- Simple functions, such as square waves and triangular waves, can be represented as Fourier series.
- The Fourier series of a function can reveal its frequency content.
- Fourier series can be used to approximate functions with a high degree of accuracy.
- Different forms of Fourier series can be used to represent functions with different periods.
Important Formulas to Remember in these topic
- Examples of Fourier series of simple functions in (0, 2π) and (–π, π):
$$f(x) = x$$
$$f(x) = \begin{cases} -1, &-\pi < x < 0 \\ 1, &0 < x < \pi \end{cases}$$