Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

I can't solve this problem. Can you explain why? A wide sense stationary process X (t) with mean ux = 2 and auto-correlation Rx (T)

I can't solve this problem. Can you explain why?

image text in transcribed
A wide sense stationary process X (t) with mean ux = 2 and auto-correlation Rx (T) = 4+ 106(T) is applied as an input to a short-time integrator (STI) to obtain the process Y (t). The impulse response of the STI is given by h(t) = 0.1 [u(t) - u(t - 10)]. (a) Determine the mean My (t). (b) Determine the crosscorrelation Rxy (t1, t2). (c) Determine the autocorrelation Ry (t1, t2). Explanation: Here the continuous-time system is LTI and the input random process is WSS so the output is also WSS. Therefore, system operations are done using convolution integral and simplified formulas can be used. Note that it would be advantageous to determine covariance quantities first and then the required correlations, although covariances are not asked for in the problem. Answers: (a) My = 2, (c) Ry (t1, t2) = 4+ A(0.1(t1- t2)) where A(t) is a triangular pulse (see Linear Systems Review)

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Essentials of Business Analytics

Authors: Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

2nd edition

1305627733, 978-1305861817, 1305861817, 978-0357688960, 978-1305627734

More Books

Students also viewed these Mathematics questions

Question

=+1. Why did Jack Ma decide it was time to take Alibaba public?

Answered: 1 week ago