Question

Part 1 (Calculation):

The Z-transform (ZT) converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation. It is the equivalent of the Laplace transform for discrete systems. The one-sided ZT, used for causal signals and systems, is defined as follows:

Consider the digital system (filter) described by the input/output difference equation and z-domain transfer function Hz:  

yn-0.88 yn-1=0.52 xn-0.4 xn-1

Hzz=Y(z)X(z)=0.52-0.4 z-11-0.88 z-1=0.52 z-0.4z-0.88

1. Assuming a unit step function input, i.e., x[n]=u[n], find the output y[n] for n=0,1,2 and 3. y[-1]=0.

Answer 1