signal and system lecture 12
TRANSCRIPT
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1. Linear and Nonlinear Phase
2. Ideal and Nonideal Frequency-SelectiveFilters
3. CT & DT Rational Frequency Responses
4. DT First- and Second-Order Systems
Signals and SystemsFall 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
φ
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Ideal Lowpass Filter
CT
← → ⎯
• 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 responseFreq. 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
of DT first-order systems
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DT Second-Order System
oscillations
decaying
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Demo: Unit-sample, unit-step, and frequency response of
DT second-order systems