Consider the LTI system shown in Figure P2.98. The input to this system, e[n], is a stat...

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 σ²_e. 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 φ_ff (e^jω), the power spectrum of f [n], and plot this expression for −2π < ω <2π.

(b) Determine an expression for φ_ff [m], the autocorrelation function of f [n].

(c) Determine an expression for Φ_gg(e^jω), 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.