matlab实现DFT傅里叶变换频率域滤波

function output_img = dft2d(input_img, flags) %Input - input_img 灰度图 % - flags 用于指定DFT或IDFT %Output - output_img 空间滤波后的灰度图 %dft2d 对灰度图进行离散傅里叶变换和反变换 %input_img = '../hw3_input/20.png'; if flags == 0 %DFT [ih,iw] = size(input_img); %获取行和列，即原图的高度和宽度 img = double(input_img); output_img = zeros(ih, iw); rowvec = zeros(1, iw); %创建原图一个行 colvec = zeros(ih, 1); %创建原图一个列 %中心化 for row = 1 : ih for col = 1 : iw img(row, col) = img(row, col) * (-1)^(row+col); end end %列复数赋值 for x = 0 : ih-1 colvec(x+1, 1) = exp((-1i*2*pi) * (x/ih)); end %行复数赋值 for y = 0 : iw-1 rowvec(1, y+1) = exp((-1i*2*pi) * (y/iw)); end %2维DFT公式 for u = 0 : ih-1 for v = 0 : iw-1 colvec2 = colvec.^u; rowvec2 = rowvec.^v; output_img(u+1, v+1) = sum(sum(colvec2 * rowvec2 .* img)); end end output_img = 1/(ih*iw) * output_img; elseif flags == 1 %IDFT [ih, iw] = size(input_img); output_img = zeros(ih, iw); rowvec = zeros(1, iw); colvec = zeros(ih, 1); %-2变2而已 for x = 0 : ih-1 colvec(x+1, 1) = exp((1i*2*pi) * (x/ih)); end %-2变2而已 for y = 0 : iw-1 rowvec(1, y+1) = exp((1i*2*pi) * (y/iw)); end %少了1/(ih*iw)而已 for u = 0 : ih-1 for v = 0 : iw-1 colvec2 = colvec.^u; rowvec2 = rowvec.^v; output_img(u+1, v+1) = sum(sum(colvec2 * rowvec2 .* input_img)); end end %取实部 output_img = real(output_img); %中心化移到最后 for row = 1 : ih for col = 1 : iw output_img(row, col) = output_img(row, col) * (-1)^(row+col); end end end end