Question

Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation 

3y[n] – 7y[n – 1] + 2y[n – 2] = 3x[n] – 3x[n – 1] (2.1) 

The fact that sequences x[ ] and y[ ] are in input-output relation and satisfy (2.1) does not yet determine which LTI system. 

a) We assume each possible input sequence to this system has its Z-transform and that the impulse response of this system also has its Z-transform. Express the Z-transform, H(z), of the impulse response as a rational function of complex variable z. Specify all possible regions of convergence.

b) From part a) select every possible region convergence of H(z) associated with a causal system and specify the time-domain impulse response h[n].

Answer 1