a) x₁[n] = sin (™), where n € Z. t -1 ≤ t ≤ 1 { otherwise (c) x3[n] = 4", where n E Z. b) x₂(t) = 0 where t E R.
a) x₁[n] = sin (™), where n € Z. t -1 ≤ t ≤ 1 { otherwise (c) x3[n] = 4", where n E Z. b) x₂(t) = 0 where t E R.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Question
Determine if each signal is even, odd, or neither
![### Transcription for Educational Use
#### Mathematical Functions:
(a) \( x_1[n] = \sin\left(\frac{\pi n}{4}\right) \), where \( n \in \mathbb{Z} \).
(b)
\[
x_2(t) =
\begin{cases}
t & \text{for } -1 \leq t \leq 1 \\
0 & \text{otherwise}
\end{cases}, \text{ where } t \in \mathbb{R}.
\]
(c) \( x_3[n] = 4^n \), where \( n \in \mathbb{Z} \).
#### Explanations:
- **Equation (a):** This equation represents a discrete-time sinusoidal function with angular frequency \(\frac{\pi}{4}\). The variable \(n\) is an integer, indicating the function is defined over discrete time steps.
- **Equation (b):** This is a piecewise continuous-time function. It is linear between \( t = -1 \) and \( t = 1 \), with \( x_2(t) \) equaling \( t \) over this interval. Outside of this interval, the function is \(0\).
- **Equation (c):** This represents an exponential discrete-time function where the base is \(4\), and the exponent is the variable \(n\). Each step \(n\) provides a power of \(4\), indicating exponential growth of the function values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F039207b8-632a-4dc4-a3c4-fd77b3c684b4%2F60e98a7a-9df2-49bb-a2e2-bdea177740ab%2Faddqbe_processed.png&w=3840&q=75)
Transcribed Image Text:### Transcription for Educational Use
#### Mathematical Functions:
(a) \( x_1[n] = \sin\left(\frac{\pi n}{4}\right) \), where \( n \in \mathbb{Z} \).
(b)
\[
x_2(t) =
\begin{cases}
t & \text{for } -1 \leq t \leq 1 \\
0 & \text{otherwise}
\end{cases}, \text{ where } t \in \mathbb{R}.
\]
(c) \( x_3[n] = 4^n \), where \( n \in \mathbb{Z} \).
#### Explanations:
- **Equation (a):** This equation represents a discrete-time sinusoidal function with angular frequency \(\frac{\pi}{4}\). The variable \(n\) is an integer, indicating the function is defined over discrete time steps.
- **Equation (b):** This is a piecewise continuous-time function. It is linear between \( t = -1 \) and \( t = 1 \), with \( x_2(t) \) equaling \( t \) over this interval. Outside of this interval, the function is \(0\).
- **Equation (c):** This represents an exponential discrete-time function where the base is \(4\), and the exponent is the variable \(n\). Each step \(n\) provides a power of \(4\), indicating exponential growth of the function values.
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We need to check whether the given signal are odd , even ,
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