An image can be blurred by means of a Gaussian filter which has an impulse response

(a) If h[m, n] = h₁[m]h₁[n], i.e., separable determine h₁[n]. Find the DFT of h[m, n] and plot its magnitude response. Use the functions mesh and contour to display the characteristics of the Gaussian filter (normalize the frequencies (ω₁, ω₂) to [-1, 1] - [-1, 1]. What are these?

(b) To see the effect of blurring read the test image cameraman.tif and convolve it several times using two-dimensional FFTs and IFFTs. Use the function imagesc to display the resulting images. Why do the images besides being display the blurring seem to be moving down towards the right?

Transcribed Image Text:

-(m²+n²) e 4σ4 h[m, n] - 3σ< m< 3σ, -3σ