1. Math for CSTutorial 101 Fourier Transform

2. Math for CSTutorial 102 Fourier Series The series With a n and b n generated by Is called a Fourier series of function f(x). (3)

3. Math for CSTutorial 103 Orthonormality of Fourier Basis Let us check that Fourier basis is orthonormal:

4. Math for CSTutorial 104 Orthonormality of Fourier Basis To check this it is enough to use trigonometric formulas: And the integral values

5. Math for CSTutorial 105 Example 1 Find a fourier series for the function: Solution: a n =0, since f(x)cos(x) is antisymmetric.

6. Math for CSTutorial 106 Example 2 Find a fourier series for the function: Solution: b n =0, since f(x)sin(x) is antisymmetric.

7. Math for CSTutorial 107 Example 2 a 0 =1. Integrating by parts ( using ug’=(ug)’-u’g ), we obtain:,while n=1,3,5,…