Signal and Systems Chapter 6: Time-Frequency Characterization of Systems Magnitude/Phase of Transforms and Frequency Responses Linear and Nonlinear Phase Ideal and Nonideal Frequency-Selective Filters CT & DT Rational Frequency Responses DT First- and Second-Order Systems

Magnitude and Phase of FT, and Parseval Relation Book Chapter#: Section# Magnitude and Phase of FT, and Parseval Relation Computer Engineering Department, Signal and Systems

Book Chapter#: Section# Effect of Phase Not on signal energy distribution as a function of frequency Can have dramatic effect on signal shape/character Constructive/Destructive interference Is that important? Depends on the signal and the context Computer Engineering Department, Signal and Systems

Book Chapter 6 Computer Engineering Department, Signal and Systems

Log-Magnitude and Phase Book Chapter 6 Log-Magnitude and Phase Computer Engineering Department, Signal and Systems

Plotting Log-Magnitude and Phase Book Chapter 6 Plotting Log-Magnitude and Phase Plot for ω ≥ 0, often with a logarithmic scale for frequency in CT Computer Engineering Department, Signal and Systems

A Typical Bode plot for a second-order CT system Book Chapter 6 A Typical Bode plot for a second-order CT system 40 dB/decade Changes by -π Computer Engineering Department, Signal and Systems

Book Chapter 6 A typical plot of magnitude and phase of second order DT frequency response Computer Engineering Department, Signal and Systems

Linear phase Question: What about H (ejω) = e-j ω α, α ≠ integer? CT Book Chapter 6 Linear phase CT Result: Linear phase ⇔ simply a rigid shift in time, no distortion Nonlinear phase ⇔ distortion as well as shift DT Question: What about H (ejω) = e-j ω α, α ≠ integer? Computer Engineering Department, Signal and Systems

All-Pass Systems Book Chapter 6 Computer Engineering Department, Signal and Systems

Book Chapter 6 Demo:Impulse response and output of an all-pass system with nonlinear phase Computer Engineering Department, Signal and Systems

Book Chapter 6 How do we think about signal delay when the phase is nonlinear? Group Delay Computer Engineering Department, Signal and Systems

Ideal Low pass Filter Book Chapter 6 Computer Engineering Department, Signal and Systems

Nonideal Low pass Filter Book Chapter 6 Nonideal Low pass Filter Computer Engineering Department, Signal and Systems

CT Rational Frequency Responses Book Chapter 6 CT Rational Frequency Responses CT: If the system is described by LCCDEs, then Prototypical System 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 Computer Engineering Department, Signal and Systems

DT Rational Frequency Responses Book Chapter 6 DT Rational Frequency Responses If the system is described by LCCDE’s (Linear-Constant-Coefficient Difference Equations), then Computer Engineering Department, Signal and Systems

DT First-Order Systems Book Chapter 6 DT First-Order Systems Computer Engineering Department, Signal and Systems

Book Chapter 6 Demo: Unit-sample, unit-step, and frequency response of DT first-order systems Computer Engineering Department, Signal and Systems

DT Second-Order System Book Chapter 6 DT Second-Order System Computer Engineering Department, Signal and Systems

Book Chapter 6 Demo: Unit-sample, unit-step, and frequency response of DT second-order systems Computer Engineering Department, Signal and Systems