4. FOURIER SERIES
Any periodic function or waveform can be representing as a (possibly infinite) sum of sine and cosine functions. This type of representation is called Fourier series. It is analogous to a Taylor series, which represents functions as possibly infinite sums of monomial terms.
[tex]f(x) = \frac{a_0}{2} + \sum_{k=1}^{\infty} a_k \cos \frac{2 \pi k x}{T} + \sum_{k=1}^{\infty} b_k \sin \frac{2 \pi k x}{T} ,[/tex]
[tex]a_k = \frac{2}{T} \int_0^T f(x) \cos \frac{2 \pi k x}{T}\:dx, \quad b_k = \frac{2}{T} \int_0^T f(x) \sin \frac{2 \pi k x}{T}\:dx[/tex]
Contents
4. | FOURIER SERIES | ||
4.1 | Trigonometric Fourier Series | ||
4.2 | Evaluation of Fourier Coefficients | ||
4.3 | Waveform Symmetry | ||
4.4 | Fourier Series in Optimal Sense | ||
4.5 | Exponential Form of Fourier Series | ||
4.6 | Fourier Transform | ||
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