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Signals and Systems

by: Lucienne Smith

Signals and Systems ECE 3793

Lucienne Smith
GPA 3.77

Joseph Havlicek

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Joseph Havlicek
Class Notes
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This 2 page Class Notes was uploaded by Lucienne Smith on Monday October 26, 2015. The Class Notes belongs to ECE 3793 at University of Oklahoma taught by Joseph Havlicek in Fall. Since its upload, it has received 17 views. For similar materials see /class/229326/ece-3793-university-of-oklahoma in ELECTRICAL AND COMPUTER ENGINEERING at University of Oklahoma.

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Date Created: 10/26/15
Formulas from Trigonometry sinzA COSZA 1 sinA i B sinAcosB i cosAsinB cosA i B cosAcosB sinAsinB tanA i B sin 2A 2 sinAcosA cos 2A cosz A 7 sin2 A tan 2A 2fo sing i1 71 C205A cos i 71 tang 7130 sinzA700s2A COSZACOS2A sinA sinB 2sinA B cos A 7 B sinA 7 sinB 2cosA B sinA 7 B cosA cos B 200s A B cos A 7 B cosA 7 cosB 2sin A B sinB A sinAsinB COSA 7 B 7 cosA B cosAcosB COSA 7 B cosA B sinAcos B sinA 7 B sinA B Differentiation Formulas i 7 d7v d7u i a 7 dzltuv iudzd dz dz 1 i 12 Chain rule ji sinucosuj7 cosu 7sinud7g tanu seczujig i771717u71 A71 1 i 71771d7u 71 ddmsm u7 fu2lidm7lt 2lts1n ult2 dices ud7mdm0ltcos ult7r i 71 7 1 in 71 71 1 i u 7 uiu ddmtan 11 de 2lttan ult2 1de 76 m1 d 7 717M 7 77057 dzlnuiudz dlegaui u dz7a7 071 Integration Formulas Integration by parts udv M 7 v du du 71n u e due u an d du177 dgt07d7 1 sinudu7cosu nd cosudusinu tanudu7lncosu sinzudu g 7 511142 u7sinucosu tanzudu tanu7u 2 7 u sinZu 7 1 cos udu 7 5 T 7 usmucosu du i1nltuiagt 7012 2a ua du 2 2 7 lnuu a 2 2 xu d e asinbz7bcosbz a2b2 5 sin bz dz E N am 7 e a cos bzbsinbz 5 cos bz dz 7 W i i i 2 zs1ndzdz5 7L z2s1ndzdzsmdzlt7gtCOSdz 2 7 z sinZaz 7 cos dz zsinaz sm dzdz7 2 74a zCOSdzdz7 a2 a 2 i z2 cos dz dz 2 cos dz 7 sm dz 7 sin Zaz a2 2 7g cos dzdz7 2 4a m tanz dz dz Ln 7 z ze m dz 75 z 7 l 04 04 04 lnzdzzlnz7z zlnzdz2lnz7 E N l l E Q 10 l SN Summation Formulas N2 Zak7 ay l iakf1a lallt1 kN1 k0 00 k a n k 1 an Zkam lallt1 a ay l kio a 1 k0 i 17 n 1a 71a gkak 7 1 7 02 Signals d 6t Eu t 6M 7 un 71 lt961t7962tgt 1 1t tdt lt1lnlwzlnlgt Z llnl ilnl EM9600 t 94 WWW t 94 Complex Exponential Signals ejwet ejwen Distinct signals for distinct we Identical signals for values of we separated by multiples of 27139 Periodic for any choice of we Periodic only if we27r mN E Q Fundamental frequency we Fundamental frequency we m Fundamental period Fundamental period we O unde ned we 0 one we 7 0 27rwe we 7 0 27rmwe Systems System H is linear if Hax1t bz2t aHz1t bHx2t System H is time invariant if Ht 7 te yt 7 te System H is memoryless if the current output does not depend on future or past inputs System H is invertible if distinct inputs produce distinct outputs System H is invertible if an inverse system G exists which undoes77 the action of H System H is causal if the current output does not depend on future inputs LTl system H is causal iff ht 0 V t lt 0 Bounded t is bounded if 3 B E R B gt 07 such that S B V t E R System H is BlBO stable if every bgunded input produces a bounded output LTl system H is BlBO stable i ht dt lt 00 yo 7 m W 7 m xnhn Z zkhn7k Z mile1m k7oo k00 x7 ht 7 739 dT 00 zt 7 Th7 dT 5t h7d7 htst 5M 2 Mk hnsn7sn71


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