Howtosignalprocessing
- What is complex spectrum?
- How do you know if a signal is imaginary or real?
- Do complex signals exist?
- Can a signal take complex value?
What is complex spectrum?
The spectrum of a complex signal can be found by using the usual expressions for the Fourier transform. In the following we will derive the spectrum X(f) of the complex signal x(t) = x1(t) + jx2(t) as a linear combination of the spectra X1(f) and X2(f) of the real-valued signals x1(t) and x2(t).
How do you know if a signal is imaginary or real?
In signal processing "real" denotes a signal component that is in phase with (i.e. has a 0° phase shift from) some reference signal. Imaginary denotes a signal component that is in quadrature with (i.e. has a 90° phase shift from) the same reference signal.
Do complex signals exist?
Also complex signal exists in electronics, where voltage is real component and current is imaginary component of complex signal. Complex signals occur with AC current and plus inductors or capacitors in electronic circuits.
Can a signal take complex value?
While the domain set determines the arguments of the signal, the range set determines the values of it. Therefore a real valued signal is a function whose range set is the real numbers. Consequently a complex valued signal is the one whose range set is the complex numbers.
