The specifications for a low-pass filter are (0)=20 dBs p = 1500 rad/sec, 1 =

The specifications for a low-pass filter are

α(0)=20 dBs

Ω_p = 1500 rad/sec,           α₁ = 20.5 dBs

Ω_s = 3500 rad/sec,           α₂ = 50 dBs

(a) Determine the minimum order of the low-pass Butterworth and Chebyshev filters, and determine which is smaller.

(b) Give the transfer function of the designed low-pass Butterworth and Chebyshev filters (make sure the dc loss is as specified).

(c) Determine the half-power frequency of the designed filters by letting α(Ω_p) = α_max.

(d) Find the loss function values provided by the designed filters at Ω­_p and ­Ω_s. How are these values related to the α_max and α_min specifications? Explain. Which of the two filters provides more attenuation in the stop-band?

(e) If new specifications for the passband and stopband frequencies are ­Ω_p = 750(rad/sec) and ­Ω_s = 1750(rad/sec), are the minimum order the same as before? Explain.