Window Function Coefficient Calculator

About this calculator

When you take a finite chunk of a signal for an FFT, the abrupt cut at each edge creates spectral leakage; window functions taper the signal smoothly toward zero at both ends to reduce that leakage. Common windows have closed-form coefficient formulas — the Hann window is w(n) = 0.5 − 0.5·cos(2πn/(N−1)), the Hamming window is w(n) = 0.54 − 0.46·cos(2πn/(N−1)) — and each window trades off main-lobe width against side-lobe suppression, summarized by its coherent gain and equivalent noise bandwidth (ENBW).

This calculator takes a window type and length and returns the per-sample coefficient weights along with coherent gain and ENBW. DSP and audio engineers use these coefficients when implementing FFT-based spectral analysis, filter design, or spectrogram generation, choosing a window (Hann for general-purpose analysis, Hamming for narrower main-lobe needs, Blackman for lower side lobes, etc.) that matches whether they need frequency resolution or amplitude accuracy more.