Engineering Three Problems

2. Consider the transfer function:

H(z)=z-L-z-a

a. Sketch the impulse response

b. What type of filter is this (FIRI ,2,3,4)

c. Find the zeros of the transfer function, and accurately sketch the zero diagram d. Sketch the magnitude of tle frequency response lU(ei.11.

3. We want to design an FtR differentiator using the frequency sampling design method. The ideal desired frequency response of the differentiator is:

Hlsio ) = jo "'iot

(N-r)/2

Note that this is just jat with a linear phase corresponding to the delay of a = (N _t)12 samples.

a. What filter type would you use (type 1, 2, 3 or 4)?

b. Sketch the desired amplitude function, Aako),for the filter.

c. Write down the exact complex length -ly' sequence whose inverse DFT you would take to obtain the actual (designed)filter impulse response, ft(n)

4. Consider an FIR filt€r with characteristics shown below.