Warping effect of the bilinear transformationThe non-linear relation between the discrete frequency (rad) and the continuous frequency

Warping effect of the bilinear transformation—The non-linear relation between the discrete frequency ω(rad) and the continuous frequency ­(rad/sec) in the bilinear transformation causes warping in the high frequencies. To see this consider the following:

(a) Use MATLAB to design a Butterworth analog band-pass filter of order N = 12 and with half-power frequencies ­Ω₁ = 10 and ­Ω₂ = 20(rad/sec). Use MATLAB bilinear function, with K = 1, to transform the resulting filter into a discrete filter. Plot the magnitude and the phase of the discrete filter. Plot the poles and zeros of the continuous and the discrete filters.

(b) Increase the order of the filter to N = 14 and keep the other specifications the same. Design an analog bandpass filter and use again the bilinear function, with K = 1, to transform the analog filter into a discrete filter. Plot the magnitude and the phase of the discrete filter. Plot the poles and zeros of the continuous and the discrete filters. Explain your results.