Please help me write a matlab code for the books.tif gray level image. Filter the gray level image in the frequency domain using 2D fft (fft2), after performing the operation you can use 2D ifft (ifft2) to display the filtered image in the spatial domain for:

a- Apply a Rectangular low pass filter using cutoff frequency of (uc=N/16, vc=M/16) where N and M are the row and column sizes of the image (initialize a matrix of zeros of size N rows by M columns, generate a rectangle of ones, centered at N/2 and M/2 with width and height of N/8, M/8, split the rectangle with fftshift, then multiply the whole matrix point by point with the output of the fft2 of the image).

b- Apply a Circular low pass filter using cutoff frequency of Circular filter the cutoff frequency is given by Rc=[(uc) 2+(vc) 2]0.5where N and M are the row and column sizes of the image (replace the rectangle in a with a circle centered at N/2 and M/2 with radius Rc).

c- Apply a Rectangular high pass filter that has the same cutoff as part (a), replacing the zeros with ones and the ones with zeros for the output generated by fftshift.

d- Apply a Circular high pass filter that has the same cutoff as part (b), replacing the zeros with ones and the ones with zeros for the output generated by fftshift.