i would like a step by step answer or a great walkthrough for this question.
if it is full answer i will tip greatly and thanx in advance for your help.

a) By horizontal and vertical scaling and by a vertical shift,
transform the real valued trigonometric polynomial in the function
below into one which approximates the 2pi periodic function: Q(angel)
= 0 if ?pi<= angel <= -pi/2 1 if ?pi/2 <= angel <= pi/2 0 if pi/2
<=angel <=pi Elsewhere by periodicity

(b) Design (i.e. determine h[n] for) a low pass filter L for which |H(W?)| = Q(W?).

(c) Give the system function for this L, then use the MATLAB function
roots to Determine all its zeroes.

(d) Sketch an Argand diagram showing the unit circle and the location
of all these Zeroes.

Function is: Sum K=1 to infinity of : (2/(K*PI)) * Sin ((K*pi)/2) * 2
Cos ((pi/2)* Kt

This is equal to : (4/pi) Cos(pi/2)t ? (4/3pi) Cos (3pi/2)t + (4/5pi)
Cos(5pi/2)t - ....

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Clarification of Question by shoma911-ga on 12 Apr 2006 14:16 PDT

btw i forgot to mention there will be a $20 tip.