The process x() is normal with zero mean. Show that if y(1) = x²(1), then Sy(w) = 2π R²(0)8 (w) + 25x (w) * S₂ (w) Piot S, (w) if S, (w) is (a) ideal LP, (b) ideal BP.
The process x() is normal with zero mean. Show that if y(1) = x²(1), then Sy(w) = 2π R²(0)8 (w) + 25x (w) * S₂ (w) Piot S, (w) if S, (w) is (a) ideal LP, (b) ideal BP.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Problem 9-41**
The process \( x(t) \) is normal with zero mean. Show that if \( y(t) = x^2(t) \), then
\[
S_y(\omega) = 2\pi R_x^2(0)\delta(\omega) + 2S_x(\omega) * S_x(\omega)
\]
**Task:**
Plot \( S_y(\omega) \) if \( S_x(\omega) \) is
(a) an ideal low-pass filter (LP),
(b) an ideal band-pass filter (BP).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F428a9a94-6a00-41c3-b8bc-a63848ce2f56%2F3e8dcadf-9a54-4832-b263-7aec056c2f12%2Fqeviidb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 9-41**
The process \( x(t) \) is normal with zero mean. Show that if \( y(t) = x^2(t) \), then
\[
S_y(\omega) = 2\pi R_x^2(0)\delta(\omega) + 2S_x(\omega) * S_x(\omega)
\]
**Task:**
Plot \( S_y(\omega) \) if \( S_x(\omega) \) is
(a) an ideal low-pass filter (LP),
(b) an ideal band-pass filter (BP).
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