问二维卷积定理

EN

% 1- Read image and create a domain frequqncy window
im = imread('High_Detail.jpg');
im = imresize(im,[100,100]);
im = rgb2gray(im);
im = im2double(im);
window_fft_shifted = zeros([100,100]);
window_fft_shifted(50-11:50+11,50-11:50+11) = 1;

% 2- FFT then Multiplying it by window then get IFFT, a blurred image expected
im_fft = fft2(im);
im_fft_shifted = fftshift(im_fft);
im_fft_shifted_W = im_fft_shifted .* window_fft_shifted;
im_result_1 = ifft2(ifftshift(im_fft_shifted_W));

% 3- Get IFFT of window, convolve im with it, the same blurred image is expected
window = ifft2(ifftshift(window_fft_shifted));
im_result_2 = conv2(im, window);

% 4- Plot
figure;
subplot(2,2,1); imshow(im);
subplot(2,2,3); imshow(im_result_1);
subplot(2,2,4); imshow(im_result_2);