Figure 8
Illustration above represents the idea of a Fourier Transform: Consider a signal, \(f(t) = \sin {(10\pi t)} + 0.2\cos {(16\pi t)}\) in the time-amplitude space(represented by the gray curve). This signal can be decomposed into \(f_1(t) = \sin {(10\pi t)}\) and \(f_2(t) = 0.2\cos {(16\pi t)}\) 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).
