113_1_Week04_print

113_1_Week04_print - 1 EE 113: Digital Signal Processing...

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1 EE 113: Digital Signal Processing Week 4 1. Zero input and zero state responses 2. The z-transform
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2 Goal ± Devise
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3 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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4 In this lecture ± we are interested in the more general case in which the CCDE need not describe an LTI system ± the techniques developed 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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5 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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6 Solutions ± Second, we present another procedure for general input sequences; the procedure will rely on the use of convolution and on the concept of the zero-state response. ± Z-transform techniques
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7 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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8 Particular solution ± A particular solution of a CCDE is a solution that satisfies the CCDE for the given input sequence x[n]. ± No initial conditions enter into the calculation. ± Procedure: ± Assume that the solution y(n) is given by a sum of functions of the same mathematical form as the input x(n), and of delayed versions of it that differ in form from x(n).
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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_Week04_print - 1 EE 113: Digital Signal Processing...

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