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From: ARH on 10 Jul 2008 04:23
Hi

I am looking for a FFT algorithm for fixed number of sampling input.
usual FFT algorithms like Cooly-Tuky, radix-2, give dynamic number of
input samples an then divide and concoure it for calculation of the
output, but in my case study the number of input samples is static and
I can easily compute all of the twiddle factors before run time and
save them in a twiddle factor table.
Using twiddle factor table, FFT algorithm simplify to the matrix
multiplication algorithm which gave inputs them multiply proper
twiddle factor on it and generate output.
but this algorithm is similar to DFT not FFT, would you mind help me
to found an efficient algorithm for this purpose ?

Are there any material which described radix-2 FFT algorithm in
detail ? most of the textbook like "numerical receipts" just give the
implementation of algorithm and have pure description detail.

Regards
Alireza Haghdoost
From: Stephane Lesage on 10 Jul 2008 04:42
ARH a �crit :

> I am looking for a FFT algorithm for fixed number of sampling input.
> usual FFT algorithms like Cooly-Tuky, radix-2, give dynamic number of
> input samples an then divide and concoure it for calculation of the
> output, but in my case study the number of input samples is static and
> I can easily compute all of the twiddle factors before run time and
> save them in a twiddle factor table.
> Using twiddle factor table, FFT algorithm simplify to the matrix
> multiplication algorithm which gave inputs them multiply proper
> twiddle factor on it and generate output.
> but this algorithm is similar to DFT not FFT, would you mind help me
> to found an efficient algorithm for this purpose ?
> Are there any material which described radix-2 FFT algorithm in
> detail ? most of the textbook like "numerical receipts" just give the
> implementation of algorithm and have pure description detail.

Hi,

Oh my, still stuck in your FFT ?

Your original post was "Pure ANSI-C DIF FFT code".
There are plenty of libraries out there.
So, why, oh, why, don't you give a look at one of those:

* FFTW
http://www.fftw.org/

* Kiss FFT
http://sourceforge.net/projects/kissfft/

This one is used by Speex, and as far as I remember, it's split into
- functions to generate the twiddle factor table
- functions to compute the FFT using the table

I don't know about performance. If you have a good compiler, it should
be OK. Anyway you can use it as a start point, understand how it works,
and make your own implementation later.

--
Stephane Lesage
From: ARH on 10 Jul 2008 08:47
> * FFTWhttp://www.fftw.org/
>
> * Kiss FFThttp://sourceforge.net/projects/kissfft/
>
> This one is used by Speex, and as far as I remember, it's split into
> - functions to generate the twiddle factor table
> - functions to compute the FFT using the table
>
> I don't know about performance. If you have a good compiler, it should
> be OK. Anyway you can use it as a start point, understand how it works,
> and make your own implementation later.
> --
> Stephane Lesage


Dear Stephan

Thanks for your reply and your precise tracking of my posts, I was
download kissFFT and as you said it is split into the two part first
part for butterfly operation in the different radixes and second part
for recursive calling of the proper butterfly operation.
One thing that increase complexity of these kind algorithms is dynamic
FFT length. when the length predefined the complexity of algorithm
should be decreased.

I have 2 doubts in using twiddle factor table for my work :

1. If I use twiddle factor table for saving precomputed twiddle
factors and then generate FFT output by simple matrix multiplication,
the complexity of algorithm increased to O(N^2) because I need two
loops for matrix multiplication.

2. If I compute outputs with this method, could we called it FFT ? it
is very similar to conventional DFT computations.


I should appreciate you again for tracking my challenge, thanks
Alireza Haghdoost
From: raymond.toy on 10 Jul 2008 12:05
>>>>> "ARH" == ARH <haghdoost(a)gmail.com> writes:

ARH> Hi
ARH> I am looking for a FFT algorithm for fixed number of sampling input.
ARH> usual FFT algorithms like Cooly-Tuky, radix-2, give dynamic number of
ARH> input samples an then divide and concoure it for calculation of the
ARH> output, but in my case study the number of input samples is static and
ARH> I can easily compute all of the twiddle factors before run time and
ARH> save them in a twiddle factor table.
ARH> Using twiddle factor table, FFT algorithm simplify to the matrix
ARH> multiplication algorithm which gave inputs them multiply proper
ARH> twiddle factor on it and generate output.
ARH> but this algorithm is similar to DFT not FFT, would you mind help me
ARH> to found an efficient algorithm for this purpose ?

ARH> Are there any material which described radix-2 FFT algorithm in
ARH> detail ? most of the textbook like "numerical receipts" just give the
ARH> implementation of algorithm and have pure description detail.

Don't know of any online references, but you can find pretty good
detailed explanations of FFT algorithms in an DSP (digital signal
processing) book, like Oppenheim and Schafer. My old copy shows
a nice diagram for an 8-point radix-2 FFT algorithm.

Ray
From: Rick Lyons on 10 Jul 2008 12:25
On Thu, 10 Jul 2008 01:23:57 -0700 (PDT), ARH <haghdoost(a)gmail.com>
wrote:

>Hi
>
>I am looking for a FFT algorithm for fixed number of sampling input.
>usual FFT algorithms like Cooly-Tuky, radix-2, give dynamic number of
>input samples an then divide and concoure it for calculation of the
>output, but in my case study the number of input samples is static and
>I can easily compute all of the twiddle factors before run time and
>save them in a twiddle factor table.
>Using twiddle factor table, FFT algorithm simplify to the matrix
>multiplication algorithm which gave inputs them multiply proper
>twiddle factor on it and generate output.
>but this algorithm is similar to DFT not FFT, would you mind help me
>to found an efficient algorithm for this purpose ?
>
>Are there any material which described radix-2 FFT algorithm in
>detail ? most of the textbook like "numerical receipts" just give the
>implementation of algorithm and have pure description detail.
>
>Regards
>Alireza Haghdoost

Hi,
here are more FFT references than you probably
want but, who knows, maybe something here will
help you.

[-Rick-]
-----
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and the history of the FFT," IEEE Acoustics, Speech, and Signal
Processing Magazine, vol. 1, pp. 14-21, October 1984. also in IEEE
Press FFT Reprints, by P. Duhamel, 1995.
[2] H. V. Sorensen, C. S. Burrus, and M. T. Heideman, Fast Fourier
Transform Database. Boston: PWS Publishing, 1995. Update of
Technical Report TR-8402.
[3] L. R. Rabiner and C. M. Rader, eds., Digital Signal Processing,
selected reprints. New York: IEEE Press, 1972.
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York: IEEE Press, 1979.
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IEEE Press, to appear in 1995.
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Processing. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1979.
[8] H. J. Nussbaumer, Fast Fourier Transform and Convolution
Algorithms. Heidelberg, Germany: Springer-Verlag, second ed., 1981,
1982.
[9] R. E. Blahut, Fast Algorithms for Digital Signal Processing.
Reading, MA: Addison-Wesley, Inc., 1984.
[10] M. T. Heideman, Multiplicative Complexity, Convolution, and the
DFT. Springer-Verlag, 1988.
[11] R. Tolimieri, M. An, and C. Lu, Algorithms for Discrete Fourier
Transform and Convolution. New York: Springer-Verlag, 1989.
[12] D. G. Myers, Digital Signal Processing, Efficient
Convolution and Fourier Transform Techniques. Sydney, Australia:
Prentice-Hall, 1990.
[13] R. E. Blahut, Algebraic Methods for Signal Processing and
Communications Coding. New York: Springer-Verlag, 1992.
[14] W. L. Briggs and V. E. Henson, The DFT: An Owner's Manual for
the Discrete Fourier Transform. Philadelphia: SIAM, 1995.
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Transforms. New York: IEEE Press, 1995.
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Algorithms. New York: John Wiley & Sons, 1985.
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tables," IEEE Transactions on Signal Processing, vol. 39, pp.
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