1. 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

2. 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

3. 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

4. Book Chapter 6
Computer Engineering Department, Signal and Systems

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

6. 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

7. 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

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

9. 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

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

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

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

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

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

15. 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

16. 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

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

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

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

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