Consider the LTI system shown in Figure. The input to this system, e[n], is a stationary zero-mean white-noise signal with average power ?²_e. The first system is a backward difference system as defined in Eq. 2.45 with f[n] = e[n] ? e[e ? n]. The second system is an ideal low pass filter with frequency response.

(a) Determine an expression for ?_?ff(e ^j?), the power spectrum of f [n], and plot this expression for - 2?

(b) Determine an expression for ?_ff(e ^j?), the autocorrelation function of ?f [n].

(c) Determine an expression for ?_gg(e ^j?), the power spectrum of g[n], and plot this expression for - 2?

(d) Determine an expression for ?²_g, the average power of the output.

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1, Jwl < wc. 0, < Wc. H2(el") = LTI system LTI system # 2 #1 e[n] f[n] 8In]