🚀 go-pugleaf

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!!!!!!!!!!!!!!!!!!!!!!!!!
:)