# Blurring an image using FFT (Fast Fourier Transform)

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Kanak Dhotre on 26 Sep 2021
Answered: yanqi liu on 27 Sep 2021
I have an image of a ramp (Fig 1.1). Since every row of in this image is the same, I just picked the first row and ran FFT over it, then since convolution is equivalent to multiplication in the frequency domain, I multiplied it with the FFT of a gaussian vector. But when I run IFFT over the product, I don't get a blur image, instead I just get a completely white image (Fig 1.2) . What am I doing wrong?
Figure 1.1 Figure 1.2 My Code:
%Import the image
%Convert to grayscale
I = rgb2gray(I);
imshow(I)
%Pick a row
row = I(1,:);
plot(row)
%Define the gaussian vector
time_vector = 1:500
gaussian_vector = gaussmf(time_vector,[1 0]);
%Compute IFFT(FFT()*FFT())
row_fill = ifft(fft(row).*fft(gaussian_vector))
plot(row_fill)
%Stack the resultant rows
I_fill = repmat(row_fill,500,1);
%Plot the resultant image
imshow(I_fill)

Image Analyst on 27 Sep 2021
Try []:
imshow(I_fill, [])
but you'll likely notice no difference at all because of how smooth the function already is.

yanqi liu on 27 Sep 2021
sir, may be use the follows code to ref
clc
close all
clear all
%Import the image
%Convert to grayscale
I = rgb2gray(I);
imshow(I) %Pick a row
row = I(1,:);
figure;plot(row) %Define the gaussian vector
time_vector = 1:500;
gaussian_vector = gaussmf(time_vector,[1 0]);
%Compute IFFT(FFT()*FFT())
row_fill = ifft(fft(row).*fft(gaussian_vector));
plot(row_fill) %Stack the resultant rows
I_fill = repmat(row_fill,500,1);
%Plot the resultant image
figure; imshow(mat2gray(I_fill)) R2021a

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