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Let h[n] be the impulse response of the following system. -2 you] 2 2 D For what values of A and B do we have h[n]=Au[n]+B u[n]?

Let h[n] be the impulse response of the following system. -2 you] 2 2 D For what values of A and B do we have h[n]=Au[n]+B u[n]?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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### Question 14 Let \( h[n] \) be the impulse response of the following system: ![Block Diagram](system.jpg) The block diagram provided consists of: - An input \( x[n] \) and an output \( y[n] \). - Two branches dividing the input signal, each with branches containing the gain \( \frac{1}{2} \). - Two delay elements represented by \( D \). - A negative feedback loop with a gain of \( -2 \). The task is to find for what values of \( A \) and \( B \) the impulse response \( h[n] \) satisfies the equation: \[ h[n] = A \, u[n] + B \left( -\frac{1}{2} \right)^n u[n] \] Here, \( u[n] \) is the unit step function. ### Options: - \( A = -2 \) and \( B = -2 \) - \( A = -2 \) and \( B = -\frac{7}{2} \) - \( A = -\frac{2}{3} \) and \( B = -\frac{7}{6} \) - \( A = -\frac{2}{3} \) and \( B = \frac{2}{3} \) Choose the correct option.
Transcribed Image Text:### Question 14 Let \( h[n] \) be the impulse response of the following system: ![Block Diagram](system.jpg) The block diagram provided consists of: - An input \( x[n] \) and an output \( y[n] \). - Two branches dividing the input signal, each with branches containing the gain \( \frac{1}{2} \). - Two delay elements represented by \( D \). - A negative feedback loop with a gain of \( -2 \). The task is to find for what values of \( A \) and \( B \) the impulse response \( h[n] \) satisfies the equation: \[ h[n] = A \, u[n] + B \left( -\frac{1}{2} \right)^n u[n] \] Here, \( u[n] \) is the unit step function. ### Options: - \( A = -2 \) and \( B = -2 \) - \( A = -2 \) and \( B = -\frac{7}{2} \) - \( A = -\frac{2}{3} \) and \( B = -\frac{7}{6} \) - \( A = -\frac{2}{3} \) and \( B = \frac{2}{3} \) Choose the correct option.
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