User:GabrielaV: Difference between revisions

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where
where
<math>\bold alpha_k={1/T}\int_{-{T\over 2}}^{{T\over 2}} \x(t) e^{-j2\pi kt\over T},dt</math>
<math>\bold alpha_k={1/T}\int_{-{T\over 2}}^{{T\over 2}} x(t) e^{-j2\pi kt\over T},dt</math>

Revision as of 20:43, 13 October 2005

Welcome to Gabriela's Wiki page

Introduction

Do you want to know how to contact me or find out some interesting things about me? [[1]]

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]

        
        

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



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

Fourier Transform

As previously discussed Fourier Series is an expansion of a periodic function so therefore we can not use it to transform a non-periodic funcitons from the time to the frequency domain. Fortunately the Fourier Transform allows for the transformation to be done for a non-periodic function.


In order to understand the relationship between a non-periodic function and it's counterpart we must go back to fourier series. Remember the complex exponential signal? [5]

where