The specifica-tions for a low-pass filter are p = 1500 rad/sec, max = 0.5 dBs s = 3500 rad/sec, min =

The specifica-tions for a low-pass filter are

Ω_p = 1500 rad/sec,           α_max = 0.5 dBs

Ω_s = 3500 rad/sec,           α_min = 30 dBs

(a) Determine the minimum order of the low-pass Butteworth filter and compare it to the minimum order of the Chebyshev filter. Which is the smaller of the two? Use MATLAB functions buttordand cheb 1 ord to verify your results.

(b) Determine the half-power frequencies of the designed Butterworth and Chebyshev low-pass filters by letting α(Ω_p) = α_max.

(c) For the Butterworth and the Chebyshev designed filters, find the loss function values at ­pand ­s. How are these values related to the α_max and α_min specifications? Explain.

(d) If new specifications for the passband and stopband frequencies are ­Ω_p =750(rad/sec) and Ω­_s = 1750(rad/sec), are the minimum orders of the Butterworth and the Chebyshev filters changed? Explain.