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# A zero-mean white noise sequence with average power W = 1 is input into acascade of two systems.

A zero-mean white noise sequence with average power σW = 1 is input into acascade of two systems. System 1 has impulse response h[n] = (1/2)nu[n] and system 2has impulse response g[n] = (1/4)nu[n], where u[n] is the discrete-time step function.

(a) What are the frequency response functions H(f) and G(f) for systems 1 and 2respectively.

(b) Determine the power spectral densities, SY (f) and SZ(f), of sequences Y [n] and Z[n]respectively.

(c) Determine the autocorrelation functions, RY [k] and RZ[k].

(d) Determine the mean power of the output sequence E[Z2[n]].

(e) Find the cross-correlation functions RW,Y [k] and RW,Z[k].

(f) Find the cross spectral densities SW,Y [f] and SW,Z[f].

(g) What type of filtering systems are h[n] and g[n]?