I tried to make the code very simple:

first create this one dimensional DFT function

%----------------------------------------------------------------

function [Xk] = dft(xn)

N=length(xn);

n = 0:1:N-1; % row vector for n

k = 0:1:N-1; % row vecor for k

WN = exp(-1j*2*pi/N); % Twiddle factor (w)

nk = n'*k; % creates a N by N matrix of nk values

WNnk = WN .^ nk; % DFT matrix

Xk = (WNnk*xn );

%----------------------------------------------------------------

now, use this function which is the second dimension:

%----------------------------------------------------------------

function out=dft2(x)

y=zeros(size(x));

y1=y;

C=size(x,2); %number of columns

for c=1:C

y(:,c)=dft(x(:,c));

end

R=size(x,1); %number of rows

for r=1:R

y1(r,:)=dft(y(r,:).');

end

out=y1;

%----------------------------------------------------------------

Note: do not forget to save them as the names of the functions as dft.m and dft2.m both in the same folder. Now make the folder your current working folder, now, you can call the one dimensional dft or the two dimensions dft

Enjoy

Montadar

I tried to make the code very simple:

first create this one dimensional DFT function

%----------------------------------------------------------------

function [Xk] = dft(xn)

N=length(xn);

n = 0:1:N-1; % row vector for n

k = 0:1:N-1; % row vecor for k

WN = exp(-1j*2*pi/N); % Twiddle factor (w)

nk = n'*k; % creates a N by N matrix of nk values

WNnk = WN .^ nk; % DFT matrix

Xk = (WNnk*xn );

%----------------------------------------------------------------

now, use this function which is the second dimension:

%----------------------------------------------------------------

function out=dft2(x)

y=zeros(size(x));

y1=y;

C=size(x,2); %number of columns

for c=1:C

y(:,c)=dft(x(:,c));

end

R=size(x,1); %number of rows

for r=1:R

y1(r,:)=dft(y(r,:).');

end

out=y1;

%----------------------------------------------------------------

Note: do not forget to save them as the names of the functions as dft.m and dft2.m both in the same folder. Now make the folder your current working folder, now, you can call the one dimensional dft or the two dimensions dft

Enjoy

Montadar

Thanks Montadar for your help.

Looking for some more codes and other methods.

Regards,

Nitish

You can use the eye function to create the DFT matrix, then you can use it as per your need.

DFTmatrix=fft(eye(N));

Please visit the link. http://www.mathworks.in/matlabcentral/fileexchange/30346-discrete-fourier-series-without-using-fft-function/content/DFT_nik.m.

You might want to also review an advanced math book, but here is a wiki for now.

http://en.wikipedia.org/wiki/Discrete_Fourier_transform

http://www.amazon.com/Mathematical-Methods-Physicists-Seventh-Edition/dp/0123846544

Dear Vijay

The code given in your link is of 1-Dimensional DFT.

Regards,

Nitish

Dear Robert

I am aware about the concepts of DFT. I just need some help regarding its coding part.

If you can provide some references regarding code of 2-dimensional DFT (image transform) then it will be helpful for me.

Regards,

Nitish

Refer this link may helpful for you,

http://www.mathworks.in/help/vision/ref/vision.fftclass.html

Thanks Ganga Devi and Tria Tsam for your contribution but sadly, I found nothing relevant.

Again I want to make it clear that I am aware of basic concepts of DFT. I just want MATLAB codes for 2-D DFT and its properties.

Regards,

Nitish

Http://www-personal.umich.edu/~hyunjinp/notes/n-dft.pdf

Thanks Robert for the link but the document contains nothing about MATLAB codes.

Regards,

Nitish

Hi there,

This is my implementation of the 2D DFT and IDFT using vectorized operations... i.e. no for loops

======

% 2D DFT

function [X] = dft(x, N)

% If we don't specify how many points for the DFT we want,

% then assume it is the length of the sequence

if(nargin == 1)

N = length(x);

end

% If we don't specify the right parameters, spit out an error

if(nargin < 1 || nargin > 2)

error('Not enough parameters');

end

% Check if we're supplying a row vector. If we are,

% the transpose as a column for the matrix multiplication.

dim = size(x,2);

if(dim ~= 1)

x = x.'; % Make sure we don't conjugate

end

% Create indices for DFT matrix

% First create values of K

ind = 0:(N-1);

ind = ind(ones(1,N),:);

% Now create values of N

ind2 = ind.';

% Create DFT matrix

DN = exp(-1j*2*pi*ind.*ind2/N);

% Calculate N-pt DFT

X = DN * x;

X = X.';

% Sweet... no for loops!

end

======

% 2D IDFT

function [x] = idft(X, N)

% If we don't specify how many points for the DFT we want,

% then assume it is the length of the sequence

if(nargin == 1)

N = length(X);

end

% If we don't specify the right parameters, spit out an error

if(nargin < 1 || nargin > 2)

error('Not enough parameters');

end

% Check if we're supplying a row vector. If we are,

% the transpose as a column for the matrix multiplication.

dim = size(X,2);

if(dim ~= 1)

X = X.'; % Make sure we don't conjugate

end

% Create indices for DFT matrix

% First create values of K

ind = 0:(N-1);

ind = ind(ones(1,N),:);

% Now create values of N

ind2 = ind.';

% Create DFT matrix

DN = exp(-1j*2*pi*ind.*ind2/N);

% Now find its inverse so we can find the inverse DFT

DN = (1/N)*DN';

% Calculate N-pt IDFT

x = DN * X;

x = x.';

% Sweet... no for loops!

end

========

Hope this helps,

- Ray.

Dear Raymond Phan, I appreciate your good effort, however, your functions are both for one dimension DFT!!!

Oops. I'm sorry. I gave you the wrong one. I'll have to search my archives further to give you the 2D version. Give me a few moments or so. Thanks for noticing!

Thanks Raymond for your contribution but as Montadar has already mentioned, it is for 1-D DFT.

Thanks Montadar for your concern.

Regards,

Nitish

Please see attached an old code I wrote in Scilab 3.3.(open source) similar to matlab.Hope it is helpful

I notice you don't want to use predefined functions .Please see if attached pdf

is useful in scilab 5.3.3 of course..

Dear Ramesh,

Thanks for your contribution but as you said, your 1st pdf (FFT ANALYSIS) consists of direct use of functions and your 2nd pdf (twod dft) consists of codes but I think it will give only real part of the result and no analysis about complex part is done here.

Regards,

Nitish

Please see if attached doc in .odt format (open office 3.3) helps ... these were written sometime back...

cheers

Thanks Dear Ramesh, The above code for 2-D DFT worked! (with a bit syntax change)

If possible provide some code for proofing its properties(like translation, rotation and scaling of image) also.

Regards,

Nitish

I am tied up at the moment .. but my immediate suggestion is..

1. take a large bitmap image say gray im=100 by 100 , next predefined filled object A say rectangle(20*20)

2 do Dft on im+A .. this is the ref..

3. translate / rotate /scale A separately say At / Ar /As using some

matrix operation and repeat step 2..

may take quie some time..

Cheers

Thanks for the suggestion Ramesh. You take your own time and in the mean time I am also trying the same. After finishing your code, please let me know.

Regards,

Nitish

This topic is amazing.

"Can anyone give me the code to do x,y,z?...

...I want to program it from the basic level."

Seems like you don't want to implement anything.

What exactly is the difference of running someone elses code and using the MATLAB provided functions? Even when using the built in fft, imrotate, etc. you would gain more insight if you program some basic examples like shift and rotation properties yourself.

Besides, there's plenty of source codes available on this topic. e.g. openCV just to name a popular library.

Beerend.. Sometimes to have flexibility and incorporate new thinking

, algorithms for speed etc we may need to code from basics..eg there may be some

assumptions or limitations that are to be removed...some new intermediate transformations.. I did find differences eg in OCTAVE/ Scilab /Matlab..

the roots for high order L(order 44) Legendre polynomial are not at

accurate in Matlab ..try it..

but it is true as you mention if our immediate objective is to understand

the concepts ,,we may as well use available software.. and dwell more on the theory..

It all depends I suppose on our interest..at hand...

@Beerend

Learning from codes or understanding codes is also a process of learning, we call it inverse learning.

I don't want only to be my work done or just find the answer using Matlab predefined functions. I want to know/understand the logic behind the operation of particular function.

Also, different people has different approach to a particular problem so codes of different people can help us to understand their approach and logic behind that.

And for your last part ("there's plenty of source codes available on this topic"), everything is available on the internet now a days, then why we are discussing on any topic???

For getting views of different persons on the topic, same is my motive behind posting this question here. I want to know different approaches to this particular problem.

Regards,

Nitish

%% Centralized 2D DFT without using built-in function

Img=double(imresize(imread('cameraman.tif'),0.3));

[Img_M, Img_N] = size(Img);

Output=zeros(Img_M,Img_N);

SumOutner = 0;

% Centralized 2D Discrete Fourier Transform

[nx,ny]=ndgrid([0:Img_M-1]-(Img_M-1)/2,[0:Img_N-1]-(Img_N-1)/2 );

du=1;

for u = [0:Img_M-1]-(Img_M-1)/2

dv=1;

for v = [0:Img_N-1]-(Img_N-1)/2

SumOutner=sum(sum(Img.*exp(-1i*2*3.1416*(u*nx/Img_M+v*ny/Img_N))));

Output(du,dv) = SumOutner;

dv=dv+1;

end

du=du+1;

end

% Calculate Spectrum and show

imshow(uint8(abs(Output)/60))

%% Centralized 2D IDFT without using built in function

Img=double(imresize(imread('cameraman.tif'),0.3));

[Img_M, Img_N] = size(Img);

Output=zeros(Img_M,Img_N);

SumOutner = 0;

% Centralized Inverse 2D Discrete Fourier Transform

[nx,ny]=ndgrid([0:Img_M-1]-(Img_M-1)/2,[0:Img_N-1]-(Img_N-1)/2 );

du=1;

for u = [0:Img_M-1]-(Img_M-1)/2

dv=1;

for v = [0:Img_N-1]-(Img_N-1)/2

SumOutner=sum(sum(Img.*exp(1i*2*3.1416*(u*nx/Img_M+v*ny/Img_N))));

Output(du,dv) = SumOutner;

dv=dv+1;

end

du=du+1;

end

% Calculate Spectrum and show

imshow(uint8(abs(Output)/60))

%% Centralized 2D DFT - Rotation in frequency domain vs rotation in spatial domain

Img=double(imresize(imread('cameraman.tif'),0.2));

Img=padarray(Img,[14 14],0,'both'); % pad zeros to retain information in original image and rotated image the same

t=90; % rotation angle in degrees

teta=t/180*pi; % rotation angle in radians

c1=cos(teta); s1=sin(teta);

[Img_M, Img_N] = size(Img);

rotDFT=zeros(Img_M,Img_N);

% Centralized rotated form of 2D Discrete Fourier Transform

SumOutner = 0;

[nx,ny]=ndgrid([0:Img_M-1]-(Img_M-1)/2,[0:Img_N-1]-(Img_N-1)/2 );

du=1;

for u = [0:Img_M-1]-(Img_M-1)/2

dv=1;

for v = [0:Img_N-1]-(Img_N-1)/2

u2=(u);

v2=(v);

u1=u2*c1+v2*s1;

v1=u2*-s1+v2*c1;

SumOutner=sum(sum(Img.*exp(-1i*2*3.1416*(u1*nx/Img_M+v1*ny/Img_N))));

rotDFT(du,dv) = SumOutner;

dv=dv+1;

end

du=du+1;

end

% Calculate Spectrum and show

imshow(uint8(abs(rotDFT)/60))

% find 2d IDFT

freq_rot_img=zeros(Img_M,Img_N);

SumOutner = 0;

du=1;

for u = [0:Img_M-1]-(Img_M-1)/2

dv=1;

for v = [0:Img_N-1]-(Img_N-1)/2

SumOutner=sum(sum(rotDFT.*exp(1i*2*3.1416*(u*nx/Img_M+v*ny/Img_N))));

freq_rot_img(du,dv) = SumOutner;

dv=dv+1;

end

du=du+1;

end

freq_rot_img=freq_rot_img/(Img_M*Img_N); % normalization

% rotation in spatial domain

spat_rot_img=imrotate(Img,teta*180/pi,'bicubic','crop');

figure

subplot(3,1,1)

imshow(uint8(abs(freq_rot_img)));

subplot(3,1,2)

imshow(uint8(abs(spat_rot_img)));

subplot(3,1,3)

imshow(uint8(abs(abs(freq_rot_img)-abs(spat_rot_img))));