Shows the effects of coefficient quantization on frequency response and pole/zero positions.

Do This:

1. Notice the black plot on the top left figure matches Figure 6.40a on page 380.
2. Click on the zoom control below the figure and zoom in on the flat part of the frequency response around 0 dB. Once zoomed it should look like Figure 6.40b.
3. Select Fixed which is above the right plot. The plots now show the frequency response and poles and zeros for the fixed-point coefficients.
4. Notice there are poles outside the unit circle and the impulse reponse, plotted below, "blows up".
5. Click on the zoom control for the frequency reponse and select the bottom left icon. This will show the whole plot again. Notice the fixed-point response (shown in red) is very different from the floating response. This is for a IIR Direct Form I implementation.
6. Change the target structure to IIR Cascaded Second-Order Sections Form I. This different structure is a much better implementation for fixed-point. Notice the fixed- and floating-point responses are almost the same. Also notice the poles and zeros are in almost the sample positions, and the filter is stable.
7. Reduce the number of bits used per a coeffient by adjusting the top left slider. How few bits can you use before the frequency response changes much?
8. Notice the poles moving around as you reduce the number of bits. At what point does the filter become unstable?
9. Try changing the number of bits per b coefficient. What affect does that have?
10. How few bits can you use for both poles and zeros and still have a stable filter?
11. Switch back to the IIR Direct Form I structure. How few bits do you need for stability?

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Oppenheim and Schafer, Discrete-Time Signal Processing ISBN 0-13-198842-5.
© 2016 Pearson Education, Inc.