Wonderful! Digital Filter (Part One)
One of typical applications of digital signal processing is digital filter. Filtering is to cut unnecessary parts of a signal or extract necessary frequency area from a signal. In analog circuits, filtering is realized by composing capacitors, inductors and registers. The following figure shows the simplest low-pass filter circuit.
As people who have learned the basics of AC circuits may easily understand, higher capacitor value relatively to the register value makes the cutoff frequency lower. This is supposed to be sensuously understood if one has a basic knowledge of capacitors and registers.
Now, what is the simplest digital filer? The following figure shows the configuration of a first order low-pass digital filter corresponding to the analog filter shown in the previous figure.
Triangles in the figure represent a multiplier and the Z-1 represents one sample delay. Since the multiplier connected directly to the output operates only for the gain adjusting, filtering is actually realized by one multiplication and one addition.
The frequency characteristic shown in the above figure is based on a1 as 0.9 and b0 is 0.1. You can see the gain is gradually attenuated in frequencies higher than approximately 0.01Fs. You can also find in around 0.1Fs that the gain halves as the frequency doubles, that is, the attenuation characteristics is -6dB/Octave. Therefore, we can call it a decent first order filter.
Fiddling the a1 and b0 values in this first order filter, we may get desired frequency characteristics but it would be impossible in higher order filters. (Clicking the "Calc" button after putting values on a1 and b0, you can get the corresponding frequency characteristics.) What is required in real situations is a higher order filter with sharp frequency characteristics in the most cases. What we should do? It will be explained in the next page.
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