Let the signal x[n] shown in Figure P3.3.1. This signal is the input to three di

Question

Let the signal x[n] shown in Figure P3.3.1. This signal is the input to three different LTI systems with the

frequency responses H1(ej?) through H3(ej?) shown in Figure P3.3.2.

(a) Specify which kind of filter each system is, i.e., highpass, lowpass or bandpass.

(b) Find an expression for the output y[n] from each system and sketch that signal. Look at each H(ej?) carefully as the vertical scale is not the same on all three plots.

(c) Do the outputs y[n] match what you would have predicted from part (a)?

Explanation / Answer

as frequency around 0 and 2*pi are low frequency and frequency values around pi are high frequencies,

H1 is band pass.

H2 is low pass.

H3 is high pass

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