Making Complex Fourier Transform Real
Description
This is an illustration of the Complex Fourier Transform of a real function. Using the Step play function step through the following
1. An initial function that is neither even or odd.
2. An even function can be made by the formula shown.
3. The odd part of the function. Note:
4. The positive part of the even function and its Fourier Cosine Transform
5. The positive part of the odd function and its Fourier Sine Transform.
6. Even extension of the Cosine Transform and odd extension of the Sine Transform.
7. The real part of the Complex Fourier Transform of the original function
8. The imaginary part of the Complex Fourier Transform of the original function.
9. The negative of the Sine transform of the odd function.
It can be seen how the Complex Fourier Transform is related to the Cosine Transform and Sine Transforms of the even and odd parts of the original function that extends from to .