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

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

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

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

Basic Digital Filters  

Let’s Simplify This  

Which Defines a FIR Filter

Let’s Simplify This  

Which Defines an IIR Filter

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.

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

Basic Filter Specification

Butterworth Low-pass Filter

Determining Structure  

Coefficients  

Coefficients  

And there is our filter

Chebyshev  

Chebyshev vs Butterworth

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

Comparison

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

Please stick around as I answer your questions! Please give me a moment to scroll back through the chat window to find your questions 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) c.j.lord@ieee.org http://www.blueridgetechnc.com http://www.linkedin.com/in/charleslord Twitter: @charleslord