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Unformatted text preview: Massachusetts Institute of Technology Department of Mechanical Engineering 2.160 Identification, Estimation, and Learning Spring 2006 Problem Set No. 7 Out: April 24, 2006 Due: May 3, 2006 Problem 1 Answer the following questions about power spectral density. 1-1 Obtain the power spectrum density function of a sinusoid: ( ) cos u t A t ω = and plot it against frequency , ω ω − ∞ < < +∞ . 1.2 A common autocorrelation function encountered in physical problems is τ ω σ τ τ β 2 cos ) ( − = e R a). Find the corresponding spectral density function. b). ) ( τ R will be recognized as a damped cosine function. Sketch both the autocorrelation and spectral density functions for the lightly damped case. 1-3 A stationary random process has a spectral density function of the form: ) ( t X ) 1 )( 4 ( 12 6 ) ( 2 2 2 + + + = ω ω ω ω X S What is the mean-square value of ? [Hint: Expand ) ( t X ) ( ω X S into two terms: ) 1 ( ) 4 ( ) ( 2 2 + + + = ω ω ω B A S X , and then integrate each term using standard integral tables.] , and then integrate each term using standard integral tables....
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.160 taught by Professor Harryasada during the Spring '06 term at MIT.
- Spring '06
- Mechanical Engineering