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.