Window Function Bandwidth Calculator Formula

Understand the math behind the window function bandwidth calculator. Each variable explained with a worked example.

Use the Window Function Bandwidth Calculator

Formulas Used

Rectangular ENBW

rect_enbw = bin_width * 1.0

Hann ENBW

hann_enbw = bin_width * 1.5

Hamming ENBW

hamming_enbw = bin_width * 1.36

Blackman ENBW

blackman_enbw = bin_width * 1.73

Flat Top ENBW

flat_top_enbw = bin_width * 3.77

Bin Width (no window)

bin_width_out = bin_width

Variables

VariableDescriptionDefault
sample_rate_hzSampling Rate(Hz)48000
fft_sizeFFT Size1024
bin_widthDerived value= sample_rate_hz / fft_sizecalculated

How It Works

Window Function Bandwidth

Window functions reduce spectral leakage but widen the effective frequency resolution.

Equivalent Noise Bandwidth (ENBW)

ENBW = Bin Width x ENBW Factor

ENBW factors for common windows:

  • Rectangular: 1.00 (narrowest but worst leakage)
  • Hamming: 1.36
  • Hann: 1.50
  • Blackman: 1.73
  • Flat Top: 3.77 (best amplitude accuracy)

    • The choice of window balances frequency resolution against spectral leakage. No window is universally best.

    Worked Example

    1024-point FFT at 48 kHz comparing window functions.

    sample_rate_hz = 48000fft_size = 1024
    1. 01Bin width: 48,000 / 1,024 = 46.875 Hz
    2. 02Rectangular ENBW: 46.875 x 1.0 = 46.88 Hz
    3. 03Hann ENBW: 46.875 x 1.5 = 70.31 Hz
    4. 04Blackman ENBW: 46.875 x 1.73 = 81.09 Hz

    Ready to run the numbers?

    Open Window Function Bandwidth Calculator