On Apr 18, 5:11 am, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 18 Apr, 03:27, dbd <d...@ieee.org> wrote:
>
> > 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'
>
> OK. I have mentioned them briefly throughout this thread,
> but here are those I can find just by scanning my bookshelf
> quickly:
>
> Book{papoulis,
> author = {Papoulis, {A.}},
> title = {Probability, Random Variables and
> Stochastic Processes},
> publisher = {McGraw-Hill International Editions},
> year = 1991,
> edition = {third},
>
> }
>
> @Book{kay-book,
> author = {Kay, {S.M.}},
> title = {Modern Spectral Estimation, Theory \& Application},
> publisher = {Prentice Hall},
> SERIES = {Signal Processing Series},
> year = 1988,
> }
>
> @Book{proakis-manolakis-3,
> author = {Proakis, {J.G.} and Manolakis, {D. G.}},
> title = {Digital Signal Processing,
> Principles, Algorithms and Applications},
> publisher = {Prentice Hall},
> edition = {3rd},
> year = 1996,
> }
>
> @Book{bendat-piersol,
> author = {Bendat, {J.S.} and Piersol,{A.G.}},
> title = {Random Data. Analysis and Measurement Procedures},
> publisher = {Wiley},
> edition = {3rd.},
> year = 2000
>
> }
>
> @Book{oppenheim-schafer-75,
> author = {Oppenheim, {A.V} and Schafer, {R.W.}},
> title = {Digital Signal Processing},
> publisher = {Prentice Hall},
> year = 1975
>
> }
>
> @Book{oppenheim-schafer-99,
> author = {Oppenheim, {A.V} and Schafer, {R.W.}},
> title = {Discrete-Time Signal Processing},
> publisher = {Prentice Hall},
> edition = {2nd},
> year = 1999
>
> }
>
> @book{antoniou,
> author = {Antoniou, {A.}},
> title = {Digital Signal Processing -- Signals, Systems and Filters},
> publisher = {McGraw-Hill},
> year = 2006
>
> }
>
> There might be at least one of these available to you.
> Except for Papoulis, who defends the N-period form with
> N being large, all of these use the N-1-period form.
> It N-1 vs N form is not my 'discovery'. I'm stating what
> is de facto standard 'gospel' in the DSP community.
>
> I know I have a copy of both the Leland B. Jackson 1989 book,
> and a Dover edition of Hamming's book somewhere. Would you like
> me to dig them up and check them as well?
>
Why do you need to try to distract with a list of references we don't
all have access to instead of talking with respect to a source
available to all?
> > and
> > their context to see if there is any relevance to your discovery of
> > N's and N-1's.
>
> Just to be totally clear about what I we are talking about,
> in an earlier post I wrote that
>
> I use the term
> 'N-period window' for N-length window with divisor N
> in the cosine terms, and 'N-1-period window' for N-length
> windows with divisor N-1 in the cosine terms.
>
> So a window
>
> w[n] = 0.5 + 0.5 cos(2pin/N), n = 0,...,N
>
> is on the N-1-period form since the window is of length N+1.
> It's not sufficient to just scan the formula for the period
> of the cosine; you need to find the length of the window as
> well..
>
> I am sure this comes as a surprise to you (honestly, no
> irony or sarcasm here), but *you* are the one who introduce
> the off-the-beaten-path arguments here. Which is why I have
> pushed so hard for you to come up with an argument other
> than 'Harris said so.'
>
> > 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.
>
> The problem is that your one, old, journal reference
> is at odds with every textbook I have available. Every
> single text - apart form Papoulis - use the N-1-period
> form everywhere.
>
.> Imagine yourself in my place, just having read the textbooks
.> and having no personal reason to trust the writings of any
.> one particular person.
Imagine the readers of this thread who read the three examples of
advantageous windowing in the frequency domain that I posted in this
thread on April 4 and you deny the existence of. Why should anyone be
surprised that you haven't found what you aren't honest enough to look
for?
>
> Wouldn't you ask the same question?
>
> > Matlab will help you
>
> Here is a direct implementation of Proakis & Manolakis'
> Hann window. It's taken from table 8.1 in their 3rd
> edition (p. 626). The only change I've made is to
> center the window on (M-1)/2, not 0:
>
> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
> M = 9;
>
> h = zeros(1,M); % Window is of length M
>
> for n=0:M-1
> h(n+1) = 0.5+0.5*cos(2*pi*(n-(M-1)/2)/(M-1));
> % Cosine term is of period M-1
> end
> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>
> The output is:
>
.> ans =
.>
.> 0 4.0000
.> 0.1464 2.3349
.> 0.5000 0.2103
.> 0.8536 0.0607
.> 1.0000 0.0154
.> 0.8536 0.0154
.> 0.5000 0.0607
.> 0.1464 0.2103
.> 0 2.3349
.>
.> As you can see, no non-zero coefficients in
.> the spectrum.
Actually,
>> fft(h)'
ans =
4.0000
-2.1941 + 0.7986i
0.1611 - 0.1352i
0.0303 - 0.0525i
0.0027 - 0.0152i
0.0027 + 0.0152i
0.0303 + 0.0525i
0.1611 + 0.1352i
-2.1941 - 0.7986i
Your example h is correct for a 9 point filter design window. For the
DFT case, the circularity of the process (or 'periodic' in Matlab's
terminolgy) makes the final element of h wrap to the first position.
The 'FFT-even' application of this window is the 8 point window h(1:8)
and:
>> fft(h(1:8))'
ans =
4
-2
0
0
0
0
0
-2
Lots of zero terms.
The point of 'FFT-even' appears in the left column on page 52 of the
harris paper. I'm not going to retype it or paraphrase it here. It is
accessible to all of us. Try agreeing or disagreeing with something we
all can view. It's nice you have texts. Let's see if you can read what
the rest of us can read.
>
> > tell the difference between
> > windows applied to filter design and windows for
> > DFT application
>
> So there *is* a difference? Why, then, isn't this
> mentioned by any of the authors who write textbooks
> on PSD estimation? Not to mention general DSP texts
> that cover both filters and PSD estimation?
>
> If you, as it seems, have so strong opinions about the
> N-period form being 'correct' and the N-1-period form
> being 'wrong', then you might want to have a word
> with the authors and editors of what are the de facto
> standard textbooks on DSP. Both those on general DSP
> and those on PSD estimation.
>
> Rune
I don't know the earliest usage of the small frequency domain kernel
windowing approach. It goes back at least to Blackman and Tukey in the
Bell System Technical Journal in 1958. (And the Dover reprints in 1959
and on) Maybe Von Hann's implementation was in the frequency domain.
Dale B. Dalrymple