Consider a discrete-time linear time-invariant (LTI) system , where

Let

where  is the discrete-time unit impulse function. For an input signal , the output  is

Two discrete-time linear time-invariant systems with impulse responses  and  are connected in cascade, where  is the Kronecker delta. The impulse response of the cascaded system is

Consider a causal and stable LTI system with rational transfer function H(z), whose corresponding impulse response begins at n = 0. Furthermore,

. The poles of H (z) are  for k = 1, 2, 3, 4.

The zeros of H(z) are all at z = 0. Let . The value of g[8] equals ___________________. (Given the answer up to three decimal places).  

A cascade system having the impulse responses and is shown in the figure below, where symbol denotes the time origin.

The input sequence x(n) for which the cascade system produces an output sequence  is

Let y[n] denote the convolution of h[n] and g[n], where  and g[n] is a casual sequence. If  and , then g[1] equals

Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below, the impulse response h[n] of the system is  

x[n] = 0; n <-1&n>0, x[-1]=-1, x[0]=2 is the input and y[n]=0; n<-1&n>2, y[-1]=–1=y[1], y[0]=3, y[2]=-2 is the output of a discrete time LTI system.  The system impulse response h[n] will be