# Does baseband signal has negative frequency?

Does baseband signal has negative frequency? In wiki baseband signal means that can include frequencies that are very near zero. I wonder whether baseband signal has negative frequency.

• yes. search for "negative frequencies" on this site, you get plenty of information. If you're researching this at the beginning of a course on communications engineering, just keep reading the course material: the representability of negative frequencies in complex baseband is the very basis for (nearly) all of modern communications technology. Jan 25 at 11:01

If a signal is real valued, then it will have negative frequencies when represented by complex-exponential Fourier transforms.

But if you use the trigonometric Fourier series representation you do not need a negative frequency concept.

If the signal is complex valued, such as an analytic signal, it may or may not have negative frequencies when represented by complex-exponential Fourier transforms.

It might help to watch my YouTube video explaining negative frequency: https://youtu.be/gz6AKW-R69s

I'm a professor and I've been building what I think of as an on-line video textbook for Signals, Systems, and Digital Communications.

• It's quite strange that people react to the concept of negative frequency, as if the concepts of negative length (as suggested by a cartesian coordinate system), or negative area (as suggested by an integral of a function) are very natural and physical. When it's negative length or negative area, people quite agree with the convention that they are mathematical abstractions and not of physical relevance. But then we stilll have to explain the physical significance of the negative frequency to those skeptical minds... :-))) Feb 17 at 22:50
• As well as the negative temperature...! :-) Have you ever had a student objecting to negative Fahrenheits? No they can't exist because negative molecular kinetic energy cannot exist.. :-) Feb 17 at 22:57
• You're right. I've never thought about it like that. I guess a difference is that all the things you listed are measured from a reference (length, temperature in Fahrenheits, etc), but frequency is measured from absolute zero (ie. zero oscillations), so it's a different concept to think of "negative oscillations". It would be like trying to think of negative temperature measured in Kelvin - it the particles stop moving at zero Kelvin, then what does negative Kelvin mean? Feb 17 at 23:08
• Yes that's one part of the answer, (however, a signed area is not measured from a reference?) And for the oscillations, I think we have a clockwise vs counter-clockwise reference to differentiate between them. Nevertheless, despite I'm not sure about the negative Kelvins (which I believe do not exist), it could be the temperatue of a negative mass gas ? :-) (or a positive mass with imaginary speeds) Feb 17 at 23:29