Basis and practice for Fourier series expansion

1.Introduction…..5

2. Basic theory of Fourier series expansion…..6
2.1 Basic theory of Fourier series expansion-1
2.2 Basic theory of Fourier series expansion-2
2.3 Basic theory of Fourier series expansion-3
2.4 Basic theory of Fourier series expansion-4

3. Square wave …..64
3-1 square wave - 1
3-2 square wave - 2
3-3 square wave - 3
3-4 square wave - 4
3-5 square wave - 5
3-6 square wave - 6
3-7 square wave - 7

4.Sawtooth waveform…..99
4-1 Sawtooth waveform - 1
4-2 Sawtooth waveform - 2
4-3 Sawtooth waveform - 3
4-4 Sawtooth waveform - 4
4-5 Sawtooth waveform - 5
4-6 Sawtooth waveform - 6
4-7 Sawtooth waveform - 7
4-8 Sawtooth waveform - 8
4-9 Sawtooth waveform - 9
4-10 Sawtooth waveform - 10
4-11 Sawtooth waveform - 11
4-12 Sawtooth waveform - 12

5. triangular waveform…..179
5-1 triangular waveform - 1
5-2 triangular waveform - 2
5-3 triangular waveform - 3
5-4 triangular waveform - 4
5-5 triangular waveform - 5
5-6 triangular waveform - 6
5-7 triangular waveform - 7

6. trapezoidal waveform…..256
6-1 trapezoidal waveform - 1
6-2 trapezoidal waveform - 2
6-3 trapezoidal waveform - 3
6-4 trapezoidal waveform - 4
6-5 trapezoidal waveform - 5

7. Sine wave, etc……304
7-1 Full rectified wave form
7-2 Half rectified wave form
7-3 sine wave
7-4 Cosine wave
7-5 Constant value K
7-6 sine wave-2
7-7 Waveform of y=x2

References…..340

Fourier series expansion in electrical circuits is not a major educational field in electrical circuits. There are few examples, and the answers to the examples are often omitted, and it is often difficult to understand.

Therefore, in this book, basic examples are calculated without omitting intermediate answers. The content was designed to promote understanding of Fourier series expansion. In addition, for verification purposes, the results of calculations up to the 1000th term are graphed, and you can see that the calculation results are correct. How have the past confirmed the results of such calculations?

By the way, around 1800, when Mr. Fourier from France was active, it was a turbulent time when the French Revolution and Napoleon were active. Lagrange, famous for Lagrangian points, is a master professor, Laplace who Laplace transform, Ohm of Ohm's Law, Ampere, who has a name in the unit of current, and other achievements. Maclaurin's expansion, Taylor expansion, and Fourier series are methods for finding approximate functions, but they are indispensable for modern engineering.