Diskrete FOURIER-Transformation (DFT)

Abstract

Das diskrete FOURIER-Transformationspaar lautet:

$$ {{\text{x}}_{\text{a}}}\left( {\text{n}} \right){\text{ = }}\sum\limits_{{\text{k = 0}}}^{{\text{N - 1}}} {{\text{x}}\left( {\text{k}} \right)} {{\text{e}}^{{\text{ - j2}}\pi {\text{kn/N}}}} = {\text{DFT}}\left( {{\text{x}}\left( {\text{k}} \right)} \right) $$

((7.1))

$$ {\text{x}}\left( {\text{k}} \right){\text{ = }}\frac{{\text{1}}}{{\text{N}}}\sum\limits_{{\text{n = 0}}}^{{\text{N - 1}}} {{{\text{x}}_{\text{d}}}} \left( {\text{n}} \right){{\text{e}}^{{\text{k2}}\pi {\text{kn/N}}}}{\text{ = IDFT}}\left( {{{\text{S}}_{\text{d}}}\left( {\text{n}} \right)} \right) $$

((7.2))