Download presentation

Presentation is loading. Please wait.

Published byKaitlyn Templeton Modified over 4 years ago

1
Signals and Systems Fall 2003 Lecture #7 25 September 2003 1.Fourier Series and LTI Systems 2.Frequency Response and Filtering 3.Examples and Demos

2
The Eigenfunction Property of Complex Exponentials CT: DT: "System Function" CT DT "System Function"

3
Fourier Series: Periodic Signals and LTI Systems So or powers of signals get modified through filter/system Includes both amplitude & phase

4
The Frequency Response of an LTI System CT Frequency response: DT Frequency response:

5
Frequency Shaping and Filtering By choice of H(j ω ) (or H(e j ω )) as a function of ω, we can shape the frequency composition of the output - Preferential amplification - Selective filtering of some frequencies Example #1: Audio System Adjustable Equalizer Speaker Filter Bass, Mid-range, Treble controls For audio signals, the amplitude is much more important than the phase.

6
Example #2:Frequency Selective Filters Filter out signals outside of the frequency range of interest Lowpass Filters: Only show amplitude here. Note for DT: Stopband PassbandStopband

7
Highpass Filters Remember: high frequency highest frequency in DT

8
Bandpass Filters Demo:Filtering effects on audio signals

9
Idealized Filters CT DT Note: |H| = 1 and H = 0 for the ideal filters in the passbands, no need for the phase plot. ω c cutoff frequency Stopband PassbandStopband

10
Highpass CT DT

11
Bandpass CT lower cut-off upper cut-off DT

12
Example #3:DT Averager/Smoother FIR (Finite Impulse Response) filters LPF

13
Example #4:Nonrecursive DT (FIR) filters Rolls off at lower ω as M+N+1 increases

14
Example #5:Simple DT Edge Detector DT 2-point differentiator Passes high-frequency components

15
Demo:DT filters, LP, HP, and BP applied to DJ Industrial average Original signFiltered sign Dollars Year

16
Example #6: Edge enhancement using DT differentiator Courtesy of Jason Oppenheim. Used with permission.

17
Example #7:A Filter Bank HPF BPF #1 BPF #M LPF

18
Demo:Apply different filters to two-dimensional image signals. Face of a monkey. Note: To really understand these examples, we need to understand frequency contents of aperiodic signals the Fourier Transform Image removed do to copyright considerations

Similar presentations

Presentation is loading. Please wait....

OK

Lecture 7: Basis Functions & Fourier Series

Lecture 7: Basis Functions & Fourier Series

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on abstract art definition Ppt on latest technology Ppt on field study 6 Ppt on content development services Ppt on wildlife and natural resources Ppt on sedimentation decantation and filtration Ppt on life of william shakespeare Ppt on instrument landing system theory Ppt on sources of energy for class 8th science Full ppt on electron beam machining metal