Question: (a) Show that the frequency response function of a second-order Butter worth filter is where f 3 is the 3-dB frequency in hertz. (b) Find

(a) Show that the frequency response function of a second-order Butter worth filter is

H(f) =

where f3 is the 3-dB frequency in hertz.

(b) Find an expression for the group delay of this filter. Plot the group delay as a function of f / f3.

(c) Given that the step response for a second-order Butter worth filter is

2nfzt y,(1) = |1- exp 2nfzt cos 2лfst + sin и(t)

where u(t) is the unit step function, find the 10% to 90% rise time in terms of f3.

H(f) = 2nfzt y,(1) = |1- exp 2nfzt cos 2fst + sin (t)

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