**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 \( x(t) \).

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Answered: 9-35 Show that if y(t) = x(1 +…

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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)

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

**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 \( x(t) \).

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