Complex

Complex numbers and fourier transform

Complex numbers and fourier transform
  1. Does Fourier transform use complex numbers?
  2. Why do we use complex numbers in Fourier transform?
  3. What is Fourier transform of complex exponential?

Does Fourier transform use complex numbers?

Fourier Transforms are performed using complex numbers. Since Fourier Transforms are used to analyze real-world signals, why is it useful to have complex (or imaginary) numbers involved at all? It turns out the complex form of the equations makes things a lot simpler and more elegant.

Why do we use complex numbers in Fourier transform?

The basis into which the FFT changes your original signal is a set of sine waves instead. In order for that basis to describe all the possible inputs it needs to be able to represent phase as well as amplitude; the phase is represented using complex numbers.

What is Fourier transform of complex exponential?

Hence, the Fourier transform of the complex exponential function is given by, [ejω0t]=2πδ(ω−ω0) Or, it can also be represented as, ejω0tFT↔2πδ(ω−ω0)

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