(c) A linear time (shift) invariant system is shown in Figure Q1(c) with q[n], p[n] and r[n] represent the impulse response, the input signal and the output signal of the system respectively. The following difference equation defines the system: r[n] = 4p[n] + 3p[n-1] -3p[n-2] + 2p[n-3] (i) (ii) Find and draw the impulse response q[n] of the system. Compute and draw the output response r[n] of the system given the input signal p[n] = [231]. (iii) Discuss and show that the output response of the system r[n] can also be obtained using the circular convolution operation between p[n] and q[n]. p[n] q[n] Figure Q1(c) r[n]

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(c)
A linear time (shift) invariant system is shown in Figure Q1(c) with q[n], p[n] and
r[n] represent the impulse response, the input signal and the output signal of the
system respectively. The following difference equation defines the system:
r[n] = 4p[n] + 3p[n 1] - 3p[n - 2] + 2p[n-3]
(i)
(ii)
Find and draw the impulse response q[n] of the system.
Compute and draw the output response r[n] of the system given the input
signal p[n] = [1 2 3 1].
(iii) Discuss and show that the output response of the system r[n] can also be
obtained using the circular convolution operation between p[n] and q[n].
p[n].
q[n]
Figure Q1(c)
►r[n]
Transcribed Image Text:(c) A linear time (shift) invariant system is shown in Figure Q1(c) with q[n], p[n] and r[n] represent the impulse response, the input signal and the output signal of the system respectively. The following difference equation defines the system: r[n] = 4p[n] + 3p[n 1] - 3p[n - 2] + 2p[n-3] (i) (ii) Find and draw the impulse response q[n] of the system. Compute and draw the output response r[n] of the system given the input signal p[n] = [1 2 3 1]. (iii) Discuss and show that the output response of the system r[n] can also be obtained using the circular convolution operation between p[n] and q[n]. p[n]. q[n] Figure Q1(c) ►r[n]
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