fft.zip_fft逆变换matlab_二维fft

%Manoj Karkee %BSYSE 530: Lect 9 %derive FFT and inverse FFT clear all; close all; x = 1:100; for(i=1:100); X(i,:) = x; end; Y = X'; y = x'; %2D Sinosoidal function z = 100*cos(2*pi*(32*X/512+24*Y./512))+100; surf(x,y,z); %2-D FFT using 1-D FFT z_fft = fftshift(fft(fft(z,size(x,2),2),size(y,1),1));%This is the equivalent statement to %use a 'for loop' for fft in each rows and %then for fft in each column %Calculating and displaying phase and magnitudes of FFT results z_log10 = log10(1+abs(z_fft)); z_phase = angle(z_fft); z_fft_direct = fftshift(fft2(z, size(y,1), size(x,2))); z_direct_log10 = log10(1+abs(z_fft_direct)); z_direct_phase = angle(z_fft_direct); colormap(gray); subplot(2,2,1), imagesc(z_log10); title('Log10 Magnitude of composite 1D FFTs'); subplot(2,2,2), imagesc(z_phase); title('Phase of composite 1D FFTs'); subplot(2,2,3), imagesc(z_direct_log10); title('Log10 Magnitude of Direct 2D FFT'); subplot(2,2,4), imagesc(abs(z_direct_phase)), title('Phase of Direct 2D FFT'); %Inversing the images z_inv=abs(ifft(ifft(z_fft, [], 2), [], 1)); %lena_fft has been origin shifted, but it does not affect the ifft %operation as the spectrum is cyclic.??????? z_inv_direct = abs(ifft2(z_fft_direct)); % 'symmetric' option causes IFFT to treat 'lena_fft_direct' as conjugate symmetric % in two dimensions so that the output is purely real. This option is % useful when 'lena_fft_direct' is not exactly conjugate symmetric merely because of % round-off error. %Displaying the final results figure; colormap(gray); subplot(1,3,1), imagesc(z); title('Original Image'); subplot(1,3,2), imagesc(z_inv); title('Inversed Image: Composite 1D FFTs'); subplot(1,3,3), imagesc(z_inv_direct); title('Inversed Image: Direct 2D FFT');