= 5+22 1-0.8z = EC) Consider the filter H(2) and assume a causal complex sinusoidal input x(n) = einwou(n) of frequency

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5 22 1 0 8z Ec Consider The Filter H 2 And Assume A Causal Complex Sinusoidal Input X N Einwou N Of Frequency 1 (39.36 KiB) Viewed 62 times

= 5+22 1-0.8z = EC) Consider the filter H(2) and assume a causal complex sinusoidal input x(n) = einwou(n) of frequency wo, u = unit step sequence. a.) Show that the total output solution is represented as 7.5 y(n) = H(elw. )einwo + B(0.8)", where B = 1 - 1.25eiwo and where Yss(n) = Heiw, Teinwo is the steady state solution and Ytr = B(0.8)" is the transient solution. b.) Show that B achieves its maximum absolute value at 0.=0. c.) Determine the “1% effective time constant" i.e. the minimum value of n for which | Yrr(n) |<0.01. (Use log10(3) = 0.48, log10(8) = 0.90.) =