Convolution property for InverseZtransform in Mathematica

In summary, the conversation discusses the use of the convolution property of the Z-transform in Mathematica, specifically in the InverseZTransform function. The speaker suggests defining simple functions to see if the inverse Z-transform is used, and raises the possibility of bugs when using newlines instead of semicolons in expressions.
  • #1
Constantinos
83
1
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!
 
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  • #2
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.
 

What is the Convolution property for InverseZtransform in Mathematica?

The Convolution property for InverseZtransform in Mathematica is a mathematical property that allows you to find the inverse Z-transform of a product of two Z-transforms by convolving their corresponding sequences in the time domain.

How is the Convolution property used in Mathematica?

The Convolution property in Mathematica is used by the function InverseZTransform[f, w, t] where f is the product of two Z-transforms, w is the independent variable, and t is the time variable. The result will be the inverse Z-transform of f.

What are the benefits of using the Convolution property in Mathematica?

The Convolution property in Mathematica allows for a more efficient and accurate method of finding the inverse Z-transform of a product of Z-transforms compared to using other methods. It also allows for easier manipulation and analysis of complex sequences.

Are there any limitations to using the Convolution property in Mathematica?

The Convolution property in Mathematica can only be used for linear time-invariant systems, meaning the system's behavior does not change over time and is not dependent on the input signal. It also only works for discrete-time signals and sequences.

Can the Convolution property be used for signals with complex values?

Yes, the Convolution property in Mathematica can be used for signals with complex values as long as the sequences are defined in the time domain. It can also handle both real and imaginary components separately.

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