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

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The specifications for a low-pass filter are

α(0)=20 dBs

Ωp = 1500 rad/sec,           α1 = 20.5 dBs

Ωs = 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(Ωp) = αmax.

(d) Find the loss function values provided by the designed filters at Ω­p and ­Ωs. How are these values related to the αmax and αmin 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 ­Ωp = 750(rad/sec) and ­Ωs = 1750(rad/sec), are the minimum order the same as before? Explain.

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