Monomial to Chebyshev basis

Monomial to Chebyshev basis conversion

A = MON2CHEB(B) converts polynomial B given in monomial basis to
Chebyshev basis A. The polynomial must be given with its coefficients
in descending order, i.e. B = B_N*x^N + ... + B_1*x + B_0
Example:
Suppose we have a polynomial in the monomial basis:
b2*x^2 + b1*x + b0,
with b2=2, b1=0, b0=-2 for example.
We want to express the polynomial in the Chebyshev base
{T_0(x),T_1(x),T_2(x)}, where T_0=1, T_1=x, T_2=2x^2-1, i.e.
a2*T_2(x) + a1*T_1(x) + a0*T_0(x) = b2*x^2 + b1*x + b0,
where a = [a2 a1 a0] is sought.
Solution:
b = [2 0 -2];
a = mon2cheb(b);