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ltistats

# ltistats - Boston University Department of Electrical and...

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Boston University Department of Electrical and Computer Engineering EC505 STOCHASTIC PROCESSES Notes on Second-Order Statistics and Linear Systems This summary is a compendium of results on second-order statistics arising from random processes passing through linear systems. I have attempted to present the real, multivariable case and use H ( t ) for the impulse response matrix and H( s ) for transformed quantities. Further, for compactness I have only presented the radian form of the transforms. This handout follows the convention for stationary systems that e.g. R XY ( τ ) = R XY ( t, t + τ ). This is the convention used in the notes, but is not universally used, so beware! Continuous Time Discrete Time u ( t ) wide sense stationary u ( n ) wide sense stationary H ( t, τ ) stable, multivariable, real , [ H ( t, τ )] ij = h ij ( t, τ ) H ( n, k ) stable, multivariable, real , [ H ( n, k )] ij = h ij ( n, k ) y ( t ) = Z -∞ H ( t, τ ) u ( τ ) y ( n ) = X k = -∞ H ( n, k ) u ( k ) m Y ( t ) = Z -∞ H ( t, τ ) m U ( τ ) m Y ( n ) = X k = -∞ H ( n, k ) m U ( k ) R Y Z ( t, s ) = Z -∞ H ( t, τ ) R UZ

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ltistats - Boston University Department of Electrical and...

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