Contents
Why do we use complex numbers in signals?
This fits very naturally with Fourier analysis, where the frequency domain is composed of two signals, the real and the imaginary parts. Complex numbers shorten the equations used in DSP, and enable techniques that are difficult or impossible with real numbers alone.
Why do electrical engineers use j instead of I?
For example, in electrical engineering and control systems engineering, the imaginary unit is normally denoted by j instead of i, because i is commonly used to denote electric current.
Is Fourier transform complex?
The Fourier transform of a function of time is a complex-valued function of frequency, whose magnitude (absolute value) represents the amount of that frequency present in the original function, and whose argument is the phase offset of the basic sinusoid in that frequency.
What are real and imaginary signals in signal processing?
“Real” and “imaginary” have technical meanings in signal processing, and more widely in mathematics, that are different from their everyday meanings. In signal processing “real” denotes a signal component that is in phase with (i.e. has a 0° phase shift from) some reference signal.
What are the two parts of 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.
Where does the imaginary signal in DSP come from?
Imaginary denotes a signal component that is in quadrature with (i.e. has a 90° phase shift from) the same reference signal. The reference signal can come from a local oscillator. (In DSP or SDR equipment the local oscillator might be a mathematical representation of one, rather than an analog circuit.)
How are complex expressions used in signal processing?
Complex expressions are a quite common representation for several signals having two components possessing special properties.