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Consider the discrete-time LTI system shown below with h(n) = (½)¹u(n). (a) Determine the system response y(n) when we apply input x(n) = u(n+4)-u(n-8), using the properties of convolution. (b) Find the impulse response of the entire system. x(n) -2 h(n) h(n) y (n)

Consider the discrete-time LTI system shown below with h(n) = (½)¹u(n). (a) Determine the system response y(n) when we apply input x(n) = u(n+4)-u(n-8), using the properties of convolution. (b) Find the impulse response of the entire system. x(n) -2 h(n) h(n) y (n)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Solve it without using z transfo

**Problem Description:** Consider the discrete-time LTI (Linear Time-Invariant) system shown below with the impulse response \( h(n) = \left(\frac{1}{3}\right)^n u(n) \). (a) Determine the system response \( y(n) \) when we apply the input \( x(n) = u(n+4) - u(n-8) \), using the properties of convolution. (b) Find the impulse response of the entire system. **Diagram Explanation:** - The diagram depicts a block diagram of the discrete-time LTI system. - The system consists of three primary components: 1. An input \( x(n) \) is fed into two parallel paths. 2. The upper path has a block labeled \( h(n) \), indicating that the input is convolved with \( h(n) \). 3. The lower path contains a delay block represented by \( z^{-2} \) followed by another convolving block \( h(n) \). - The outputs from both paths are then combined using a summation block that subtracts the lower path's output from that of the upper path. - The final output of this summation is \( y(n) \).
Transcribed Image Text:**Problem Description:** Consider the discrete-time LTI (Linear Time-Invariant) system shown below with the impulse response \( h(n) = \left(\frac{1}{3}\right)^n u(n) \). (a) Determine the system response \( y(n) \) when we apply the input \( x(n) = u(n+4) - u(n-8) \), using the properties of convolution. (b) Find the impulse response of the entire system. **Diagram Explanation:** - The diagram depicts a block diagram of the discrete-time LTI system. - The system consists of three primary components: 1. An input \( x(n) \) is fed into two parallel paths. 2. The upper path has a block labeled \( h(n) \), indicating that the input is convolved with \( h(n) \). 3. The lower path contains a delay block represented by \( z^{-2} \) followed by another convolving block \( h(n) \). - The outputs from both paths are then combined using a summation block that subtracts the lower path's output from that of the upper path. - The final output of this summation is \( y(n) \).
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