Signals and Systems Fall 2003 Lecture #12 16 October 2003 1. - - PowerPoint PPT Presentation

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Signals and Systems Fall 2003 Lecture #12 16 October 2003 1. Linear and Nonlinear Phase 2. Ideal and Nonideal Frequency-Selective Filters 3. CT & DT Rational Frequency Responses 4. DT First- and Second-Order Systems Linear Phase CT

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1. Linear and Nonlinear Phase 2. Ideal and Nonideal Frequency-Selective Filters 3. CT & DT Rational Frequency Responses 4. DT First- and Second-Order Systems

Signals and Systems

Fall 2003 Lecture #12

16 October 2003

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Linear Phase

Result: Linear phase ⇔ simply a rigid shift in time, no distortion Nonlinear phase ⇔ distortion as well as shift CT Question: DT

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All-Pass Systems

CT DT

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Demo: Impulse response and output of an all-pass system with nonlinear phase

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How do we think about signal delay when the phase is nonlinear? Group Delay

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Ideal Lowpass Filter

← → ⎯

Noncausal h(t <0) ≠ 0
Oscillatory Response — e.g. step response

Overshoot by 9%, Gibbs phenomenon

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Nonideal Lowpass Filter

Sometimes we don’t want a sharp cutoff, e.g.
Often have specifications in time and frequency domain ⇒ Trade-offs

Step response

Freq. Response

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CT Rational Frequency Responses

CT: If the system is described by LCCDEs, then Prototypical Systems — First-order system, has only one energy storing element, e.g. L or C — Second-order system, has two energy storing elements, e.g. L and C

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DT Rational Frequency Responses

If the system is described by LCCDE’s (Linear-Constant-Coefficient Difference Equations), then

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DT First-Order Systems

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Demo: Unit-sample, unit-step, and frequency response

f DT first-order systems

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DT Second-Order System

scillations

decaying

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