Image filtering using 2D-FFT — Consider the linear filtering of an image using the 2D-FFT. Load the image clown and use three different filters to process it given in different formats.

• Low-pass FIR filter with impulse response

• High-pass FIR filter with transfer function

• Six-order separable IIR Butterworth filter with coefficients of one of the filters given by the MATLAB function butter: 

[b, a] = butter(3, [0.05, 0.95])

(a) Determine the impulse response corresponding to the high-pass FIR and the IIR filter (use filter).

(b) Find the magnitude of the DFT of the image (use a logarithmic scale to plot it) to determine the frequencies present in the image.

(c) Using the pixel array from the image as input and the convolution property of 2DDFT to compute the output of the filter.

(d) Plot the magnitude response of the three filters (normalize the frequencies ω₁, ω₂ in the plots to get a support [-1, 1] - [-1, 1]). Determine the type of filter that the IIR filter is.

S 1/100 0< m, n< 10 otherwise hi[m, n] = H2(21,22) = 1 – 2ī - 2,'+2127 -1,-1