= Frequency spectrum
A <frequency spectrum> describes the <frequency> components of a <function>. A <Fourier series> supplies discrete <Fourier coefficients>; the <Fourier transform> of an <integrable function> supplies a continuous, generally complex-valued description. An <amplitude> plot shows magnitudes and omits <wave phases>, so it need not determine the original <function>. In the example with three <Fourier harmonics> above, the one-sided <amplitude> plot has heights $1$, $1/2$, and $1/4$. The corresponding complex <Fourier coefficients> at positive and negative <frequencies> each have half those heights: $\cos(2\pi\nu t)=(e^{2\pi i\nu t}+e^{-2\pi i\nu t})/2$.
Back to article page
