Howtosignalprocessing
- What is the Fourier transform of complex number?
- Can Fourier transform be complex?
- Why do we use complex numbers in Fourier transform?
What is the Fourier transform of complex number?
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.
Can Fourier transform be complex?
The complex Fourier transform is important in itself, but also as a stepping stone to more powerful complex techniques, such as the Laplace and z-transforms. These complex transforms are the foundation of theoretical DSP.
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.
