Fourier harmonic - Knowlpedia

The $m$ -th Fourier harmonic of a one-dimensional periodic function is its component $\widehat f(m)e^{im\theta}$ , for an angular coordinate of period $2\pi$ . The term harmonic can also refer to the character $e^{im\theta}$ itself. For real-valued functions, the $m$ and $-m$ components combine to a real sinusoidal component.

Several frequencies

On a unit $d$ -torus the harmonic index is $m\in\mathbb Z^d$ , and the component is $\widehat f(m)e^{2\pi i m\cdot x}$ . In an ansatz $a_m e^{ikm\Phi}$ , the integer harmonic multiplier $m$ is distinct from a chosen carrier parameter $k$ . Fourier harmonics are frequency components; they are generally not harmonic functions in the sense $\Delta f=0$ .