Thread View: comp.dsp
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Started by David Nyarko
Sat, 19 Dec 1992 03:43
windows for FFT
Author: David Nyarko
Date: Sat, 19 Dec 1992 03:43
Date: Sat, 19 Dec 1992 03:43
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Hi, In some texts I find windows defined with an "N-1" denominator and in others an " N " and would like fellow netters to clarify this apparent discrepancy. For example if a waveform whose period is (N * Ts) when synchronously sampled, has it's frequency slightly reduced so that a period would now have a duration of [(N + d) * Ts], which of the following would be appropriate , the hanning in a) or that in b). Ts = sampling period N is a positive integer d=(0,1) eg a) In article ;"On the use of windows for the Harmonic Analysis with the discrete Fourier Transform" by Harris, the hanning window is defined as w(n) = 0.5*[1 - cos(2*n*pi/N)] n=0,1,2,...N-1 b) On pg. 94 of "Introduction to Applied Statistical signal analysis " by Richard Shiavi the hanning window is defined as: dt(n) = 0.5*[1 - cos(2*pi*n/(N-1))] 0 <= n <= N-1 A few other references have either a) or b). This pattern is repeated for other windows too. When does one use a) or b). David
Re: windows for FFT
Author: axelrod
Date: Sat, 19 Dec 1992 19:38
Date: Sat, 19 Dec 1992 19:38
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nyarko@ee.ualberta.ca (David Nyarko) writes: >Hi, >In some texts I find windows defined with an "N-1" >denominator and in others an " N " and would like fellow netters >to clarify this apparent discrepancy. For example if a waveform >whose period is (N * Ts) when synchronously sampled, has it's >frequency slightly reduced so that a period would now >have a duration of [(N + d) * Ts], which of the following >would be appropriate , the hanning in a) or that in b). >Ts = sampling period >N is a positive integer >d=(0,1) >eg >a) In article ;"On the use of windows for the >Harmonic Analysis with the discrete Fourier Transform" >by Harris, >the hanning window is defined as >w(n) = 0.5*[1 - cos(2*n*pi/N)] n=0,1,2,...N-1 >b) On pg. 94 of "Introduction to Applied Statistical signal >analysis " by Richard Shiavi the hanning window is defined as: >dt(n) = 0.5*[1 - cos(2*pi*n/(N-1))] 0 <= n <= N-1 >A few other references have either a) or b). This pattern is >repeated for other windows too. >When does one use a) or b). > David 2*n*pi/N will give you values of the window evaluated from 0 to 2pi-2pi/N, and 2*n*pi/(N-1) will give you values of the window evaluated from 0 to 2pi. These are assuming you are using n from 0 to N-1, thereby having N samples. I don't know why you'd want to include the last 2pi value, since it's the same as the zero value and would create problems in certain cases. I just finished my DSP exam and am glad!!!!!!!!!!!!!!!!!!!!!!!!! :)
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