Re: digital filter in matlab and the bilinear transform

Fishilicious wrote:
Thanks for the reply! However I believe your definition of z=exp(sT) is
that of the Impulse Invariant. Also I think I should clarify my question a
little.

z = e^st is the definition of z, It applies to all digital difference equations.

When I call on a digital filter design function such as ellip() or
cheb2(), I'm asked to provide a normalized frequency from 0 to 1,
corresponding to 0 to fs/2. This means that I'm restricted to designing
filters that are restrained to that frequency range.

No digital signal can represent frequencies outside that range. Analof prototype filters go from zero to infinity. (Mathematically, anyway.) Analod signals, and hence analog filters go to to fs/2. If that limitation is irksome, stick to analog.

However, reading the
help menu for ellip() and cheb2(), the description says that the functions
first design the analog LP, then convert to the LP, HP, BP you want and use
the BILINEAR transform to get it back into discrete domain.

Yes. Moreover, since the BLT maps analog 0-oo to digital 0-fs/2, there is serious warping of significant frequencies as the upper limit is approached. For a practical design, you need to prewarp.

This is the part I'm having a tough time understanding. The bilinear
transform theoretically transforms the entire frequency axis -inf to inf Hz
to 1 rev of 0 to pi. That sounds to me like you should be able to design
anything from 0 to inf Hz. Yet the functions asks u to provide something
within a finite freq range.

Matlab is a tool for doing calculations. It has some canned black-box functions in various tool boxes. Whatever, it is nor useful for learning DSP (or bridge construction). It might, for a while, let you kid yourself that you know something that you can merely manipulate like the sorcerer's apprentice, but sooner or later you will realize that to do anything useful you actually have to learn the subject. If you find that discouraging, choose another profession, one in which the correctness of an answer is debatable.

...

Jerry
--
Engineering is the art of making what you want from things you can get.
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