EL ENG 20 Study Guide - Midterm Guide: Linear Time-Invariant Theory, Exbibyte, Frequency Response
Document Summary
1 (a) the lti system is not causal because its impulse response isn"t zero for all time less than zero. Figure 1: the system"s impulse response in 1(a). (b) recall that the original impulse response is if n = 0 if n is odd. |n|/2 if n is even, h(n) = for some (0, 1) (or in other words 0 < < 1). We can then split the summation into three parts. 1 h(m)e i m + 2 + h( n)ei n + 2 + Xn=1 (1) (2) (3) (4) where the second equality follows by setting m = n. Note that a signi cant mistake made here was people assuming the false fact that ei n = e i n. Next, we note that for n odd, h(n) = 0, so that. 1 we can consider the summation only over even numbers.
