# Notch filter to remove a small area around the fundamental frequency and the first few harmonics

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tarun on 24 Apr 2013
I have an image
After taking the log of one plus the magnitude of the transform of the this image to observe the bright spots due to the stripes. I got this
TO make it easier I used the thermal version of the image and got this
What I have to do is :-
a. Design a “notch” filter to remove a small area around the fundamental frequency and the first few harmonics.(or in other words is to remove the 'dark red strips on the coke bottle'). To remove the white spots.
b. Notch filter must be symmetric about the origin of the frequency plane.
I thought of removing the values of these pixels above a particular threshold but it is not giving me exactly what I wanted.
So this is the code I have
[M,N]=size(f); % getting the dimensions of the image
F=fft2(double(f)); % taking the fast fourier transform of the image
u=0:(M-1); %Setting the coordinates X axis
v=0:(N-1); % Setting the coordinates Y axis
idx=find(u>M/2); % looking for X axis origin
u(idx)=u(idx)-M; % setting the X axis origin
idy=find(v>N/2); % Looking fo Y axis origin
v(idy)=v(idy)-N; % Setting the X axis origin
[V,U]=meshgrid(v,u); % shifting the FFT of the image so that the origin is at the center of the image
D=sqrt(U.^2+V.^2); % Taking the square root
NF = ones(ir,ic); % setting initial coordinates to be zero
NF(21:27,45:63) = 0; % coordinates for the bright spots
NF(256-27:256-21,256-63:257-45) = 0;% coordinates for the bright spots
NF(47:53,63:81) = 0; % coordinates for the bright spots
NF(256-53:256-47,256-81:257-63) = 0;% coordinates for the bright spots
NF(73:79,81:99) = 0; % coordinates for the bright spots
NF(256-79:256-73,256-99:257-81) = 0;% coordinates for the bright spots
NF(99:105,99:117) = 0; % coordinates for the bright spots
NF(256-105:256-99,256-117:256-99) = 0;% coordinates for the bright spots
G = F.*NF; % Apply the notch filters to the Fourier spectrum of the image
imshow(uint8(log(1+abs(G))),[]);
g=real(real(ifft2(double(G)))); % getting the inverse fourier transform
imshow(f),figure,imshow(g,[ ]); % display the original image and the fourier transform of the image
but this is giving me an error
Error using .* Matrix dimensions must agree.
Error in Notchfilter (line 59) G = F.*NF; % Apply the notch filters to the Fourier spectrum of the image

Alejandro Arrizabalaga on 21 Jun 2013
Edited: Alejandro Arrizabalaga on 21 Jun 2013
Your code is not OK. ir and ic are not defined and you seem not to do iffshift, even though you say something in your comments. I think that you forgot to paste some part. By the way, I do not get the error you say. This is what I did:
[M,N]=size(f); % getting the dimensions of the image
F=fft2(double(f)); % taking the fast fourier transform of the image
u=0:(M-1); %Setting the coordinates X axis
v=0:(N-1); % Setting the coordinates Y axis
idx=find(u>M/2); % looking for X axis origin
u(idx)=u(idx)-M; % setting the X axis origin
idy=find(v>N/2); % Looking fo Y axis origin
v(idy)=v(idy)-N; % Setting the X axis origin
[V,U]=meshgrid(v,u);
% shifting the FFT of the image so that the origin is at the center of the image
F=fftshift(F);
D=sqrt(U.^2+V.^2); % Taking the square root
NF = ones(size(F,1),size(F,2)); % setting initial coordinates to be zero
NF(21:27,45:63) = 0; % coordinates for the bright spots
NF(256-27:256-21,256-63:257-45) = 0;% coordinates for the bright spots
NF(47:53,63:81) = 0; % coordinates for the bright spots
NF(256-53:256-47,256-81:257-63) = 0;% coordinates for the bright spots
NF(73:79,81:99) = 0; % coordinates for the bright spots
NF(256-79:256-73,256-99:257-81) = 0;% coordinates for the bright spots
NF(99:105,99:117) = 0; % coordinates for the bright spots
NF(256-105:256-99,256-117:256-99) = 0;% coordinates for the bright spots
G = F.*NF; % Apply the notch filters to the Fourier spectrum of the image
G=ifftshift(G);
figure;imshow(uint8(log(1+abs(G))),[]);
g=real(ifft2(double(G))); % getting the inverse fourier transform
figure;imshow(f),figure,imshow(g,[ ]); % display the original image and the fourier transform of the image