Can anybody help me about the following problem?
I need to obtain the z-transform of a periodic function. Function f(t) is "t/a" for t values in (0,a], "1" in (a,3a], "4 - t/a" in(3a,5a], "-1" in(5a,7a], "t/a - 8" in(7a,8a] where a=pi/4. Note that this is one period and the period is 2*pi. The function repeats itself until infinity. I need to find the z transform of this time function as a rational fraction format (i.e. A(z)/B(z)). Sampling time T=10ms. Is there anyone who can help me?

 

try breaking the function up using step functions that look like:

u(t-a)-u(t-b)

what is the value of the above function outside of (a,b)? what is the value inside? using this and the linearity of the z transform should make this rather easy.