Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Answer only subparts C and D please
For each of the following LTI systems, find the \( z \)-domain transfer function, and its zeros and poles. For these expressions, \( h[n] \) is the impulse response, \( x[n] \) is the input signal, and \( y[n] \) is the output signal. Express your answer as either a \( z \) polynomial of finite order or as the ratio of two \( z \) polynomials of finite order. In all cases, assume that the input signal begins at \( n = 0 \) or later. Also assume that \( y[n] = 0 \) for \( n < 0 \). State whether the system is FIR or IIR and briefly justify your answer. ### a.) \[ y[n] = 0.6y[n-1] - 0.25y[n-2] + x[n] + 3x[n-2] \] ### b.) \[ h[n] = \left(\frac{\sin(3\pi(n-1)/4)}{\pi(n-1)}\right)\left(u[n] - u[n-3]\right) \] (hint: can you express \( h[n] \) another way?) ### c.) \[ y[n] = 3x[n] + 10x[n-2] + 8x[n-4] \] ### d.) \[ h[n] = (-0.4)^nu[n] + 2(-0.75)^n u[n-1] \]
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Transcribed Image Text:For each of the following LTI systems, find the \( z \)-domain transfer function, and its zeros and poles. For these expressions, \( h[n] \) is the impulse response, \( x[n] \) is the input signal, and \( y[n] \) is the output signal. Express your answer as either a \( z \) polynomial of finite order or as the ratio of two \( z \) polynomials of finite order. In all cases, assume that the input signal begins at \( n = 0 \) or later. Also assume that \( y[n] = 0 \) for \( n < 0 \). State whether the system is FIR or IIR and briefly justify your answer. ### a.) \[ y[n] = 0.6y[n-1] - 0.25y[n-2] + x[n] + 3x[n-2] \] ### b.) \[ h[n] = \left(\frac{\sin(3\pi(n-1)/4)}{\pi(n-1)}\right)\left(u[n] - u[n-3]\right) \] (hint: can you express \( h[n] \) another way?) ### c.) \[ y[n] = 3x[n] + 10x[n-2] + 8x[n-4] \] ### d.) \[ h[n] = (-0.4)^nu[n] + 2(-0.75)^n u[n-1] \]
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