Harmonics
Sum Result
  • Sawtooth
  • 4

  • Harmonic 1: sin(x)

    Amplitude1

  • Harmonic 2: sin(2x)

    Amplitude0.5

  • Harmonic 3: sin(3x)

    Amplitude0.3333
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Fourier Series

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. The basic idea is any shaped periodic waveform, can be represented as the sum of a set of sine waves with proper phases and amplitudes. It is essential in many fields especially signal processing. Mathematically, it's defined by the following equations:

fourier

The corresponding coefficients are defined as:

a_0
a_n
b_n

For example, to form a sawtooth wave, we have the following summation:

example
sawtoothFigure 1: Expansion of a sawtooth wave with 4, 6 and 10 terms