Imaginary part of frequency

1. What is imaginary part of frequency?
2. What does the imaginary part of a signal mean?
3. Can you have an imaginary natural frequency?

What is imaginary part of frequency?

Set s= jw for frequency response , as a very simple example. for an L_R circuit I= V/ Z where Z = R+jwL. Then 1/Z wil be complex ie the system. The real part indicates damping (in case of RL C) and shows the energy lost in the system. The imaginary part indicates stored energy .

What does the imaginary part of a signal mean?

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.)

Can you have an imaginary natural frequency?

Generally speaking there are some special cases when the natural frequency can be a pure imaginary number, it means system instability, see the attachment.