noise_summary

# noise_summary - class notes M Rodwell copyrighted 2009 ECE...

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class notes, M. Rodwell, copyrighted 2009 ECE 145A / 218 C, notes set 13: Very Short Summary of Noise Mark Rodwell University of California, Santa Barbara 805-893-3244, 805-893-3262 fax

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class notes, M. Rodwell, copyrighted 2009 Background / Intent subject complex a is Noise Physics Math analysis noise Circuit models noise Device analysis noise Systems tions representa noise port - 2 here. points few a very upon only touch can We ns calculatio y sensitivit System classes. other in details More
class notes, M. Rodwell, copyrighted 2009 Probability Distribution Function: 1 Random Variable is and between lies y that probabilit The . value particular a on takes variable random a , experiment an During 2 1 x x x x X ) ( } { 2 1 2 1 dx x f x x x P x x X = < < function. on distributi y probabilit the is ) ( x f X f X (x) x x 1 x 2

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class notes, M. Rodwell, copyrighted 2009 Mean value, Variance, Standard Deviation [] +∞ = = = dx x xf X E X X X ) ( : X of Value Mean + x f alue xpected 2 2 2 2 [ ] = = dx x f x X E X X X ) ( : of value Expected value average its from deviation square - mean - root its is X of variance The 2 x σ () ) ( 2 2 2 2 X X dx x f x x x X E x X + = = = variance the of root square simply the is X of deviation standard The x ( ) . 2 2 2 x X X =
class notes, M. Rodwell, copyrighted 2009 The Gaussian Distribution ( ) p 1 : on distributi Gaussian The 2 x x . previously defined as are ) ( deviation standard the and ) ( mean The 2 exp 2 ) ( 2 2 2 x x X x x f σ π = arising processes random physical rem*, limit theo central * the of Because x Gaussian. the of that to close ons distributi y probabilit have effects small many of sum the from f X (x) ~2 σ x x x

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class notes, M. Rodwell, copyrighted 2009 Pair of Random Variables y. and x values particular specific on takes Y and X variables random of pair a , experiment an In XY y x f ) , ( on distributi joint by the described is behavior joint Their ∫∫ = < < < < D C B A XY dxdy y x f D y C B x A P ) , ( } and {
class notes, M. Rodwell, copyrighted 2009 Correlation and Covariance is Y and X of n correlatio The +∞ + [ ] ) , ( dxdy y x f xy XY E R XY XY = = ∫ ∫ −∞ ( ) ( ) [ ] is Y and X of covariance The y x R y Y x X E C Y Y = = same the are covariance and n correlatio that Note XY XY values. mean zero have or Y X either if zero. are values mean the bias), DC off ng (subtracti signals noise AC with dealing are we If

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class notes, M. Rodwell, copyrighted 2009 Random Processes time. ith randomly w sense) some (in varying voltage A V(t) . ) ( and ) ( values has ) ( , and at times Measured 2 1 2 1 t V t V t V t t v(t) v(t 2 ) v(t 1 ) t t 1 t 2
class notes, M. Rodwell, copyrighted 2009 Autocorrelation Function of A Random Process mplicity r rite = ] , [ ) , ( ) ( ), ( simplicity for Write 2 1 2 1 2 2 1 1 = V V E t t R t V V t V V VV )] ( ), ( [ )] ( ), ( [ )] ( ), ( [ and matter, not does origin time the , stationary is process the If τ + = + = t V t V E t t t V t V E t V t V E )] ( ), ( [ ) ( Then 1 2 3 3 2 1 + = t V t V E R VV

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class notes, M. Rodwell, copyrighted 2009 Power Spectral
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noise_summary - class notes M Rodwell copyrighted 2009 ECE...

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