# Find the solution for the following equation

1. Aug 27, 2007

### T.Engineer

1. The problem statement, all variables and given/known data

if H_n(t)= (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2)

where n=1,2,...,N

from the orthogonality property of Hermite polynomials we will have:

$$\int^{\infty}_{-\infty} e^{-t^2} H_n(t) H_m(t)dt$$ = $$\delta_n,m$$ 2^n n! $$\sqrt{}pi$$

this gives

N_n= $$\frac{1}{\sqrt{}2^n n! \sqrt{}pi}$$

consequently

$$\int^{\infty}_{-\infty}\varphi_n(t)\varphi_m(t) dt$$ = $$\delta_n,m$$

let g_n(t) = H_n(t) cos (2 pi fc t)

the value of fc will be chosen in such a way that still keep the orthogonality property of Hermite polynomial.

find out if cos (2 pi fc t) is positive over the relevant range as follow

$$\int^{\infty}_{-\infty}\varphi_n(t)\varphi_m(t) dt$$ = $$\delta_n,m$$

2. Relevant equations

3. The attempt at a solution

Last edited: Aug 27, 2007