Problem 2 Solely based on the lormulas a" tin) (n+1) a" ufn) y and dotermine the -transforms of the following sequences: (u) r(n} = (n-1) u[12]} (b) r[n] = (–1)"2" u[n] (c) rin] = cos(upn) u[n] %3D

Introductory Circuit Analysis (13th Edition)
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Chapter1: Introduction
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Can u do problem 2 ?
Certainly! Here is the transcription suitable for an educational website:

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**EE306 HW6**

**HW5-3**

**Problem 1**

For the feedback system shown, determine the system function of \( Y(z)/X(z) \). Does the system have any poles on the unit circle in the z-plane?

**Problem 2**

Express the following in the form \(\sum A_k z^{-k}\):
   
   (a) \(x[n] = (1/4)^n u[n]\)
   
   (b) \(x[n] = (1/4)^n u[-n-1]\)

**Problem 3**

Determine the Z-transforms of the following sequences using the Z-transform pairs and properties formulas:

   \((n+1) a^n e[n] \rightarrow \frac{z}{(z-a)^2}\) 
   
   \(\frac{(-a)^n e[n]}{2^n} - \frac{(-a)^{n+1} e[n]}{3^n}\)

Hint: Remember to express trigonometric and sin() expressions in terms of complex exponential functions.

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There are no graphs or diagrams in the given image.
Transcribed Image Text:Certainly! Here is the transcription suitable for an educational website: --- **EE306 HW6** **HW5-3** **Problem 1** For the feedback system shown, determine the system function of \( Y(z)/X(z) \). Does the system have any poles on the unit circle in the z-plane? **Problem 2** Express the following in the form \(\sum A_k z^{-k}\): (a) \(x[n] = (1/4)^n u[n]\) (b) \(x[n] = (1/4)^n u[-n-1]\) **Problem 3** Determine the Z-transforms of the following sequences using the Z-transform pairs and properties formulas: \((n+1) a^n e[n] \rightarrow \frac{z}{(z-a)^2}\) \(\frac{(-a)^n e[n]}{2^n} - \frac{(-a)^{n+1} e[n]}{3^n}\) Hint: Remember to express trigonometric and sin() expressions in terms of complex exponential functions. --- There are no graphs or diagrams in the given image.
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