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ELEN E4702 PRACTICE FINAL
PROBLEM 1.
(20 Points) The stationary process X(t) is passed through each one of the four linear time
invariant (LTI) systems shown below and the output process is denoted by Y(t).
Find the output
autocorrelation function and crosscorrelation function between the input and the output under each of the
following cases:
1.
A delay system with delay
2.
A system with
(Is this really LTI? Can you still compute the autocorrelation and cross
correlation functions?)
3.
A system with
where
4.
A system described the differential equation:
The Fourier transform relationships needed are given below:
Time Domain
Frequency Domain
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View Full Document PROBLEM 2.
(25 points) Three messages are to be transmitted over an AWGN channel with a noise
power spectral density . The messages are:
where , , &
are zero otherwise.
1.
What is the dimensionality of the signal space?
2.
Find the appropriate basis of the signal space.
3.
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This note was uploaded on 08/05/2008 for the course ELEN E4702 taught by Professor Lazano during the Summer '08 term at Columbia.
 Summer '08
 LAZANO

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