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#### Twiddle Factor matrix

```Will you please tell me how to generate the twiddle factor matrix (W
= exp(-j*2*pi/N)) if N is given . I need a N-by-N matrix:
__ __
|1 1 1 1... ... 1 |
|1 W^1 W^2 W^3... ...W^(N-1) |
|1 W^2 W^4 W^6... . |
|1 . . . . |
|1 . . |
|1 W^(N-1)..................W^((N-1)*(N_1)) |
|__ ___

This matrix is needed for computation of DFT without using FFT
```
 0
bdsatish (38)
11/16/2005 9:08:32 AM
comp.soft-sys.matlab 211266 articles. 22 followers. lunamoonmoon (257) is leader.

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```In article <ef1bb73.-1@webx.raydaftYaTP>, bdsatish <bdsatish@gmail.com> wrote:

> Will you please tell me how to generate the twiddle factor matrix (W
> = exp(-j*2*pi/N)) if N is given . I need a N-by-N matrix:
>           __ __
>           |1 1 1 1... ... 1 |
>           |1 W^1 W^2 W^3... ...W^(N-1) |
>           |1 W^2 W^4 W^6... . |
>           |1 . . . . |
>           |1 . . |
>           |1 W^(N-1)..................W^((N-1)*(N_1)) |
>           |__ ___
>
>   This matrix is needed for computation of DFT without using FFT
--------------------
This should do it:

W = exp(-j*2*pi/N);
I = repmat(0:N-1,N,1);
M = W.^(I.*I.');

(Remove "xyzzy" and ".invalid" to send me email.)
Roger Stafford
```
 0
11/16/2005 10:43:53 AM
```In article

>   This should do it:
>
> W = exp(-j*2*pi/N);
> I = repmat(0:N-1,N,1);
> M = W.^(I.*I.');
--------------------
Or a posssibly more accurate alternative:

I = repmat(0:N-1,N,1);
M = exp(-j*2*pi/N*rem(I.*I.',N));

(Remove "xyzzy" and ".invalid" to send me email.)
Roger Stafford
```
 0
11/16/2005 6:35:23 PM
```bdsatish wrote:
> Will you please tell me how to generate the twiddle factor matrix (W
> = exp(-j*2*pi/N)) if N is given . I need a N-by-N matrix:
>           __ __
>           |1 1 1 1... ... 1 |
>           |1 W^1 W^2 W^3... ...W^(N-1) |
>           |1 W^2 W^4 W^6... . |
>           |1 . . . . |
>           |1 . . |
>           |1 W^(N-1)..................W^((N-1)*(N_1)) |
>           |__ ___
>
>   This matrix is needed for computation of DFT without using FFT

>From a post by AJ Johnson:

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(k=1,N) { x(k) * exp(-2*pi*j*t(k)*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
W = exp(-2*pi*j * f*t');
X  = W * x;

Hope this helps.

Greg

```
 0
heath (3983)
11/16/2005 8:25:44 PM

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