ee338_formula_sheet

# ee338_formula_sheet - E E 338 For mulae Discrete-time...

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EE 338 Formulae Page 1 Discrete-time signals: x(n) = d(n) the unit impulse sequence x(n) = u(n) the unit step sequence x(n) = a n the exponential sequence x(n) = Asin ω ο n thesinusoidal sequence n = 2 π k if periodic = e j n the complex exponential sequence Some useful relationships: cos n = e j n + e j n 2 sin n = e j n e j n 2 j Linearity: y(n) = G a 1 x 1 (n) + a 2 x 2 [ ] = a 1 G x 1 [ ] + a 2 G x 2 [ ] Shift Invariance: = G z m [ ] [ ] = m G x(n) [ ] [ ] Convolution: if h(n) * x(n) = y(n) then x(n-m) * h(n-k) = y(n-m-k) additive delays x(n) * d(n) = x(n) identity Stability: h(n) 1 = n =−∞ n =∞ = M < ∞ LTI system Causality: h(n) = 0 for n < 0 LTI system The Difference Equation: a k y(n k) = b m x(n m) m =− M 1 M 2 k = 0 N The Discrete-Time Fourier Transform: H e j ( ) = h(n) e j n n =− ∞ Properties of the DTFT: H e j ( ) = H e j ( ) for real h(n) H e j ( ) is real if h(n) = h(-n) H e j ( ) is imaginary if h(n) = -h(-n) The Inverse Discrete-Time Fourier Transform: = 1 2 X e j ( ) e j n d The DTFT and the Difference Equation: H(e j ) = Y(e j ) X(e

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## This note was uploaded on 12/20/2010 for the course E E 338 taught by Professor Vicky during the Spring '10 term at University of Alberta.

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ee338_formula_sheet - E E 338 For mulae Discrete-time...

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