Lecture 10 EE573 S’ 2001

EXAM 1 PROBLEM 1

Develop Finite Fourier Transform Definitions for the following processes, such that the following quantity is well-defined as n -> ¥ :

• 
• x(t) white noise
• 

[Reviewed wss conditions for sine wave]

EXAM 1 PROBLEM 2

For the conveyor random process

• Assuming it is wss, evaluate how simple down sampling by a factor of 2 influences the estimated PSD
• Repeat with the Matlab "decimation" operation
• Evaluate the wss of the process

[Developed wss test for mean of 10-vector subset of r.p.]

EXAM 1 PROBLEM 3

Write Matlab code for the Levinson Algorithm, and test it on both simulated

• AR(1) process with pole z=0.9.
• AR(2) process with complex poles having radius 0.9 and angle 45 degrees

EXAM 1 PROBLEM 4

Given a family of rectangular windows, evaluate their influence on the psd obtained using theoretical correlation lags. Specifically, consider 2 cases:

1. sinusoid (A=.707, f=.25) and white noise (var=1). Use window

sizes n= 100, 500, 1000.

2. AR(2) noise with a resonance of 20 dB at .25 Hz. Use same window sizes.

Discuss results.