2
$\begingroup$

I'd like to design a Digital Differentiator with a pre-specified lowpass characteristic.

I've tried Wiener Filters (using inverseFFT to transform from frequency to time-domain), Savitzky Golay and others. Intuitively, I've come to the conclusion, that by specifying DFT points, i.e. uniformly distributed samples of the frequency response, one can achieve only a maximal low-pass frequency. For example using $N$ points, the minimal lowpass frequency would be $1/N$ bins of the FFT, thus $\pi/N$ $rad/sample$.

Is this notion correct?

And further along this path: if it's true, is this a universal boundary, or are there methods, where one can implicitly or explicitly specify not-equally sampled frequency points and thus achieve lower stopband frequencies with FIR filters?

For IIR filters I think this is no problem, since with a simple $1/(z+a)$ one can choose $a$ to achieve a variable stopband frequency just as in the continuous case.

|improve this question
$\endgroup$
1
$\begingroup$

The Remez exchange method isn't limited to DFT bin constraints so to answer your question, no FIR filters do not have the limitation you hypothesized.

If you can find METEOR, a program written in part by Tom Parks, you can be fairly free in your filter specifications provided they are feesable

and there is

http://gmeteor.sourceforge.net/

|improve this answer
$\endgroup$
  • $\begingroup$ Thanks, what remains to be stated is whether or not the limitation is true for methods using the DFT and then transform back to an impulse response. I suppose with such methods you only have so and so much freedom. $\endgroup$ – mike Jul 9 '17 at 7:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.