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
Linear Phase
Result,Linear phase? simply a rigid shift in time,no distortion
Nonlinear phase? distortion as well as shift
CT
Question:
DT
All-Pass Systems
CT
DT
Demo,Impulse response and output of an all-pass
system with nonlinear phase
How do we think about signal delay when the phase is nonlinear?
Group Delay
φ
Ideal Lowpass Filter
CT
← →?
Noncausal h(t <0) ≠ 0
Oscillatory Response — e.g,step response
Overshoot by 9%,
Gibbs phenomenon
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
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
DT Rational Frequency Responses
If the system is described by LCCDE’s (Linear-Constant-Coefficient
Difference Equations),then
DT First-Order Systems
Demo,Unit-sample,unit-step,and frequency response
of DT first-order systems
DT Second-Order System
oscillations
decaying
Demo,Unit-sample,unit-step,and frequency response of
DT second-order systems
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
Linear Phase
Result,Linear phase? simply a rigid shift in time,no distortion
Nonlinear phase? distortion as well as shift
CT
Question:
DT
All-Pass Systems
CT
DT
Demo,Impulse response and output of an all-pass
system with nonlinear phase
How do we think about signal delay when the phase is nonlinear?
Group Delay
φ
Ideal Lowpass Filter
CT
← →?
Noncausal h(t <0) ≠ 0
Oscillatory Response — e.g,step response
Overshoot by 9%,
Gibbs phenomenon
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
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
DT Rational Frequency Responses
If the system is described by LCCDE’s (Linear-Constant-Coefficient
Difference Equations),then
DT First-Order Systems
Demo,Unit-sample,unit-step,and frequency response
of DT first-order systems
DT Second-Order System
oscillations
decaying
Demo,Unit-sample,unit-step,and frequency response of
DT second-order systems