Differentiators using Remez/Parks McClellan

Kumar Appaiah wrote:
> On Mar 4, 2:11 am, wrote:
>> The magnitude response of an ideal Hilbert transformer is the same as
>> the magnitude response of a wire, ignoring delay. Kumar writes that he's
>> content to ignore phase. So what does he want? A pure delay? How long?
>> That's what I have trouble with.
> 
> You are correct, and I realize that I should have worded my question a
> bit more carefully. I apologize for my carelessness.
> 
> OK, but still, my question remains this: whether someone has managed
> to design a Hilbert transformer and/or a differentiator successfully
> with Jake's code or GNU Octave? I have tried to debug it, but I can't
> seem to find where the mistake lies, or what I'm doing wrong.
> 
>> FIR impulse responses get very long when significant frequencies are
>> very small fractions of (or come very close to) Fs/2, whatever they're
>> intended for. HTs are no different.
> 
> I really don't care about the length now. As long as I get something
> close to +90 and -90 degrees of phase shift in most parts of the -pi
> to pi interval with gain close to 1 (magnitude), I am happy. All I
> want to know is "the right way" to use Jake's code for this purpose,
> as it doesn't seem to be doing the same thing Matlab is doing.

I don't know anything about Jakes code. What about it gives it 
particular importance? If it some sort of assignment?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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On Mar 4, 6:59 am, Jerry Avins wrote:
> I don't know anything about Jakes code. What about it gives it
> particular importance? If it some sort of assignment?

No, but it is a free implementation which has readable code, and I can
correlate the information with Oppenheim and Schafer.

Finally, I have got things working. I took the version of the code
available with GNU Octave forge, and set a high grid density, and
added instrumentation to their code to see how it works. In GNU
Octave, you can get a decent differentiator with:

remez(31, [0 1], [0 pi], 4096, 'differentiator')

Hilbert transformers also seem all right with this.

Thanks for the responses.

Kumar

On Mar 4, 6:58 am, Jerry Avins wrote:
> Real signals are noisy, and differentiators emphasize high-frequency
> noise. Even most analog "differentiators" are rolled off at high
> frequencies. Digital differentiators with an odd number of taps roll off
> properly. If you have time to waste, you can use a 5-tap differentiator,
> but more than that brings only diminishing returns as you try to reach
> Fs/4. Rick Lyons published an easily computed 5-tap differentiator. Ask
> him or Google for it.
>
> If you explain what you want the differentiator to do, we might be able
> to help you.

Thanks for the suggestion. I am looking through it.

Kumar