Howtosignalprocessing
- What is complex Fourier transform?
- What is a complex signal?
- Which transform is used in complex domain?
- Can DFT be complex?
What is complex Fourier transform?
Fourier Transform of Complex Functions
Consider a complex function 𝑥(𝑡) that is represented as − x(t)=xr(t)+jxi(t) Where, 𝑥𝑟 (𝑡) and 𝑥𝑖 (𝑡) are the real and imaginary parts of the function respectively. Now, the Fourier transform of function 𝑥(𝑡) is given by, F[x(t)]=X(ω)=∫∞−∞x(t)e−jωtdt=∫∞−∞[xr(t)+jxi(t)]e−jωtdt.
What is a complex signal?
A complex signal consists of two real signals - one for the real and one for the imaginary part. The linear processing of a complex signal, such as filtration with a time-invariant linear filter, corresponds to applying the processing both to the real and the imaginary part of the signal.
Which transform is used in complex domain?
Fourier transforms in the complex domain.
Can DFT be complex?
However, the complex DFT projects the input signal on exponential basis functions (Euler's formula connects these two concepts). When the input signal in the time domain is real valued, the complex DFT zero-fills the imaginary part during computation (That's its flexibility and avoids the caveat needed for real DFT).
