

`sigmaT`: temporal width, default **0.1**.

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/confinedGaussian.svg">

Optimal RMS time-frequency bandwidth. Time-frequency analysis, audio coding.[^starosielec2014]



## Array-computed — cached

Compute the full window on first call, cache the result. Recomputed when parameters change.

### `dolphChebyshev(i, N, dB)`

`dB`: sidelobe attenuation, default **100**.

$W(k) = (-1)^k T_{N-1}\!\left(\beta\cos\frac{\pi k}{N}\right)$, &ensp; $w = \text{IDFT}(W)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/dolphChebyshev.svg">

Optimal: narrowest main lobe for given equiripple sidelobe level. Antenna design, radar.[^dolph1946]

### `taylor(i, N, nbar, sll)`

`nbar`: constant-level sidelobes (default **4**), `sll`: level in dB (default **30**).

$w(n) = 1 + 2\sum_{m=1}^{\bar{n}-1} F_m \cos\frac{2\pi m(n-(N\!-\!1)/2)}{N}$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/taylor.svg">

Monotonically decreasing sidelobes. The radar community standard for SAR image formation.[^taylor1955]

### `kaiserBesselDerived(i, N, beta)`

`beta`: shape, default **8.6**. N must be even.

$w(n) = \sqrt{\frac{\sum_{j=0}^{n} K(j)}{\sum_{j=0}^{N/2} K(j)}}$, &ensp; $K(j) = I_0\!\left(\beta\sqrt{1-\left(\frac{2j-N/2}{N/2}\right)^2}\right)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/kaiserBesselDerived.svg">

Princen-Bradley condition for perfect MDCT reconstruction. AAC, Vorbis, Opus audio codecs.[^princen1987]

### `dpss(i, N, W)`

`W`: half-bandwidth [0, 0.5], default **0.1**.

$\mathbf{T}\mathbf{v} = \lambda\mathbf{v}$, &ensp; $T_{jk} = \frac{\sin 2\pi W(j-k)}{\pi(j-k)}$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/dpss.svg">

Dominant eigenvector of sinc Toeplitz matrix — provably optimal energy concentration. Also called Slepian window. Multitaper spectral estimation, neuroscience, climate science.[^slepian1978]

### `ultraspherical(i, N, mu, xmu)`

`mu`: 0 = Dolph-Chebyshev, **1** (default) = Saramaki. `xmu`: sidelobe control (default **1**).

$W(k) = C_n^\mu\!\left(x_\mu\cos\frac{\pi k}{N}\right)$, &ensp; $w = \text{IDFT}(W)$

<img src="https://raw.githubusercontent.com/audiojs/window-function/master/docs/plots/ultraspherical.svg">

Gegenbauer polynomial window. Independent control of sidelobe level and taper rate. Antenna design, beamforming.[^streit1984]



## Choosing a window

Every window trades **frequency resolution** (narrow main lobe), **spectral leakage** (low sidelobes), and **amplitude accuracy** (flat top). No single window wins all three.

<dl>
<dt>Just get started</dt>
<dd><a href="#hanni-n"><b>hann</b></a> — good all-round, zero edges, 50% COLA</dd>

<dt>Design FIR filters</dt>
<dd><a href="#kaiseri-n-beta"><b>kaiser</b></a> or <a href="#hammingi-n"><b>hamming</b></a> — Kaiser is tunable, Hamming is the classic</dd>

<dt>Measure amplitudes accurately</dt>
<dd><a href="#flattopi-n"><b>flatTop</b></a> — &lt; 0.01 dB scalloping loss</dd>

<dt>High dynamic range (&gt;80 dB)</dt>
<dd><a href="#blackmanharrisi-n"><b>blackmanHarris</b></a> — -92 dB equiripple sidelobes</dd>

<dt>Audio codec (MDCT)</dt>
<dd><a href="#kaiserbesselderivedi-n-beta"><b>kaiserBesselDerived</b></a> or <a href="#cosinei-n"><b>cosine</b></a> — Princen-Bradley perfect reconstruction</dd>

<dt>Preserve center, taper edges</dt>
<dd><a href="#tukeyi-n-alpha"><b>tukey</b></a> — adjustable flat-top fraction</dd>

<dt>Robust spectral estimation</dt>
<dd><a href="#dpssi-n-w"><b>dpss</b></a> — optimal for multitaper method</dd>

<dt>Radar / SAR</dt>
<dd><a href="#taylori-n-nbar-sll"><b>taylor</b></a> — monotonic sidelobes, radar standard</dd>

<dt>Antenna array design</dt>
<dd><a href="#dolphchebyshevi-n-db"><b>dolphChebyshev</b></a> or <a href="#ultrasphericali-n-mu-xmu"><b>ultraspherical</b></a> — optimal equiripple or tunable taper</dd>

<dt>Tune resolution/leakage continuously</dt>
<dd><a href="#kaiseri-n-beta"><b>kaiser</b></a> or <a href="#gaussiani-n-sigma"><b>gaussian</b></a> — single-parameter adjustment</dd>

<dt>Modal / impact analysis</dt>
<dd><a href="#exponentiali-n-tau"><b>exponential</b></a> — controlled decay for underdamped systems</dd>

<dt>FTIR spectroscopy</dt>
<dd><a href="#connesi-n"><b>connes</b></a> — smooth apodization for interferograms</dd>

<dt>Gravitational waves</dt>
<dd><a href="#plancktaperi-n-epsilon"><b>planckTaper</b></a> — C∞ smooth, no spectral artifacts</dd>
</dl>

## Metrics

Three functions for quantitative window comparison:

```js
import { hann, enbw, scallopLoss, cola } from 'window-function'

enbw(hann, 1024)                 // 1.5 — noise bandwidth (bins)
scallopLoss(hann, 1024)          // 1.42 — worst-case amplitude error (dB)
cola(hann, 1024, 512)            // 0 — perfect STFT reconstruction
```

- **`enbw(fn, N, ...params)`** — equivalent noise bandwidth in frequency bins. Rectangular = 1.0, Hann = 1.5, Blackman-Harris = 2.0. Lower = less noise.
- **`scallopLoss(fn, N, ...params)`** — worst-case amplitude error in dB between DFT bins. Rectangular = 3.92, Hann = 1.42, flat-top ≈ 0.
- **`cola(fn, N, hop, ...params)`** — COLA deviation. 0 = perfect STFT reconstruction at given hop size.


[^dolph1946]: C.L. Dolph, "A Current Distribution for Broadside Arrays," *Proc. IRE* 34, 1946.
[^gabor1946]: D. Gabor, "Theory of Communication," *J. IEE* 93, 1946.
[^bartlett1950]: M.S. Bartlett, "Periodogram Analysis and Continuous Spectra," *Biometrika* 37, 1950.
[^taylor1955]: T.T. Taylor, "Design of Line-Source Antennas," *IRE Trans. Antennas Propag.* AP-4, 1955.
[^blackman1958]: R.B. Blackman & J.W. Tukey, *The Measurement of Power Spectra*, Dover, 1958.
[^connes1961]: J. Connes, "Recherches sur la spectroscopie par transformation de Fourier," *Revue d'Optique* 40, 1961.
[^parzen1961]: E. Parzen, "Mathematical Considerations in the Estimation of Spectra," *Technometrics* 3, 1961.
[^welch1967]: P.D. Welch, "The Use of FFT for Estimation of Power Spectra," *IEEE Trans. Audio Electroacoustics* AU-15, 1967.
[^rife1970]: D.C. Rife & G.A. Vincent, "Use of the DFT in Measurement of Frequencies and Levels of Tones," *Bell Syst. Tech. J.* 49, 1970.
[^kaiser1974]: J.F. Kaiser, "Nonrecursive Digital Filter Design Using the Sinh Window Function," *IEEE Int. Symp. Circuits and Systems*, 1974.
[^hamming1977]: R.W. Hamming, *Digital Filters*, Prentice-Hall, 1977.
[^harris1978]: F.J. Harris, "On the Use of Windows for Harmonic Analysis with the DFT," *Proc. IEEE* 66, 1978.
[^slepian1978]: D. Slepian, "Prolate Spheroidal Wave Functions — V," *Bell Syst. Tech. J.* 57, 1978.
[^duchon1979]: C.E. Duchon, "Lanczos Filtering in One and Two Dimensions," *J. Applied Meteorology* 18, 1979.
[^nuttall1981]: A.H. Nuttall, "Some Windows with Very Good Sidelobe Behavior," *IEEE Trans. ASSP* 29, 1981.
[^streit1984]: R.L. Streit, "A Two-Parameter Family of Weights for Nonrecursive Digital Filters and Antennas," *IEEE Trans. ASSP* 32, 1984.
[^princen1987]: J.P. Princen, A.W. Johnson & A.B. Bradley, "Subband/Transform Coding Using Filter Bank Designs Based on TDAC," *ICASSP*, 1987.
[^ha1989]: Y.H. Ha & J.A. Pearce, "A New Window and Comparison to Standard Windows," *IEEE Trans. ASSP*, 1989.
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