113_1_Week03_print

113_1_Week03_print - EE 113: Digital Signal Processing Week...

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EE 113: Digital Signal Processing Week 3 1. Convolution - recap 2. Homogeneous Diff Equations
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Linear convolution ± More examples on the board
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3 Constant-Coefficient Difference Equation (CCDE) ± General spec. of DT, LSI, finite-dim sys: ± Rearrange for y [ n ] : ± WLOG, always have d 0 = 1 ² defined by { d k }, { p k } ² order = max( N , M ) d k y [ n k ] k = 0 N = p k x [ n k ] k = 0 M y [ n ] =− d k d 0 y [ n k ] k = 1 N + p k d 0 x [ n k ] k = 0 M
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4 Homogeneous Equations ± This does not correspond to a system, since the dependence on the input sequence x[n] is not specified. 0 0 [ ] 0, WLOG, always have = 1 N k k dy n k d = −= 0 [ ] [] , w i t h 0 N k k d yn k xn = == ± Hence, we are determining all the possible responses of the above class of systems to the zero input sequence!
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5 Solving CCDEs ± “Total solution” Complementary Solution satisfies Particular Solution for given forcing function x [ n ] y [ n ] = y c [ n ] + y p [ n ] d k y [ n k ] k = 0 N = 0 N-th order homogeneous equation
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6 Complementary Solution ± General form of unforced oscillation i.e. system’s ‘natural modes’
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This note was uploaded on 11/07/2009 for the course EE 113 taught by Professor Walker during the Spring '08 term at UCLA.

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113_1_Week03_print - EE 113: Digital Signal Processing Week...

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