Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
Find Z transform of the given function x(n)

Find Z transform of the given function x(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
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

Find Z transform of the given function x(n). Need very urgent help. 

### Mathematical Expression on Discrete Signals The equation provided represents a discrete-time signal \( x[n] \): \[ x[n] = -0.5 \delta[n + 1] + \delta[n] \] #### Explanation: - **\( x[n] \)**: Represents the discrete signal at time index \( n \). - **\( \delta[n] \)**: The Kronecker delta function, a discrete analog of the Dirac delta function. It is defined as: \[ \delta[n] = \begin{cases} 1 & \text{if } n = 0 \\ 0 & \text{otherwise} \end{cases} \] This function is used to denote impulse signals in discrete time. - **\( \delta[n + 1] \)**: Represents a shifted delta function. The shift \( +1 \) indicates a delay by one sample in the positive direction of the index \( n \). - **Coefficients**: - **\(-0.5\)**: This is a scaling factor applied to the \( \delta[n + 1] \) term, indicating that the impulse at \( n = -1 \) will be scaled down by half. #### Signal Description: This equation describes a signal that consists of two impulses: - An impulse at \( n = 0 \) with a magnitude of 1. - A scaled impulse at \( n = -1 \) with a magnitude of \(-0.5\). This signal can be visualized as discrete spikes occurring at the specified indices.
Transcribed Image Text:### Mathematical Expression on Discrete Signals The equation provided represents a discrete-time signal \( x[n] \): \[ x[n] = -0.5 \delta[n + 1] + \delta[n] \] #### Explanation: - **\( x[n] \)**: Represents the discrete signal at time index \( n \). - **\( \delta[n] \)**: The Kronecker delta function, a discrete analog of the Dirac delta function. It is defined as: \[ \delta[n] = \begin{cases} 1 & \text{if } n = 0 \\ 0 & \text{otherwise} \end{cases} \] This function is used to denote impulse signals in discrete time. - **\( \delta[n + 1] \)**: Represents a shifted delta function. The shift \( +1 \) indicates a delay by one sample in the positive direction of the index \( n \). - **Coefficients**: - **\(-0.5\)**: This is a scaling factor applied to the \( \delta[n + 1] \) term, indicating that the impulse at \( n = -1 \) will be scaled down by half. #### Signal Description: This equation describes a signal that consists of two impulses: - An impulse at \( n = 0 \) with a magnitude of 1. - A scaled impulse at \( n = -1 \) with a magnitude of \(-0.5\). This signal can be visualized as discrete spikes occurring at the specified indices.
Expert Solution
steps

Step by step

Solved in 4 steps

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