Blackman Harris window

4

The Blackman-Harris window coefficients are given by the following formula

Blackman-Harris window formula

where N is the length of the filter and k = 0, 1, …, N – 1.

The Blackman-Harris window is a generalized cosine window (see Hamming window).

An example Blackman-Harris window

Consider a finite impulse response (FIR) low pass filter of length N = 201. The following is the Blackman-Harris window.

Blackman-Harris window

Given a sampling frequency of 2000 Hz and a filter cutoff frequency of 40 Hz, the impulse response of the filter with a rectangular window (with no window) and with the Blackman-Harris window is as follows.

Impulse response of a low pass filter with and without the Blackman-Harris window

The magnitude response of the same filter is shown on the graph below.

Magnitude response of a low pass filter with and without the Blackman-Harris window

Measures for the Blackman-Harris window

The following graph compares the discrete Fourier transform of the Blackman-Harris window and the rectangular window.

Discrete Fourier transform of the Blackman-Harris window

The Blackman-Harris window measures are as follows.


Coherent gain0.36
Equivalent noise bandwidth2.01
Processing gain-3.03 dB
Scalloping loss-0.82 dB
Worst case processing loss-3.85 dB
Highest sidelobe level-92.0 dB
Sidelobe falloff-14.4 dB / octave, -48.0 dB / decade
Main lobe is -3 dB1.90 bins
Main lobe is -6 dB2.66 bins
Overlap correlation at 50% overlap0.037
Amplitude flatness at 50% overlap0.435
Overlap correlation at 75% overlap0.459
Amplitude flatness at 75% overlap1.000


  Rating
Rate This Page: Poor Great   |  Rate Content |
Average rating:  4   
10003
12345
Number of Ratings : 4
  Comments
Add Comment
No Comments Yet


Copyright 2006 by Kaliopa Publishing, LLC