# What are some practical examples of complex signals? [duplicate]

I am aware that complex discrete-time signals are of the form:

$$x(n) = a(n) \cdot e^{j\omega n T}$$

However, I have not yet worked with complex signals, only real ones. What are some practical examples of complex signals? Answers with plenty of detail are appreciated.

• no, your signal is a very special case: it's a complex sinusoid with amplitude modulated over time. Overall, your question is very broad, and doesn't make very much sense: Shift any real-valued signal in frequency and you end up with a complex one. You should probably read a few more pages in a textbook that introduces complex equivalent baseband signals, see if that clarifies things to you. Asking for a list of example signals doesn't fulfill the criterion of "questions should allow for a correct answer". – Marcus Müller Feb 14 at 14:59
• The purpose of my question was to motivate the use of complex signals. So far, I have not seen them used in practice, only on paper. Similarly, I have not seen non-symmetric spectra in practice. Does this mean that all complex signals are just frequency shifted real signals? Should I re-word my question to reflect this? – mhdadk Feb 14 at 15:15
• Have you heard about analytic (Hilbert transform) or IQ signals? Apart from communications, you can find complex signals in radar processing or medicine (MRI). – jojek Feb 14 at 15:27
• motivate the use: I've given you arecommendation what to read, and you'll find what you're looking for. No, not all complex signals are just frequency-shifted real signals. – Marcus Müller Feb 14 at 15:28
• Thanks for the references – mhdadk Feb 14 at 15:32