Re: Simple question about minimum phase filters

On Feb 17, 11:48 am, Sam <samke...@xxxxxxxxx> wrote:
On Feb 16, 4:15 pm, Rune Allnor <all...@xxxxxxxxxxxx> wrote:



On 16 Feb, 20:45, Sam <samke...@xxxxxxxxx> wrote:

Can a minimum phase filter have zeroes on the unit circle? The
definition from Oppenheim and Schafer says all poles and zeros must be
outside the UC.

What edition of O&S is this? The common convention is that
poles need to be *inside* the unit circle in order to get a
stable causal filter. Not a big deal, though, but below I
stick with the common convention.

I've seen other definitions

Where?

that say the poles and
zeros can also be on the UC,

No poles on the unit circle. If there are, the system
will have an undamped sinucoidal as part of the impulse
response, which will cause the integral of the impulse
response to become unbounded. Which is no good.

This remark on poles is alone enough to question these
other sources you have seen.

and when I design a min phase filter in
MATLAB, I get one with lots of zeros on the UC. Which is correct?

If matlab did it this way, who are we to object?

I don't know if zeros exactly on the unit circle destroys
the mininum phase property or not. I would, off the top
of my head, assume that a zero exactly on the unit circle
leaves the min/max phase question undefined, as one can
choose to trace the phase function inside or outside the
zero.

Even if this hunch should turn out to be wrong, it is not
a very good idea having zeros on the unit circle anyway,
as the filter will no longer be invertible even with perfect
arithmetics. Poles must, with the common convention, be
strictly inside the unit circle. In practice, numerical
inaccuracies might push the poles just outside and cause
the filter to become unstable.

So at least for practical purposes zeros of min phase
filters need to be strictly inside the unit circle.

Rune

Oops, i'm terribly sorry. I meant to say the poles and zeros must be
INSIDE the unit circle(i should have proofread my post). However, this
definition, the UC seems to be excluded

http://www.dsprelated.com/dspbooks/filters/Definition_Minimum_Phase_F...

So, my question was basically just, do the zeros have to be completely
inside the UC, or can they be right on it and still count as a minimum
phase filter.

I would say yes. The reason being that an integrator has a pole just
on the unit circle at z=1 and is classified as stable.
(well critically stable).

H.
.

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