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Basic Signals and Systems Formulas

# Basic Signals and Systems Formulas - -= N n n N jk k e n x...

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Basic Formulas Signals and Systems Concordia University Note 1: ] [ n x and ] [ n y are input and output of a discrete LTI system, respectively. Note 2: ) ( t x and ) ( t y are input and output of a continuous LTI system, respectively. Convolution: - - = τ τ δ τ d t x t x ) ( ) ( ) ( - - = τ τ τ d t h x t y ) ( ) ( ) ( +∞ -∞ = - = k k n k x n x ] [ ] [ ] [ δ +∞ -∞ = - = k k n h k x n y ] [ ] [ ] [ Fourier series: t T jk k k e a t x ) / 2 ( ) ( π -∞ = = - = T t T jk k dt e t x T a ) / 2 ( ) ( 1 π n N jk N k k e a n x
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Unformatted text preview: -= N n n N jk k e n x N a ) / 2 ( ] [ 1 Fourier Transform: ( ) Ï‰ d e j X t x t j âˆ« âˆž âˆž-= ) ( 2 1 ( ) dt e t x j X t j âˆ« âˆž âˆž--= ) ( ( ) d e e X n x n j j âˆ« = 2 2 1 ] [ ( ) âˆ‘ +âˆž-âˆž =-= n n j j e n x e X ] [...
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