Windowing in the Frequency Domain

On Apr 17, 12:33 pm, Rune Allnor <all...@tele.ntnu.no> wrote:
>...
> Virtually all the textbook issues I have found on
> the window functions, use window functions of length
> N and cosine terms with period N-1. This means that
> all the coefficients of the DFT of the window function
> are non-zero.
> ...
> Rune

Your conclusion is incorrect. It is difficult for anyone to help you
with this error because we don't all have access to your 'texts' and
their context to see if there is any relevance to your discovery of
N's and N-1's. There is a source that has been referenced in this
thread that explains this issue with regard to windows for harmonic
analysis. If you are honest about learning you would consider actually
reading it. It is available to everyone here. You can tell us where
you think it is wrong there and we can all view what you are talking
about. That's why I provided an accessible reference.

Matlab will help you tell the difference between windows applied to
filter design and windows for DFT application:
>> % FIR window design vector
>> s = hann(8,'symmetric')
s =
         0
    0.1883
    0.6113
    0.9505
    0.9505
    0.6113
    0.1883
         0

>> fft(s)/8
ans =
   0.4375
  -0.2402 - 0.0995i
   0.0189 + 0.0189i
   0.0026 + 0.0063i
        0
   0.0026 - 0.0063i
   0.0189 - 0.0189i
  -0.2402 + 0.0995i

>> % DFT window vector for harmonic analysis
>> p = hann(8,'periodic')
p =
         0
    0.1464
    0.5000
    0.8536
    1.0000
    0.8536
    0.5000
    0.1464

>> fft(p)/8
ans =
    0.5000
   -0.2500
    0.0000
         0
         0
         0
    0.0000
   -0.2500
>>
That's how it works under Matlab's fft definition.

Dale B. Dalrymple