QUESTION 2 Consider the following systems Si where S,(x [n])=x[n]+n? Szx [n])=x[n-1]. Which of the following is true. S(X [n])=S'(x [n])=x [n-1]+n?

Introductory Circuit Analysis (13th Edition)
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**Question 2**

Consider the following systems:

A diagram is shown with two interconnected systems, labeled \( S \) and \( S' \).

- **System \( S \):** 
  - Contains two blocks: \( S_1 \) followed by \( S_2 \).
- **System \( S' \):**
  - Contains two blocks: \( S_2 \) followed by \( S_1 \).

Where:

\( S_1(x[n]) = x[n] + n^2 \)

\( S_2(x[n]) = x[n - 1] \)

Which of the following is true?

1. 
   \[
   \begin{cases}
   S(x[n]) = x[n - 1] + (n - 1)^2 \\
   S'(x[n]) = x[n - 1] + n^2 
   \end{cases}
   \]

2. 
   \[
   \begin{cases}
   S(x[n]) = x[n - 1] + n^2 \\
   S'(x[n]) = x[n - 1] + (n - 1)^2 
   \end{cases}
   \]

3. 
   \[
   \begin{cases}
   S(x[n]) = S'(x[n]) = x[n - 1] + (n - 1)^2 
   \end{cases}
   \]

4. None of the above
Transcribed Image Text:**Question 2** Consider the following systems: A diagram is shown with two interconnected systems, labeled \( S \) and \( S' \). - **System \( S \):** - Contains two blocks: \( S_1 \) followed by \( S_2 \). - **System \( S' \):** - Contains two blocks: \( S_2 \) followed by \( S_1 \). Where: \( S_1(x[n]) = x[n] + n^2 \) \( S_2(x[n]) = x[n - 1] \) Which of the following is true? 1. \[ \begin{cases} S(x[n]) = x[n - 1] + (n - 1)^2 \\ S'(x[n]) = x[n - 1] + n^2 \end{cases} \] 2. \[ \begin{cases} S(x[n]) = x[n - 1] + n^2 \\ S'(x[n]) = x[n - 1] + (n - 1)^2 \end{cases} \] 3. \[ \begin{cases} S(x[n]) = S'(x[n]) = x[n - 1] + (n - 1)^2 \end{cases} \] 4. None of the above
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Given : function in Discrete time domain

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