In this problem you will design a digital Type 1 Chebyshev lowpass filter operating at a sampling rate of 100 kHz with a passband edge frequency at 10 kHz, a passband ripple of 0.4 dB (−20 log10(1 − δ1) = 0.4), and a minimum stopband attenuation of 50 dB at 30 kHz (−20 log10(δ2) = 50). You will first design an analog filter (with prewarped passband and stopband edge freuqencies) and then convert it to digital form using the bilinear transformation. (a) Determine the order of the analog filter prototype from the filter specifications. (b) Using the matlab function cheby1, find the analog transfer function for the filter with appropriate p. The form of the function call will be [b, a] = cheby1 (N, R,Wp,’s’) to specify an analog filter. (c) Compute the pole locations of this filter (e. g. using the roots command of matlab) and verify that they are at the locations for Chebyshev filters as described in the textbook. (d) Use the matlab command bilinear to convert the analog transfer to a digital transfer function. (e) Plot the magnitude and phase response of the filter. (f) Design the filter as a digital filter using the matlab function cheby1. The form of the function call will be [b, a] = cheby1(N, R,Wp) to specify an analog filter. Compare the designed filter to what was obtained above.