4. For the three filters given below (assuming the origin is at the center): a) is the filter separable? b) find their Fourier transforms (2D DSFT); c) sketch the magnitudes of the Fourier transforms. You should sketch by hand the DSFT as a function of u, when v=0 and when v=1/2; also as a function of v, when u=0 or 1/2. d) Also use MATLAB freqz2() or python function numpy.fft.fft2() or scipy.fftpack.fft2() to compute and plot the magnitude of DSFT and compare to your answer. e) Comment on the functions of the three filters. In your calculation, you should make use of the separable property of the filter whenever appropriate. When the filter is not separable, you may be able to split the filter into several additive terms such that each term can be calculated more efficiently. 1 2 1 -1 -1 0 -1 0 1 2 4 2 H2 -1 8 -1; -1 5 -1 16 1 2 1 1 -1 0 -1 0 Hi = Hz = ' -1 4. For the three filters given below (assuming the origin is at the center): a) is the filter separable? b) find their Fourier transforms (2D DSFT); c) sketch the magnitudes of the Fourier transforms. You should sketch by hand the DSFT as a function of u, when v=0 and when v=1/2; also as a function of v, when u=0 or 1/2. d) Also use MATLAB freqz2() or python function numpy.fft.fft2() or scipy.fftpack.fft2() to compute and plot the magnitude of DSFT and compare to your answer. e) Comment on the functions of the three filters. In your calculation, you should make use of the separable property of the filter whenever appropriate. When the filter is not separable, you may be able to split the filter into several additive terms such that each term can be calculated more efficiently. 1 2 1 -1 -1 0 -1 0 1 2 4 2 H2 -1 8 -1; -1 5 -1 16 1 2 1 1 -1 0 -1 0 Hi = Hz = ' -1