process. It is assumed that X(t) and N(t) are jointly stationary. Rx(t) and RN(T) denote their autocorrelation functions. Rxn (t) denotes their cross-correlation function. The signal Y(t) is sent through an LTI system with impulse response h(t) and frequency response H(f). The output process of the LTI system is denoted by & (t), which we want to be as close to X(t) as possible. 3) Assume X(t) and N(t) are independent. N(t) is a zero-mean white Gaussian process with the power spectral density . Find the optimalH(f). 2

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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1. Let Y(t) = X(t) + N(t), where X(t) denotes a signal process and N(t) denotes a noise
process. It is assumed that X(t) and N(t) are jointly stationary. Rx(t) and RN(T) denote their
autocorrelation functions. RXN (T) denotes their cross-correlation function. The signal Y(t) is
sent through an LTI system with impulse response h(t) and frequency response H(f). The
output process of the LTI system is denoted by X (t), which we want to be as close to X(t) as
possible.
3) Assume X(t) and N(t) are independent. N(t) is a zero-mean white Gaussian process with
the power spectral density . Find the optimal H(f).
Transcribed Image Text:1. Let Y(t) = X(t) + N(t), where X(t) denotes a signal process and N(t) denotes a noise process. It is assumed that X(t) and N(t) are jointly stationary. Rx(t) and RN(T) denote their autocorrelation functions. RXN (T) denotes their cross-correlation function. The signal Y(t) is sent through an LTI system with impulse response h(t) and frequency response H(f). The output process of the LTI system is denoted by X (t), which we want to be as close to X(t) as possible. 3) Assume X(t) and N(t) are independent. N(t) is a zero-mean white Gaussian process with the power spectral density . Find the optimal H(f).
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