1. Everything You Ever Wanted to Know About Filters*
Class 5: Digital Filters III: Finite Impulse Response Filters / Conclusion
June 12, 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. Why the FIR?
Amongst all the obvious advantages that digital filters offer, the FIR filter can guarantee linear phase characteristics.
Neither analogue or IIR filters can achieve this.
There are many commercially available software packages for filter design. However, without basic theoretical knowledge of the FIR filter, it will be difficult to use them.

5. Finite Impulse Response Filter

6. Properties of an FIR Filter
Filter coefficients:
x[n] represents the filter input,
bk represents the filter coefficients,
y[n] represents the filter output,
N is the number of filter coefficients (order of the filter).

7. Properties of an FIR Filter
Filter coefficients:
FIR equation
Filter structure

8. Properties of an FIR Filter
If the signal x[n] is replaced by an impulse [n] then:

9. Properties of an FIR Filter
Finally:
where
The coefficients of a FIR filter are the same as the impulse response samples of the filter!

10. Frequency Response of an FIR Filter
By taking the z-transform of h[n] H(z):
Replacing z by ej in order to find the frequency response leads to:

11. Frequency Response of an FIR Filter
Since e-j2k = 1 then:
Therefore:
FIR filters have a periodic frequency response and the period is 2.

12. Phase Linearity of an FIR Filter
A causal FIR filter whose impulse response is symmetrical is guaranteed to have a linear phase response.
Even symmetry
Odd symmetry

13. Design Procedure
To fully design and implement a filter five steps are required:
(1) Filter specification.
(2) Coefficient calculation.
(3) Structure selection.
(4) Simulation (optional).
(5) Implementation.

14. Filter Specification - Step 1

15. Coefficient Calculation - Step 2
There are several different methods available, the most popular are:
Window method.
Frequency sampling.
Parks-McClellan.
We will just consider the window method.

16. Window Method
First stage of this method is to calculate the coefficients of the ideal filter.
This is calculated as follows:

17. Window Method
Second stage of this method is to select a window function based on the passband or attenuation specifications, then determine the filter length based on the required width of the transition band.

18. Window Method
The third stage is to calculate the set of truncated or windowed impulse response coefficients, h[n]:
for
Where:
for

19. Designing in the Real World
Matlab has been a tool of choice for many for many years for designing FIR and IIR filters
Like we saw for analog filters, there are an increasing amount of vendor-supplied tools, particularly for using ‘DSP enabled’ microcontrollers
For those of us in the ARM world, we return to CMSIS…

20. CMSIS and CMSIS-DSP

21. Filters in CMSIS DSP
• Biquad Cascade IIR Filters Using Direct Form I Structure • Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure • High Precision Q31 Biquad Cascade Filter • Convolution • Partial Convolution • Correlation • Finite Impulse Response (FIR) Decimator • Finite Impulse Response (FIR) Filters • Finite Impulse Response (FIR) Lattice Filters • Finite Impulse Response (FIR) Sparse Filters • Infinite Impulse Response (IIR) Lattice Filters • Least Mean Square (LMS) Filters • Normalized LMS Filters • Finite Impulse Response (FIR) Interpolator

22. But WAIT – There’s more…
Upcoming blog on integrating digital filters on ARM
Posted ‘hands-on’ project(s) on using CMSIS and K64
Stay tuned to Design News website as well as my company (see last slide)

23. Filters – a Review Passive filters: Active Filters:
simple to implement
require no power supplies
Have some finite Z
Active Filters:
Require power
Subject to clipping, saturation, and amp BW
More components and cost
Allow amplification

24. Filters – part 2 Digital Filters
Ideal if the signals are already digitized (sampled)
Allows for additional effects (warping, etc)
No additional parts or real estate *
Provide finite time delay
Aliasing

25. 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

26. 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)