introduction to signal processing...signal noise passband transition stopband 2ttlor demonstration...
TRANSCRIPT
![Page 1: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/1.jpg)
1. Linear and Nonlinear Phase2. Ideal and Nonideal Frequency-Selective
Filters3. CT & DT Rational Frequency Responses4. DT First- and Second-Order Systems
Introduction to Signal ProcessingSummer 2007
![Page 2: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/2.jpg)
Linear Phase
Result: Linear phase ⇔ simply a rigid shift in time, no distortionNonlinear phase ⇔ distortion as well as shift
CT
Question:
DT
![Page 3: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/3.jpg)
All-Pass Systems
CT
DT
![Page 4: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/4.jpg)
Demo: Impulse response and output of an all-pass system with nonlinear phase
![Page 5: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/5.jpg)
How do we think about signal delay when the phase is nonlinear?Group Delay
![Page 6: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/6.jpg)
Ideal Lowpass Filter
CT
← →
•Noncausal h(t <0) ≠ 0•Oscillatory Response — e.g. step response
![Page 7: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/7.jpg)
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
![Page 8: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/8.jpg)
CT Rational Frequency Responses
CT: If the system is described by LCCDEs, then
Prototypical Systems
![Page 9: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/9.jpg)
DT Rational Frequency Responses
If the system is described by LCCDE’s (Linear-Constant-Coefficient Difference Equations), then
![Page 10: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/10.jpg)
DT First-Order Systems
![Page 11: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/11.jpg)
Demo: Unit-sample, unit-step, and frequency response of DT first-order systems
![Page 12: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/12.jpg)
DT Second-Order System
![Page 13: Introduction to Signal Processing...signal noise Passband Transition Stopband 2Ttlor Demonstration of First and DT Systems 1st order system a 0.8 2nd order system rA2yln-21=xInl 0.8](https://reader033.vdocuments.us/reader033/viewer/2022042621/5f7664bb444d1c5113237d4b/html5/thumbnails/13.jpg)
Demo: Unit-sample, unit-step, and frequency response of DT second-order systems