Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
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)
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...
See similar textbooks
icon
Related questions
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.
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.
Expert Solution
Step 1

We need to check whether the given signal are odd , even ,

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Z-transform of Signal
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS