User:GabrielaV

Introduction

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Signals & Systems

Example

Find the first two orthogonormal polynomials on [-1,1]

1. What is orthogonormal? [2]

2. What is orthogonal? [3]

3. What is a polynomial? [4]

        $\mathbf{a}$
        $\mathbf{b}t+c$

4. Now we can find the values for the unknown variables.

$<a|a>=\underset{-1}{\overset{1}{\int }}aadt=1$

$\mathbf{a}=\sqrt{\frac{1}{2}}$

$<bt+c|a>=\underset{-1}{\overset{1}{\int }}a(bt+c)dt=0$

$\mathbf{c}=0$

$<bt+c|bt+c>=\underset{-1}{\overset{1}{\int }}(bt+c{)}^{2}dt=1$

$\mathbf{b}=\sqrt{(}\frac{3}{2})$

5. Now that we know what the first two orthogonormal polynomials!