[music-dsp] Poles and zeros -> entirely positive impulse response?

[Thomas Block]

Hiho,

> If i want a filter with an impulse response positive all the way,
> must the poles and zeros be real? (Intuition and little
> experimentation say complex poles cause undulation).

Some thoughts:
-    the forward part is fairly easy. Your zeroes form an FIR-filter - so,
take care that the coefficients are positive.
This means: your zeroes must form a polynom with positive coefficients.

-    the recursive part...
Afaik the impulse response of a single pole is of the form
    y(n) = a ^n
with a designing the pole position in the z-plane. For this term to be
positive (and stable), the condition is
    0< a<1.
This means: your recursive part must form a polynom with only positive roots
smaller than one.

Just my 2 Pfennige...

Where do you need this - just an academic question???

Tom
--
*****************************  TC|WORKS  *******************************
                       Dipl.-Ing. Thomas Block
            Flughafenstrasse 52B * D22335 Hamburg * Germany
              Phone +49.40.531.08 329   Fax +49.40.531 08 31

                        <http://www.tcworks.de/>
*******************     A TC Electronic company   **********************



dupswapdrop -- the music-dsp mailing list and website: subscription info,
FAQ, source code archive, list archive, book reviews, dsp links
http://shoko.calarts.edu/musicdsp/