Can anyone explain this output of 1d conv() function?

 >> u = [1 2 3];
 >> v = [1 2 3];
 >> w = conv(u, v)
 w = 1     4    10    12     9
 >>

Can anyone explain this output?

Question #1. How come two vectors of 3 elements generate 5 elements' output?

Question #2. How is the output being calculated?

[Bruno Luong]

The questions is precisely answered if you type

>> doc conv

and read

Answer 1

[Stephan]

Hi,

using:

conv([1,2,3],[1,2,3])

is the equivalent to multiply two polynomials:

(1*x^2 + 2*x + 3) * (1*x^2 + 2*x + 3)

If you simplify this (do the multiplication) you get:

1*x^4 + 4*x^3 + 10*x^2 + 12*x + 9

The coefficient matrix of this resulting polynomial is

[1 4 10 12 9]

which is the same as the result of

conv([1,2,3],[1,2,3])

See also the conv documentation for more detailed informations.

Best regards

Stephan