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## What approach does the "deconvolve" function in Prime take?

Is there documentation on this?

17 REPLIES 17

## Re: What approach does the "deconvolve" function in Prime take?

I'm sure it's the same as in the Mathcad 15 Signal Processing extension pack. See the attached pdf.

## Re: What approach does the "deconvolve" function in Prime take?

• convolve(vx, vy, [t], [s])
• deconvolve(vz, vx)

## Re: What approach does the "deconvolve" function in Prime take?

I bet it's the same function though, just with a name change.

Yes, it is.

## Re: What approach does the "deconvolve" function in Prime take?

I'm also wondering about how the zero-divides are avoided.  What kind

of artifacts might I expect.

I notice that "convolve" looks like it also uses the transform approach.

It will return complex numbers even given two purely real vectors.  The

imaginary components are big enough to cause problems sending the result

to the plots.

## Re: What approach does the "deconvolve" function in Prime take?

 I'm also wondering about how the zero-divides are avoided.  What kind of artifacts might I expect.

I don't think they are avoided. Division by zero will almost certainly cause an error. Division by something very close to zero may produce a big spike. Since that's close to a delta function it will result in big sinusoidal oscillations in the deconvolved data.

 I notice that "convolve" looks like it also uses the transform approach. It will return complex numbers even given two purely real vectors.  The imaginary components are big enough to cause problems sending the result to the plots.

Just take the real part.

## Re: What approach does the "deconvolve" function in Prime take?

The straightforward deconvolve would be to take the transform and use it

to divide into the other transform.  But there would likely be a zero

somewhere in the denominator transform.  As I understand it, there are

techniques to keep that from being a problem.

Taking the real part works.  It's just that I had to get through the error message, look

into the intermediate results in order to find out.  Noting it in the description would have

Thanks.

## Re: What approach does the "deconvolve" function in Prime take?

 The straightforward deconvolve would be to take the transform and use it to divide into the other transform.  But there would likely be a zero somewhere in the denominator transform.  As I understand it, there are techniques to keep that from being a problem.

You can find the spike (the magnitude of the derivative is huge) and interpolate through it, then do the inverse FT. I don't think the built-in Mathcad function does anything like that though. You would have to write your own deconvolve function.

Out of curiosity, what's the physical system you are looking at where you wish to deconvolve with a function that has zeros after the FT?

## Re: What approach does the "deconvolve" function in Prime take?

Essentially any signal that is aperiodic and bounded in time would have

a spectrum with zero crossings.  Consider the transform of a "square pulse",

or doing a "box car average".

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