impulse response / phase

hi,

is there a way to get the phase response from the impulse response of a
system, without the computation of the frequency response ?
or in another way: what information about the phase can I read from the
impulse response of a system ?

thanks
pascy

Pascy wrote:
> is there a way to get the phase response from the impulse response
> of a system, without the computation of the frequency response ?

The frequency response of a system is made up of the magnitude response
and the phase response. If your question is whether one can calculate
just the phase response from the impulse response withtout having to
calculate the magnitude response, then the answer is "yes".

> or in another way: what information about the phase can I read
> from the impulse response of a system ?

Well, all of it. Are you looking at an analogue or digital system?

Regards,
Andor

"Andor" <an2or@mailcircuit.com> writes:

> Pascy wrote:
> > is there a way to get the phase response from the impulse response
> > of a system, without the computation of the frequency response ?
> 
> The frequency response of a system is made up of the magnitude response
> and the phase response. If your question is whether one can calculate
> just the phase response from the impulse response withtout having to
> calculate the magnitude response, then the answer is "yes".

I'd be interested to know how, Andor. 
-- 
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124

Randy wrote:

>> The frequency response of a system is made up of the magnitude
>> response and the phase response. If your question is whether
>> one can calculate just the phase response from the impulse
>> response withtout having to calculate the magnitude response,
>> then the answer is "yes".
>
> I'd be interested to know how, Andor.

Assume a digital system with impulse response h(n). Take the
z-transform of that to compute the transfer function H(z). Then the
phase response is arg( H(e^(i w) ) ) and the magnitude response is |
H(e^(i w)) |. One doesn't need to compute the magnitude response to
compute the phase response (which was the question that I answered with
"yes").

Regards,
Andor

On 20 May 2005 09:08:55 -0700, "Andor" <an2or@mailcircuit.com> wrote:

>Randy wrote:
>
>>> The frequency response of a system is made up of the magnitude
>>> response and the phase response. If your question is whether
>>> one can calculate just the phase response from the impulse
>>> response withtout having to calculate the magnitude response,
>>> then the answer is "yes".
>>
>> I'd be interested to know how, Andor.
>
>Assume a digital system with impulse response h(n). Take the
>z-transform of that to compute the transfer function H(z). Then the
>phase response is arg( H(e^(i w) ) ) and the magnitude response is |
>H(e^(i w)) |. One doesn't need to compute the magnitude response to
>compute the phase response (which was the question that I answered with
>"yes").
>
>Regards,
>Andor

Hi Andor,

  Ha ha.  Words words words.

The original poster asked if we compute the 
phase response *without* computation of the frequency 
response.

You answered with "One doesn't need to compute the 
magnitude response to compute the phase response",
which I believe is correct.  But it seems to me that 
to compute the phase response we must compute the 
frequency response.  

I could be wrong.

See Ya',
[-Rick-]

> But it seems to me that
> to compute the phase response we must compute the
> frequency response.

If the Impulse Response is FIR we dont need to "compute" anything to
know the frequency response...

If h(n) is impulse response then the frequency response is

H(ejw) = h(0) + h(1)e-jw + h(2)e-2jw + ...

No computation needed.
Phase response is the angle of H(ejw)

Andor wrote:
> Randy wrote:
>
> >> The frequency response of a system is made up of the magnitude
> >> response and the phase response. If your question is whether
> >> one can calculate just the phase response from the impulse
> >> response withtout having to calculate the magnitude response,
> >> then the answer is "yes".
> >
> > I'd be interested to know how, Andor.
>
> Assume a digital system with impulse response h(n). Take the
> z-transform of that to compute the transfer function H(z). Then the
> phase response is arg( H(e^(i w) ) ) and the magnitude response is |
> H(e^(i w)) |. One doesn't need to compute the magnitude response to
> compute the phase response (which was the question that I answered
with
> "yes").

But the OP didn't use the term "magnitude response", he said
"frequency response". As far as I'm concerned, the frequency
response consists of the magnitude response and the phase
response.

But then, I agree with your answer to the *rephrased* question.

Rune

porterboy76@yahoo.com wrote:
> > But it seems to me that
> > to compute the phase response we must compute the
> > frequency response.
>
> If the Impulse Response is FIR we dont need to "compute" anything to
> know the frequency response...

It might be that I am particularly grumpy on a monday morning,
but this seems to be a very bold statement... to me, "know the
frequency response" means that a human can read/plot the numbers
without modifications and learn something about stop bands, pass
bands etc of the filter.

It is true that the impulse response contains this information,
but I am not capable of interpreting it, except in the very
crudest forms, from impulse response data. I need to tranform
the impulse response to the frequency domain to see the details.

> If h(n) is impulse response then the frequency response is
>
> H(ejw) = h(0) + h(1)e-jw + h(2)e-2jw + ...

Formally correct, yes, but I'm not capable of deducting anything
about stop-bands or pass-bands in the filter from this sort
of expression. I can only see that from the frequency response.

> No computation needed.
> Phase response is the angle of H(ejw)

And how do you plot arg(H(ejw)) versus w from the above
without doing any more computations?

Rune

I agree with you of course. I was just making the point that the
"frequency response" is known, technically, but doesn't tell you very
much. Extra computation is needed to obtain the phase response. But
this will generally give you the magnitude response as well.

In some specific cases the phase response can be deduced by simple
observation of the impulse response (symmetric or anti-symmetric
coefficients, Kronecker delta function etc.) but these cases are
probably way too trivial to be of interest to the OP.

> In some specific cases the phase response can be deduced by simple
> observation of the impulse response (symmetric or anti-symmetric
> coefficients, Kronecker delta function etc.) but these cases are
> probably way too trivial to be of interest to the OP.

Then again, I have heard of some people, geniuses or idiot savants, who
can perform instantaneous factorisation of arbitrary polynomials of
large degree... if you are one of them, you can tell a lot from the
impulse response by observation... whether you will know what to do
with it or not is another question...