Given a lienar time-invariant system with frequency response H(jw) shown in the
ID: 2990006 • Letter: G
Question
Given a lienar time-invariant system with frequency response H(jw) shown in the graphs: (Note that the magnitude response is shown in the graphs: (Note that the magnitude response is shown in a linear scale, not in dB)
(a) Find (approximately) the steady-state output for input x(t) = sin(11t + pi/7).
(b) They system has a real value impulse response. Why is it common practice to only plot H(jw) for w > or equal to 0?
Given a lienar time-invariant system with frequency response H(jw) shown in the graphs: (Note that the magnitude response is shown in the graphs: (Note that the magnitude response is shown in a linear scale, not in dB) (a) Find (approximately) the steady-state output for input x(t) = sin(11t + pi/7). (b) They system has a real value impulse response. Why is it common practice to only plot H(jw) for w > or equal to 0?Explanation / Answer
a)
The input has a frequency of w = 11 from the equation
For w = 11, |H(w)| = 0.51 (from the opper graph) and
the angle of |H(w)| = -2 (from the lower graph)
So output y(t) = x(t) * |H(w)| * <H(w)
= 0.51 sin(11t + pi/7 - 2)
b)
It is a common practice to obtain H(w) because we can represent any signal as a sum of sinusoidal signals by fourier analysis. So the response of the system to any arbitrary input can be found by superimposing its response to its fourier components