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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).

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).

MATLAB: An Introduction with Applications
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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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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