Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
9-35 Show that if y(t) = x(1 + a)-x(t-a), then Ry(t) = 2R₂(T) - R₂(t+2a) — R₂(t – 2a) Sy(w) = 4S, (w) sin² aw

9-35 Show that if y(t) = x(1 + a)-x(t-a), then Ry(t) = 2R₂(T) - R₂(t+2a) — R₂(t – 2a) Sy(w) = 4S, (w) sin² aw

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
**Problem Statement 9-35:** Show that if \( y(t) = x(t + a) - x(t - a) \), then the following results hold: 1. Autocorrelation Function: \[ R_y(\tau) = 2R_x(\tau) - R_x(\tau + 2a) - R_x(\tau - 2a) \] 2. Power Spectral Density: \[ S_y(\omega) = 4S_x(\omega) \sin^2(a\omega) \] These equations display the relationships for the autocorrelation function and power spectral density for a signal \( y(t) \) defined in terms of signal \( x(t) \).
Transcribed Image Text:**Problem Statement 9-35:** Show that if \( y(t) = x(t + a) - x(t - a) \), then the following results hold: 1. Autocorrelation Function: \[ R_y(\tau) = 2R_x(\tau) - R_x(\tau + 2a) - R_x(\tau - 2a) \] 2. Power Spectral Density: \[ S_y(\omega) = 4S_x(\omega) \sin^2(a\omega) \] These equations display the relationships for the autocorrelation function and power spectral density for a signal \( y(t) \) defined in terms of signal \( x(t) \).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Divergence theorem
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