1. Everything You Ever Wanted to Know About Filters*
Class 4: Digital Filters II: Infinite Impulse Response Filters
June 11, 2015
Charles J. Lord, PE President, Consultant, Trainer Blue Ridge Advanced Design and Automation
* But were afraid to ask

2. This Week’s Agenda
6/8 Analog Filters I: Resonant Circuits and Passive Filters 6/9 Analog Filters II: Active Filters 6/10 Digital Filters I: Sampling and the Z-Transform 6/11 Digital Filters II: Infinite Impulse Response Filters 6/12 Digital Filters III: Finite impulse response filters and Conclusion

3. This Week’s Agenda
6/8 Analog Filters I: Resonant Circuits and Passive Filters 6/9 Analog Filters II: Active Filters 6/10 Digital Filters I: Sampling and the Z-Transform 6/11 Digital Filters II: Infinite Impulse Response Filters 6/12 Digital Filters III: Finite impulse response filters and Conclusion

4. Basic Digital Filters
We saw yesterday that the digital filter has a basic structure of:

5. Basic Digital Filters

6. Let’s Simplify This

7. Which Defines a FIR Filter

8. Let’s Simplify This

9. Which Defines an IIR Filter

10. IIR Infinite Impulse Response (IIR) filters are the first choice when:
Speed is paramount.
Phase non-linearity is acceptable.
IIR filters are computationally more efficient than FIR filters as they require fewer coefficients due to the fact that they use feedback or poles.
However feedback can result in the filter becoming unstable if the coefficients deviate from their true values.

11. IIR Filter Design
IIR Filters are typically based on a direct transform of known analog filters
Thus we have very similar design stages:
Filter specification
(2) Structure and coefficient calculation
(3) Simulation (optional)
Implementation
Let’s look at an example

12. Basic Filter Specification

13. Butterworth Low-pass Filter

14. Determining Structure

15. Coefficients

16. Coefficients

17. And there is our filter

18. Chebyshev

19. Chebyshev vs Butterworth

20. Elliptic Filter
If we look at the zeroes of the Chebyshev filter, we note that they fall on a well-known ellipse within the unit circle
We can modify this slightly and come up with a familiar filter that now has equal ripple in both the passband and stopband as well as desirable cutoff characteristics
This is the Elliptic filter

21. Comparison

22. This Week’s Agenda
6/8 Analog Filters I: Resonant Circuits and Passive Filters 6/9 Analog Filters II: Active Filters 6/10 Digital Filters I: Sampling and the Z-Transform 6/11 Digital Filters II: Infinite Impulse Response Filters 6/12 Digital Filters III: Finite Impulse Response Filters and Conclusion

23. Please stick around as I answer your questions!
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I will stay on chat as long as it takes to answer!
I am available to answer simple questions or to consult (or offer in-house training for your company)