Given a lienar time-invariant system with frequency response H(jw) shown in the

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

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