Demystifying the Fourier transform

Figure 1. Time and frequency domain representation of a signal with a single frequency
Figure 2. Time and frequency domain representation of a signal with multiple frequencies
Eq1. Equation of a sine wave
Figure 3. Fourier Series Representation
Figure 4. Signal Decomposition by Fourier Transform
Eq2. Equation of Fourier Transform
Figure 5. Concept of Fourier Transform
Eq3. The Euler’s Formula
  1. By fundamental limit of uncertainty, it can not provide simultaneous time and frequency localization. To know a highly certain spectrum of a signal, a long-duration time-domain signal is required. Hence it is not suitable for non-stationary signals.
  2. Fourier transform can not completely resolve information when periodic oscillations are superimposed on decaying signals.

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Aniket kamat

Aniket kamat

Electronic Engineer, Aerospace Enthusiastic, Amateur Astronomer