Mathematica Convolution property for InverseZtransform in Mathematica

[Constantinos]

Hey!

So when I enter this in Mathematica

In[246] = ZTransform[Sum[f[k] g[k - n], {k, 0, n}], n, z]
InverseZTransform[%, z, n]

I get:
Out[246] = ZTransform[f[n], n, z] ZTransform[g[-n], n, z]
Out[247] = InverseZTransform[ZTransform[f[n], n, z] ZTransform[g[-n], n, z], z,
n]

Which means that although the software uses the convolution property of the Z-transform, it doesn't use it for the InverseZTransform. Any ideas how to make it use it?

Thanks!

 

[Bill Simpson]

Perhaps it cannot determine what the inverse Z is. Did you define what f[] and g[] were or are you assuming this is true for all possible f and g? Are there special cases where it is not?

Try defining a really simple f[] and g[] where you know a simple Z exists and the simple inverse exists. See if that uses the inverse.

It also isn't clear to me what you input is. Not separating expressions with semicolons and using newlines instead may come back to bite you. There has been a history of bugs and surprises when doing that.