Consider the LTI system shown in Figure P2.98. The input to this system, e[n], is a stationary zero-mean white-noise signal with average power σ2e. The first system is a backward difference system as defined by f [n] = e[n]−e[n−1]. The second system is an ideal lowpass filter with frequency response
(a) Determine an expression for φff (ejω), the power spectrum of f [n], and plot this expression for −2π < ω <2π.
(b) Determine an expression for φff [m], the autocorrelation function of f [n].
(c) Determine an expression for Φgg(ejω), the power spectrum of g[n], and plot this expression for −2π < ω <2π.
(d) Determine an expression for σ2 g, the average power of the output.
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