🚀 go-pugleaf

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