Contents
What is the imaginary component of a signal?
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.)
What is a real signal?
A real signal is said to be an even signal if we have the following: (3.10) for all time t, even signals are thus symmetric about the vertical axis (i.e., around the line ). A signal is said to be an odd signal if we have the following: (3.11)
What is real and complex signals?
A real discrete-time signal is defined as any time-ordered sequence of real numbers. Similarly, a complex discrete-time signal is any time-ordered sequence of complex numbers. Mathematically, we typically denote a signal as a real- or complex-valued function of an integer, e.g., , .
Is the spectrum of a strictly real signal complex?
The spectrum of a strictly real signal has a complex conjugate mirror image so that all the imaginary components cancel out to zeo. If the imaginary spectrum didn’t cancel out to zero, the signal could not be strictly real.
How is a signal that is only imaginary?
Similarly a signal that is only imaginary will be have the FFT real components to be odd and the FFT odd components to be even.
Why are complex signals used in real life?
Complex signals are often used to represent signals or data with 2 degrees of freedom (magnitude and phase, or kinetic and potential energy, etc.) The spectrum of a strictly real signal has a complex conjugate mirror image so that all the imaginary components cancel out to zeo.
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.