This is an illustration of the Complex Fourier Transform of a real function. Using the Step play function step through the following[br]1. An initial function that is neither even or odd.[br]2. An even function can be made by the formula shown.[br]3. The odd part of the function. Note: [math]f=f_{odd}+f_{even}[/math][br]4. The positive part of the even function and its Fourier Cosine Transform[br]5. The positive part of the odd function and its Fourier Sine Transform.[br]6. Even extension of the Cosine Transform and odd extension of the Sine Transform.[br]7. The real part of the Complex Fourier Transform of the original function[br]8. The imaginary part of the Complex Fourier Transform of the original function.[br]9. The negative of the Sine transform of the odd function.[br][br]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 [math]-\infty[/math] to [math]\infty[/math]. [br][br][br]