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SP 2005 CH 3 DT Systems 1

SP 2005 CH 3 DT Systems 1 - EE 3120 Chapter 3 Time Domain...

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EE 3120 Chapter 3 Time Domain Analysis of Discrete-Time Systems
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Examples of D-T systems Savings Account (natural) Sales Estimate (natural) Population Model (natural) Loan amortization schedule Digital Differentiator (sampled C-T) Digital Integrator (sampled C-T)
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Classification of D-T systems (Similar to C-T systems) Linearity – homogeneous and additive Time variance – shifted input result sin shifted output Causality – out due to current or past input (not future) Invertibility – system can be created to eliminate effect of another system Stability – BIBO Memory – Output depends on past input
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Describing DT LITL Systems D-T LTIL : Discrete-time linear time invariant lumped systems can be described a few different ways. Impulse response Difference equation Recursive (iterative) Advanced form Delayed form Non-recursive The total response of a linear system can be broken up into the zero input response and the zero state response total zsr zir y y y = +
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Deriving the System Equation A system equation can be derived from a signal flow graph or from our knowledge of the physical laws of the system. (KVL, KCL) Example: Savings account. Initial investment x is made at the first month. Interest accrues at
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