A linear-phase FIR system has a real impulse response h[n] whose z-transform is known to...

A linear-phase FIR system has a real impulse response h[n] whose z-transform is known to have the form

where a, b, and c are zeros of H(z) that you are to find. It is also known that H(e^jω) = 0 for ω = 0. This information and knowledge of the properties of linear-phase systems are sufficient to completely determine the system function (and therefore the impulse response) and to answer the following questions:

(a) Determine the length of the impulse response (i.e., the number of nonzero samples).

(b) Is this a Type I, Type II, Type III, or Type IV system?

(c) Determine the group delay of the system in samples.

(d) Determine the unknown zeros a, b, and c. (The labels are arbitrary, but there are three more zeros to find.)

(e) Determine the values of the impulse response and sketch it as a stem plot.