EL ENG 120 Study Guide - Midterm Guide: High-Pass Filter, Time Shifting
Document Summary
8>>>< if n = 0 if n = 1 if n = 2 otherwise. The system is causal since h[n] = 0 for all n < 0. It is a simple cosine shifted up (no deducted points) c). The system is linear phase: a(ej ) , (0. 5 0. 5 cos( )) is real and nonnegative, and h(ej ) = a(ej )e j . Comments: two points for correct answer, three points for correct justi cation/explanation/derivation, just because a function has a cosine or sine does not mean it automatically takes on positive and negative values d). x[n] X(ej0) = 4 1 + 3 2 + 3 1 + 4 = 10 b). |x(ej )|2d = 2 p6 n=0 |x[n]|2 = 112 e). Note that x[n] , x[n + 3] is even symmetric, thus the transform of x[n] is real. Fourier transforms, e 3j a(ej ) is the fourier transform of x[n] where a(ej ) is the (real) fourier transform of x[n].
