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Advanced DSP - FFT windows: figures of merit

The measures of the quality of an FFT window function are:

Sidelobe level- the attenuation to the top of the highest sidelobe
Fall off - the rate of fall off to the side lobe
6 dB bandwidth - the bandwidth in which the window function's kernel falls by 6 dB
Coherent Power Gain - the normalised DC gain
Equivalent Noise Bandwidth- the bandwidth of an ideal rectangular filter which would accumulate the same noise power from white noise as the window function's kernel with the same peak power gain
Worst Case Processing Loss - the ratio of input signal-to-noise to output signal-to-noise, including scalloping loss for the worst case

Sidelobe level, fall offand 6 dB bandwidth measure a window function's quality in terms of resolving close frequency components.

Coherent Power Gainmeasures the amount by which a frequency component's measured value is attenuated by the window function

Equivalent Noise Bandwidth and Worst Case Processing Loss measure a window function's quality in terms of detecting a signal in noise.

Window function	Sidelobe (dB)	Fall off (dB/octave)	Coherent Power Gain	Equivalent Noise Bandwidth (FFT bins)	6 dB bandwidth (FFT bins)	Worst Case Processing Loss (dB)
Rectangular	- 13	- 6	1.00	1.00	1.21	3.92
Triangular	- 27	- 12	0.50	1.33	1.78	3.07
Hanning	-32	-18	0.50	1.50	2.00	3.18
Hamming	- 43	- 6	0.54	1.36	1.81	3.10
Poisson (3.0)	- 24	- 6	0.32	1.65	2.08	3.64
Poisson (4.0)	- 31	- 6	0.25	2.08	2.58	4.21
Cauchy (4.0)	- 35	- 6	0.33	1.76	2.20	3.83
Cauchy (5.0)	- 30	- 6	0.28	2.06	2.53	4.28
Gaussian (3.0)	- 55	- 6	0.43	1.64	2.18	3.40
Kaiser-Bessel (3.0)	- 69	- 6	0.40	1.80	2.39	3.56
Kaiser-Bessel (3.5)	- 82	- 6	0.37	1.93	2.57	3.74

You can download a copy of this technical note in Adobe Acrobat format:

FFT windows technical note