R help - Aug 2008 - deconvolution: Using the output and a IRF to get the input

Hi,

Maybe someone could give me some pointers for my problem. So far I have 
not found a good solution, maybe it is just ill posed?

I have a signal that is the result of an input signal convolved with a 
given impulse response function (IRF) plus noise. I want to use the this 
signal and the IRF to determine the underlying input signal. In my 
naivety I thought this just might be a deconvolution problem. But here I 
found only routines that use the input signal and the output signal to 
get the IRF. Is it possible to derive the input signal when output and 
IRF are given? If so, how could I do this with R?

Thanks a lot for any hints,
wolf

Hi Wolf,

Without noise you could use FFT, i.e. FFT of a convolution is the product of the
individual FFTs and so you get the FFT of your input signal and using inverse
FFT you get the signal itself.
When there is noise you must experiment. You may want to filter the response
before doing FFT. Whay do you know about the noise?

Regards,

Moshe.


--- On Mon, 25/8/08, wolf zinke <wolfzinke at gmx.net> wrote:
> From: wolf zinke <wolfzinke at gmx.net>
> Subject: [R] deconvolution: Using the output and a IRF to get the input
> To: r-help at r-project.org
> Received: Monday, 25 August, 2008, 8:22 AM
> Hi,
> 
> Maybe someone could give me some pointers for my problem.
> So far I have 
> not found a good solution, maybe it is just ill posed?
> 
> I have a signal that is the result of an input signal
> convolved with a 
> given impulse response function (IRF) plus noise. I want to
> use the this 
> signal and the IRF to determine the underlying input
> signal. In my 
> naivety I thought this just might be a deconvolution
> problem. But here I 
> found only routines that use the input signal and the
> output signal to 
> get the IRF. Is it possible to derive the input signal when
> output and 
> IRF are given? If so, how could I do this with R?
> 
> Thanks a lot for any hints,
> wolf
> 
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