Create vectorsuandvcontaining the coefficients of the polynomials $$x^2+1$$and $$2x+7$$.

u = [1 0 1]; v = [2 7];

Use convolution to multiply the polynomials.

w = conv(u,v)

w =1×42 7 2 7

wcontains the polynomial coefficients for $$2x^3+7x^2+2x+7$$.

Create two vectors and convolve them.

u = [1 1 1]; v = [1 1 0 0 0 1 1]; w = conv(u,v)

w =1×91 2 2 1 0 1 2 2 1

The length ofwislength(u)+length(v)-1, which in this example is9.

Create two vectors. Find the central part of the convolution ofuandvthat is the same size asu.

u = [-1 2 3 -2 0 1 2]; v = [2 4 -1 1]; w = conv(u,v,'same')

w =1×715 5 -9 7 6 7 -1

whas a length of7. The full convolution would be of lengthlength(u)+length(v)-1, which in this example would be 10.