Input function of convolution

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?

[Matt J]

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.

Answer 1

[Matt J]

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,

Answer 2

[Matt J]

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