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 Presented by:

This Weeks 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 Presented by: 2

This Weeks 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 Presented by: 3 Basic Digital Filters

We saw yesterday that the digital filter has a basic structure of: Presented by: 4 Basic Digital Filters Presented by: 5

Lets Simplify This Presented by: 6 Which Defines a FIR Filter Presented by: 7

Lets Simplify This Presented by: 8 Which Defines an IIR Filter Presented by: 9

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. Presented by: 10 IIR Filter Design IIR Filters are typically based on a direct transform of known analog filters Thus we have very similar design stages: (1) (2)

(3) (4) Filter specification Structure and coefficient calculation Simulation (optional) Implementation Lets look at an example Presented by: 11

Basic Filter Specification |H(f)| pass-band stop-band 1 f c : cut-off frequency

f(norm) f s /2 (a) |H(f)| (dB) pass-band transition band

|H(f)| (linear) stop-band p 1 p 0 1

1 p pass-band ripple -3 stop-band ripple s

f s /2 f sb : stop-band frequency f c : cut-off frequency f pb : pass-band frequency s f(norm)

(b) Presented by: 12 Butterworth Low-pass Filter Presented by: 13

Determining Structure Presented by: 14 Coefficients Presented by: 15

Coefficients Presented by: 16 And there is our filter Presented by: 17

Chebyshev Presented by: 18 Chebyshev vs Butterworth Presented by: 19

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 Presented by: 20

Comparison Presented by: 21 This Weeks 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 Presented by: 22 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) [email protected] http://www.blueridgetechnc.com http://www.linkedin.com/in/charleslord Twitter: @charleslord Presented by: 23

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