Figure 8.

Illustration above represents the idea of a Fourier Transform: Consider a signal, $f(t)=sin(10\pi t)+0.2cos(16\pi t)$ in the time-amplitude space(represented by the gray curve). This signal can be decomposed into $f_1(t)=sin(10\pi t)$ and $f_2(t)=0.2cos(16\pi t)$ in the time-amplitude space (represented by the blue and red curves respectively). Fourier Transform of the signal, $f(\omega )$ shows these two peak frequencies respectively in the frequency-amplitude space (represented by the black curve).