How to Design Higher-Order Discrete-Time Filters?

I've gotten a lot of mileage out of this:

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and this:

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I've implemented both of these filters in fixed-point integer forms for the STM8A and one for the ARM. They work as advertised.

They are parameterized so that one can choose "alpha" ... this is the way most folks would do it, I'm sure.

How would I approach "notch" filters or higher-order filters if I were to implement them for microcontrollers?

There is more than one degree of freedom for a second-order filter ... how should I think about that?

Any books out there that I should read?

Decades ago I had a signals and systems class where all the transforms were covered, but it has been a while ...


Reply to
David T. Ashley
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It is certainly one very sensible way to go.

Look for an appropriate recipe...

Seriously, that's not too far off. Notch filters happen to be particularly difficult to get the math right if you're making one from scratch, by the way.

It depends on what you're trying to do. Generally, when you build a 2nd- order filter (or a higher-order filter from 2nd-order sections), you use one of the common "direct form" architectures. There's advantages to each -- and danged if it hasn't been long enough since I've needed to make one that I can't remember!!

Q or damping ratio for 2nd-order filters.

Passband ripple, stopband ripple, and shape factor (or transition band steepness) for higher-order filters.

Often neglected, but essential, is the degree to which quantization noise gets amplified (there's a whole direct-form 1 vs. direct-form 2 spiel out there on just this subject).

Rick Lyons' "Understanding Digital Signal Processing" is probably best if you have just one book to go on. I feel that it doesn't quite get the beginner all the way up from nothing to understanding -- but there's no one book that does, to my knowledge.

If you were interested in control systems I'd direct you to my book. In fact, where Rick's book glosses over the z transform, I think mine does better. Oppenheim & Wilski's "Signal Processing" is the de-facto standard book, but you may find it rough going without taking a class to go with it (for that matter, you may find it rough going _with_ a class).

Do you still have the book?

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Reply to
Tim Wescott

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