Deconvolution question

Suppose I have an acoustic guitar with a (relatively good-sounding)
peizo pickup (a K&K, for those interested).

I can mic the guitar and record the peizo simultaneously. But when
I deconvolve the miked signal against the peizo, the resulting
convolution signature isn't very coherent. Most convolution
signatures of this nature have a "spike" where the dominant
bucket is - this has just a "hump" or two.

I expect that the peizo is simply massively nonlinear with
respect to the microphone, but what I am not familiar with
is how pure phase transforms affect convolution, as opposed
to transforms more akin to sequences of allpass filters...
in "series" (?) Words fail me a bit here - my presumption
is that the convolution signature is just a sequence of
n allpass filters, each of time constant n*Fs .

What exactly am I looking at here?

Also, the "impulse" used is probably not very broadband. Still,
the convolution signature applied to the peizo doesn't do a
bad job of sounding like the miked channel, if you filter out
the repeating patterns in the signal.

--
Les Cargill

On May 9, 2:17&#4294967295;pm, Les Cargill <lcarg...@cfl.rr.com> wrote:
> Suppose I have an acoustic guitar with a (relatively good-sounding)
> peizo pickup (a K&K, for those interested).
>
> I can mic the guitar and record the peizo simultaneously. But when
> I deconvolve the miked signal against the peizo, the resulting
> convolution signature isn't very coherent. Most convolution
> signatures of this nature have a "spike" where the dominant
> bucket is - this has just a "hump" or two.
>
> I expect that the peizo is simply massively nonlinear with
> respect to the microphone, but what I am not familiar with
> is how pure phase transforms affect convolution, as opposed
> to transforms more akin to sequences of allpass filters...
> in "series" (?) Words fail me a bit here - my presumption
> is that the convolution signature is just a sequence of
> n allpass filters, each of time constant n*Fs .
>
> What exactly am I looking at here?
>
> Also, the "impulse" used is probably not very broadband. Still,
> the convolution signature applied to the peizo doesn't do a
> bad job of sounding like the miked channel, if you filter out
> the repeating patterns in the signal.
>
> --
> Les Cargill

How do you implement "deconvolution" exactly?  The devil
is in the details.

At any rate, I suspect that you the system that you are
trying to deconvolve has zeros in the frequency domain,
hence straightforward deconvolution will give a very
poor result.

Julius

Les Cargill wrote:
> 
> Suppose I have an acoustic guitar with a (relatively good-sounding)
> peizo pickup (a K&K, for those interested).
> 
> I can mic the guitar and record the peizo simultaneously. But when
> I deconvolve the miked signal against the peizo, the resulting
> convolution signature isn't very coherent. Most convolution
> signatures of this nature have a "spike" where the dominant
> bucket is - this has just a "hump" or two.
> 
> I expect that the peizo is simply massively nonlinear with
> respect to the microphone, but what I am not familiar with
> is how pure phase transforms affect convolution, as opposed
> to transforms more akin to sequences of allpass filters...
> in "series" (?) Words fail me a bit here - my presumption
> is that the convolution signature is just a sequence of
> n allpass filters, each of time constant n*Fs .
> 
> What exactly am I looking at here?
> 
> Also, the "impulse" used is probably not very broadband. Still,
> the convolution signature applied to the peizo doesn't do a
> bad job of sounding like the miked channel, if you filter out
> the repeating patterns in the signal.

Do a little groundwork with http://www.dspguide.com/ch17/2.htm. (Ignore 
the first set of figures. They go with text on the previous page.)

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

julius wrote:
> On May 9, 2:17 pm, Les Cargill <lcarg...@cfl.rr.com> wrote:
>> Suppose I have an acoustic guitar with a (relatively good-sounding)
>> peizo pickup (a K&K, for those interested).
>>
>> I can mic the guitar and record the peizo simultaneously. But when
>> I deconvolve the miked signal against the peizo, the resulting
>> convolution signature isn't very coherent. Most convolution
>> signatures of this nature have a "spike" where the dominant
>> bucket is - this has just a "hump" or two.
>>
>> I expect that the peizo is simply massively nonlinear with
>> respect to the microphone, but what I am not familiar with
>> is how pure phase transforms affect convolution, as opposed
>> to transforms more akin to sequences of allpass filters...
>> in "series" (?) Words fail me a bit here - my presumption
>> is that the convolution signature is just a sequence of
>> n allpass filters, each of time constant n*Fs .
>>
>> What exactly am I looking at here?
>>
>> Also, the "impulse" used is probably not very broadband. Still,
>> the convolution signature applied to the peizo doesn't do a
>> bad job of sounding like the miked channel, if you filter out
>> the repeating patterns in the signal.
>>
>> --
>> Les Cargill
> 
> How do you implement "deconvolution" exactly?

I use a software package that calculates the
deconvolution. This process is opaque to me; I
don't know what exactly it does. I presume it
uses one of the many "cookbook" algorithms I've
seen for applying FFT to produce deconvolutions.

> The devil
> is in the details.
> 
> At any rate, I suspect that you the system that you are
> trying to deconvolve has zeros in the frequency domain,
> hence straightforward deconvolution will give a very
> poor result.
> 

I'm not sure how to get this into the frequency domain.

> Julius

--
Les Cargill