（2） 对以下程序产生的图像做傅里叶变换的平移性操作，将频谱中心移至中央。 f(1000,1000)=0; f=mat2gray(f); [Y,X]=meshgrid(1:1000,1:1000); f(350:649,475:524)=1;

首先，我们需要将图像进行傅里叶变换：

f_pad = padarray(f, [500, 500], 'post');
F = fftshift(fft2(f_pad));

然后，我们可以将频谱中心移至中央：

[m, n] = size(F);
[X, Y] = meshgrid(1:n, 1:m);
centerX = ceil(n/2);
centerY = ceil(m/2);
distX = abs(X - centerX);
distY = abs(Y - centerY);
distX(centerX, centerY) = 1; % avoid division by zero
distY(centerX, centerY) = 1; % avoid division by zero
shiftedF = F ./ (distX .* distY);

最后，我们可以进行逆傅里叶变换，得到平移后的图像：

shifted_f_pad = ifft2(ifftshift(shiftedF));
shifted_f = shifted_f_pad(1:size(f, 1), 1:size(f, 2));
imshow(shifted_f);

完整代码如下：

f(1000,1000)=0;
f=mat2gray(f);
[Y,X]=meshgrid(1:1000,1:1000);
f(350:649,475:524)=1;

f_pad = padarray(f, [500, 500], 'post');
F = fftshift(fft2(f_pad));

[m, n] = size(F);
[X, Y] = meshgrid(1:n, 1:m);
centerX = ceil(n/2);
centerY = ceil(m/2);
distX = abs(X - centerX);
distY = abs(Y - centerY);
distX(centerX, centerY) = 1; % avoid division by zero
distY(centerX, centerY) = 1; % avoid division by zero
shiftedF = F ./ (distX .* distY);

shifted_f_pad = ifft2(ifftshift(shiftedF));
shifted_f = shifted_f_pad(1:size(f, 1), 1:size(f, 2));
imshow(shifted_f);