noise_notes_set5

noise_notes_set5 - ECE594I notes, M. Rodwell, copyrighted...

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ECE594I notes, M. Rodwell, copyrighted ECE594I Notes set 5: More Math: Random Processes Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu 805-893-3244, 805-893-3262 fax
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ECE594I notes, M. Rodwell, copyrighted References and Citations: Devices State - Solid in Noise : Ziel der Van Physics Thermal : Kroemer and Kittel : Citations / Sources g. ngineeri ns ommunicat f rinciple cobs ozencraft ory) (introduct s Principle Signal Random Variables, Random ty, Probabili : Peebles Z. Peyton ive) comprehens (hard, Variables Random and ity Probabil : Papoulis 982 rca tanford ellman artin otes cture robabilit 1982 circa Stanford, Cover, Thomas : notes lecture theory n Informatio Design c Electroni Noise Low : er Motchenbak ng. Engineeri ions Communicat of s Principle : Jacobs & Wozencraft d f t d circuits. in Noise : Notes ns Applicatio tor Linear Semiconduc National 1982 circa Stanford, Hellman, Martin : notes lecture y Probabilit design) receiver (optical Personik & Smith noise), (device by Fukui Papers Kroemer and Kittel Peebles, Jacobs, & Wozencraft Ziel, der Van study. for references Suggested Theory n Informatio of Elements : Williams and Cover ) (! Notes App. Semi. National
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ECE594I notes, M. Rodwell, copyrighted ndom processes random processes
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ECE594I notes, M. Rodwell, copyrighted Random Processes time. vs. voltage of functions of paper, of sheets separate on graphs, of set a Draw can. garbage a into Put them space. sample y probabilit the called is can garbage This ime f nction ndom ur his random. at sheet one out Pick ). ( is process random The time. of function random our is This t V v(t) is outcome particular The
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ECE594I notes, M. Rodwell, copyrighted ariable ndom f (X) nction f pectatio he f efinion he ecall Time Averages vs. Sample Space Averages [] + = = ) ( ) ( ) ( X variable random a of g(X) function a of n expectatio the of definion the Recall X g dx x f x g x g E space. sample over the is average the where , of * value average * the is g g ime articular me ace mple over the average an define can we , definition process random our With + = 1 1 1 1 1 ) ) ( ( )) ( ( )) ( ( )) ( ( : time particular some at space sample V t v d t v f t v g t v g E t : over time function outcome one any of average an define also can We + = 2 / 2 / )) ( ( 1 lim )) ( ( T T i T i dt t v g T t v g A
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ECE594I notes, M. Rodwell, copyrighted What is Random in a Random Process ? time". ith randomly w varies " signal that the n expectatio the have somehow We random. is which sample the of selection the is it , definition our in Yet, y. discrepanc this addresses Ergodicity suprising. are ns implicatio Its
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ECE594I notes, M. Rodwell, copyrighted Ergodic Random Processes to equal over time averages has process random Ergodic An [ ] [ ] all , all for )) ( ( )) ( ( space sample l statistica over the averages t i t v g A t v g E = made have we sense, some In 1 1 i ace" mple ver the ariation ndom " to equivalent time" with variation random " space sample over the variation random
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ECE594I notes, M. Rodwell, copyrighted Time Samples of Random Processes ). ( and ) ( values has ) ( process random the and at times samples time With 2 1 2 1 t V t V t V t t on. distributi y probabilit joint some have ) ( and ) ( 2 1 t
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noise_notes_set5 - ECE594I notes, M. Rodwell, copyrighted...

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