>I'm told that the Numerical Recipes in
>> (FORTRAN,C,...) books have an implementation.
>
>Yes. NR has a section on spectral analysis on unevenly sampled data.
>goto http://www.nr.com for a free copy of the book.
>
>if the sample is not that non-uniform you can pad with zeros..you can
>check more on how exactly this can be done in the book
>http://www.dspguide.com
>
>--Ramoj Paruchuri
>
***************************************************************************
Hello to all,
Dear thanks for the nice tip, but i have another problem which is that
there is always a wideband noise whenever we try to perform spectral
analysis of a non uniformly sampled signal. Do you have some solution to
this problem?
Waiting for the reply.
This message was sent using the Comp.DSP web interface on
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Reply by AJ "no z" Johnson●August 18, 20042004-08-18
"walala" <mizhael@yahoo.com> wrote in message
news:6f348bd1.0408151717.3bd80eda@posting.google.com...
> Hi all,
>
> Can anybody point me to some helps/tutorials/references/stories on how
> to do non-uniform (sampling) DFT?
>
> Thank you very much for your help,
>
> -Walala
This might help.
function X=dft(t,x,f)
% function X=dft(t,x,f)
% Compute DFT (Discrete Fourier Transform) at frequencies given
% in f, given samples x taken at times t:
% X(f) = sum { x(k) * e**(2*pi*j*t(k)*f) }
% k
shape = size(f);
t = t(:); % Format 't' into a column vector
x = x(:); % Format 'x' into a column vector
f = f(:); % Format 'f' into a column vector
% It's just this simple:
W = exp(-2*pi*j * f*t');
X = W * x;
X = reshape(X,shape);
-Aj
Reply by Ramoj Paruchuri●August 17, 20042004-08-17
I'm told that the Numerical Recipes in
> (FORTRAN,C,...) books have an implementation.
Yes. NR has a section on spectral analysis on unevenly sampled data.
goto http://www.nr.com for a free copy of the book.
if the sample is not that non-uniform you can pad with zeros..you can
check more on how exactly this can be done in the book
http://www.dspguide.com
--Ramoj Paruchuri
Reply by Ramoj Paruchuri●August 17, 20042004-08-17
I'm told that the Numerical Recipes in
> (FORTRAN,C,...) books have an implementation.
Yes. NR has a section on spectral analysis on unevenly sampled data.
goto http://www.nr.com for a free copy of the book.
if the sample is not that non-uniform you can pad with zeros..you can
check more on how exactly this can be done in the book
http://www.dspguide.com
--Ramoj Paruchuri
Reply by Ramoj Paruchuri●August 17, 20042004-08-17
I'm told that the Numerical Recipes in
> (FORTRAN,C,...) books have an implementation.
Yes. NR has a section on spectral analysis on unevenly sampled data.
goto http://www.nr.com for a free copy of the book.
if the sample is not that non-uniform you can pad with zeros..you can
check more on how exactly this can be done in the book
http://www.dspguide.com
--Ramoj Paruchuri
Reply by Ramoj Paruchuri●August 17, 20042004-08-17
I'm told that the Numerical Recipes in
> (FORTRAN,C,...) books have an implementation.
Yes. NR has a section on spectral analysis on unevenly sampled data.
goto http://www.nr.com for a free copy of the book.
if the sample is not that non-uniform you can pad with zeros..you can
check more on how exactly this can be done in the book
http://www.dspguide.com
--Ramoj Paruchuri
Reply by Bergers●August 16, 20042004-08-16
>Subject: How to do non-uniform (sampling) DFT?
>From: mizhael@yahoo.com (walala)
>Date: 8/15/2004 9:17 PM Eastern Daylight Time
>Message-id: <6f348bd1.0408151717.3bd80eda@posting.google.com>
>
>Hi all,
>
>Can anybody point me to some helps/tutorials/references/stories on how
>to do non-uniform (sampling) DFT?
>
>Thank you very much for your help,
>
>-Walala
>
>
>
>
>
>
Try the following paper:
Duijndam A. J. W. and Schonewille M. A., Nonuniform fast Fourier transform,
Geophysics, Vol 64, No 2 (March-April 1999), pages 539-551.
I have not actual reviewed the article in-depth, so it may not be of any help.
Scott
Reply by Jonathon●August 16, 20042004-08-16
You could try Googling for the Lomb-Scargle Periodogram method. It
works with unevenly sampled data. I believe it is used in the
astrophysics community. I'm told that the Numerical Recipes in
(FORTRAN,C,...) books have an implementation.
I've never tried using it, but filed the reference away, just in case.
Let me know how you get on.
Jon
mizhael@yahoo.com (walala) wrote in message news:<6f348bd1.0408151717.3bd80eda@posting.google.com>...
> Hi all,
>
> Can anybody point me to some helps/tutorials/references/stories on how
> to do non-uniform (sampling) DFT?
>
> Thank you very much for your help,
>
> -Walala
Reply by Robert Israel●August 15, 20042004-08-15
In article <6f348bd1.0408151717.3bd80eda@posting.google.com>,
walala <mizhael@yahoo.com> wrote:
>Can anybody point me to some helps/tutorials/references/stories on how
>to do non-uniform (sampling) DFT?
I assume you mean something like this:
There is a function f(t), assumed to be periodic with period (for
convenience) 2 pi, and at some more-or-less arbitrary N points t_1,...,t_N
you know f(t_k) = y_k.
You want to (approximately) calculate the Fourier series coefficients
c_k such that f(t) = sum_k c_k exp(ikt).
Well, one thing you can do is assume only N coefficients count, e.g.
f(t) = sum_{k=a}^b c_k exp(ikt) where a=-(N-1)/2,b=(N-1)/2 if N is odd,
or perhaps a=-N/2+1,b=N/2 if N is even, and solve the N x N system
of equations
y_j = sum_{k=a}^b exp(ik t_j) c_k
But this is really equivalent to a Lagrange interpolation problem:
y_j exp(-ia t_j) = sum_{k=0}^{N-1} exp(ik t_j) c_{k+a}
= P(exp(i t_j))
where P(z) = sum_{k=0}^{N-1} c_{k+a} z^k. One way of solving
the Lagrange problem is this: if
w(z) = product_{j=1}^N (z - exp(i t_j))
then
P(z) = sum_{j=1}^n y_j exp(-ia t_j) product_{k <> j}
(z - exp(i t_k))/(exp(i t_j) - exp(i t_k))
In particular the solution is unique as long as the t_j are
distinct mod 2 pi.
I make no claims about numerical stability.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
Reply by One Usenet Poster●August 15, 20042004-08-15
walala wrote:
> Hi all,
>
> Can anybody point me to some helps/tutorials/references/stories on how
> to do non-uniform (sampling) DFT?
>
> Thank you very much for your help,
>
> -Walala
Here is a good source:
Technique for frequency analysis of unevenly sampled radar data
House, M.G. Mountcastle, P.D.
XonTech Inc., Huntington Beach, CA, USA
This paper appears in: Radar Conference, 2002. Proceedings of the IEEE
Publication Date: 22-25 April 2002
On page(s): 63 - 67
ISSN: 1097-5659
Number of Pages: xix+508
Inspec Accession Number: 7366627
Abstract:
A new technique is described that generalizes the usefulness of the
discrete Fourier transform for spectral analysis of radar data to
applications where the discrete data points to be analyzed are not
sampled at regular intervals and/or do not have equal statistical
weight. This method finds a frequency-domain representation which best
represents the given time-domain data in the least-square-residual
sense. The theoretical implications of such an approach are discussed,
and an example of the technique applied to a Doppler processing task is
given. The merits of the approach relative to other spectral analysis
techniques are discussed.
Good luck,
OUP