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\subsection{Fourier-Reihen} Eine Anwendung der (Schnellen) Fourier-Transformation (FFT) ist die Komprimierung eines Bildes und sie wird im JPEG-Format verwendet. -\shade{purple}{Intuition:} Wir haben eine Datenmenge $D$, die die $y$-Werte einer Frequenzmessung an $N$ äquidistanten Punkten enthält. +\inlineintuition Wir haben eine Datenmenge $D$, die die $y$-Werte einer Frequenzmessung an $N$ äquidistanten Punkten enthält. Die Fourier-Transformation dieser Datenmenge ergibt eine neue Datenmenge, nennen wir sie $F$, die, wenn geplottet, einem Plot der Frequenzanalyse entsprechen. Dies ist auch korrekt, denn die Fourier-Transformation macht (vereinfacht) genau das; Sie macht einen Basiswechsel auf der Datenmenge $D$, so dass die Frequenz auf der $x$-Achse und die ``Häufigkeit'' deren auf der $y$-Achse aufgetragen werden,

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