Talk:Negative frequency

message: I tried to fix it to have some physical meaning, so the conclusion is more than some theoretical blah, but it doesn't make much sense. Here is what I wrote before I gave up: 
Sometimes a physical system involves two related sinusoids with the same frequency, and a known phase difference. For instance, the AC current through an ideal inductor trails the voltage by \begin{matrix} \frac{\pi }{2} \end{matrix}\, radians. Assuming 1V and respectively 1A peak amplitude, we have :
:V(t) = \cos(\omega t + \theta)\,
and
:I(t) = \cos(\omega t + \theta -\begin{matrix}\frac{\pi }{2} \end{matrix}) = \sin(\omega t + \theta )\,
When \omega > 0\,, V(t)\, appears to lead I(t)\, by \begin{matrix} \frac{1}{4} \end{matrix}\, cycle (=\begin{matrix}\frac{\pi }{2} \end{matrix}\, radians). But when \omega < 0\,, (which corresponds to what?) the roles are reversed, which corresponds to different circuit: in a capacitor the AC current leads the voltage by \frac{\pi }{2}. So in that case it is possible to distinguish negative and positive frequencies. The diagram depicts a negative frequency. V(t)\, and I(t)\, are referred to as real and imaginary, respectively. And \theta = 0\,.
Doesn't make much sense. Nobody refers to current an voltage as "real" and "imaginary" parts of something else...
If instead the I and R in the original/current write-up are about complex modulation (i.e. they are the time-varying amplitude and phase modulation of a carrier wave, which seems to be the case given the discussion about analytic signal above), then there's a well-known result that there's no clear distinction between amplitude and phase modulation of a real signal. See  for instance. But what does that have to do with negative frequencies or constant phase difference?
On the topic of signals of negative frequency, while not necessarily the ultimate word, this book says: "Negative frequency signals are not physical signals, rather they are only a mathematical concept required to give a compact mathematical description of a real signal by combining complex exponentials of positive and negative frequencies." Suresh and Kumar say the same thing  "There is no negative cyclic frequency or negative angular frequency." A different interpretation of the same math is given here; while he doesn't claim that phasors are physical entities, perhaps he assumes that, because he compares them with velocity.
So, I think there are some major question marks in this article. Finally, there's something to be said about negative frequencies in quantum physics, but I don't feel very qualified to write about that. Cheers, Tijfo098 (talk) 13:33, 25 September 2010 (UTC)
thread_title:  What's the I/R example about? 

message: Here is a copy/paste from an earlier discussion (above):
In the Doppler section, aren't we really talking about positive or negative differential frequency?  The waveform shifts upwards or downwards in frequency as the object moves closer or farther. — Omegatron 16:09, 29 November 2005 (UTC)
thread_title: is negative frequency use in [[doppler effect]] if the source travel toward the observer or the observer travel away from the source twice the speed of sound

message: Deleting:  https://ccrma.stanford.edu/~jos/mdft/Positive_Negative_Frequencies.html
The link misleadingly claims that e^{i\omega t} is "simpler and more basic" than \cos(\omega t).  But the opposite is clearly true.  \cos(\omega t) = (e^{i\omega t} + e^{-i\omega t})/2 is simpler, because the addition is actually a cancellation, resulting in less information.  (One-dimension is simpler than 2-dimensions.   ())  I think what the article actually means to say is that the simplicity of \cos(\omega t) results in analytical complexities, such as trigonometry instead of algebra and multiple responses in the Fourier transform.--Bob K (talk) 12:34, 12 February 2024 (UTC)
thread_title: Unhelpful Further reading link