how to calculate convolution in mathematica

[Ana-Maria]

mathematica convolution

Hi all,

Does anyone know how to calculate the linear convolution in Mathematica (Wolfram)?This is the formulla for linear convolution:

Thank in advance!

 

[diegobb]

convolution mathematica

If it's a discrete serie of values, please take a look to the page 23 of "Discrete-Time Signal Processing" from Oppenheim, the second edition (the spanish edition, but i think it's the same in others editions).

The "method" in the book is:
1) Invert the time in the signal y[n], so you get: y[-k]=y[0-k]
2) Displace the signal by n, so you get: y[n-k]
3) Make the sum for every k, with a fixed n, for every n.
(It's a good idea to take a simple discrete signal as y[n], for example four values, and do the steps graphically)

result[n] = Σ (x[k]*y[n-k]), in the sum, k goes from -∞ to +∞.

It's hard to explain, so if you don't understand, (due my bad english), you better take a look to the book.

Or you can use the DFT to calculate each Fourier Transform, and multiply the results, but it depends on the type of series.

Regards, Diego

 

[Ana-Maria]

how to calculate convolution

Thank you for your nice explanation. May you tell me whaht page/pages from the book I should read?

 

[diegobb]

calculate convolution

You can make a fast read from page 9, to page 24, to understand the discrete time signals, if you want, but the graphical method to calculate the convolution is at the page 25, "example 2.12".

Also the "example 2.13" can help you, this is a analytical method.

Regards, Diego.

 

[Ana-Maria]

calculating convolution

Thank you!

All the best