113_1_Week04-part1

113_1_Week04-part1 - EE 113: Digital Signal Processing Week...

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EE 113: Digital Signal Processing Week 4 1. Zero input and zero state responses 2. The z-transform
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Solving CCDEs ± “Total solution” Complementary Solution satisfies Particular Solution for given forcing function x [ n ] [] hp yn y n = + d k y [ n k ] k = 0 N = 0 N-th order homogeneous equation
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Summary of what we know already ± we know how to determine the complete solution of a CCDE for a relaxed and causal system (an LTI system) ± first determine the impulse response sequence by solving a homogeneous equation ± then convolve it with the given input sequence
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In this lecture ± we are interested in the more general case in which the CCDE need not describe an LTI system ± these techniques can therefore be applied to both LTI and non- LTI systems ± in the case of LTI systems, they can help avoid some of the effort that goes into computing the impulse response and then the required convolution
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Solutions ± First, we develop a procedure for determining the complete response of CCDE for a restricted (yet important!) class of input sequences
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113_1_Week04-part1 - EE 113: Digital Signal Processing Week...

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