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Input function of convolution

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JOB
JOB on 24 Dec 2019
Edited: Matt J on 24 Dec 2019
I have doubt about convolution. Is it possible to find the Input function that convolved, from the result of convolution? As an example y=conv(x,x). Is there a method to uniquely determine 'x', If only 'y' is known?

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Matt J
Matt J on 24 Dec 2019
Obviously not uniquely. For example, when x is a scalar, this reduces to the equation
y=x.^2
which does not have a unique solution for x.

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Accepted Answer

Matt J
Matt J on 24 Dec 2019
Edited: Matt J on 24 Dec 2019
As an example y=conv(x,x). Is there a method to uniquely determine 'x', If only 'y' is known?
If you know that x has a real, positive Fourier spectrum X(f), then you can solve for x using frequency domain methods,

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More Answers (1)

Matt J
Matt J on 24 Dec 2019
Edited: Matt J on 24 Dec 2019
If one of the convolution operands is known, you can recover the second using deconv. Example,
x = [2 7 4 9];
k = [1 0 1];
y = conv(x,k);
>> xr=deconv(y,k)
xr =
2 7 4 9

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