chapt6 - Stat 153 - 7 Oct 2008 D. R. Brillinger Chapter 6 -...

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Unformatted text preview: Stat 153 - 7 Oct 2008 D. R. Brillinger Chapter 6 - Stationary Processes in the Frequency Domain One model Another ,... 2 , 1 , ) cos( = + + = t Z t R X t t ,... 2 , 1 , ) cos( } exp{ = + +- = t Z t t R X t t R: amplitude : decay rate : frequency, radians/unit time : phase 2/: period, time units cos({t+2/}+) = cos(t++) cos(2+)=cos() f= /2: frequency in cycles/unit time 6.2 The spectral distribution function Stochastic models . Have advantages mean t.s. stationary : ) cos( i). t t t Z Z t R X + + = ) ( ) ( ) cos( ) ( h h t R t ZZ = + = ) U(0,2 : ) cos( ii). + = t R X t params in linear ), sin( ) cos( ) sin( ) sin( ) cos( ) cos( ) cos( t t t R t R t R + =- = + 2 / ) cos( 2 h h R EX t = = =3.14159... ) IU(0,2 : ) cos( iii). 1 j j j j k j t t R X + = = = = J j j j h h R 1 2 2 / ) cos( Graph like pmf, f, or cdf, F = = ,... 2 , 1 , ), ( ) cos( h dF h h t VarX F = = ) ( 6.3 6....
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This note was uploaded on 10/19/2009 for the course MATH 611 taught by Professor Jsdkasj during the Spring '09 term at Kansas.

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chapt6 - Stat 153 - 7 Oct 2008 D. R. Brillinger Chapter 6 -...

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