# Signals and group velocity

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Ahmed1029
What exactly is a signal in wave physics? Is any wave considered a signal? Like, consider a superposition of harmonic plane waves, is the signals it carries considered the envelope(that travels at the group velocity) or the individual rippes that travel at a the phase velocity?

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## Answers and Replies

Mentor

Ahmed1029
I don't understand

Mentor
I don't understand

vanhees71 and Ahmed1029
Ahmed1029
I'm Reading modern optics by Fowles, but he doesn't really discuss this in his book. He just remarked that signals travel at group velocity and said no more, so I wanted to investigate what signals actually mean and what can be considered a signal. I searched for definitions online, but those weren't detailed enough so I thought someone might be able to help me here.

vanhees71
Gold Member
What exactly is a signal in wave physics? Is any wave considered a signal?
A signal is information. The presence of a single wave is actual information that the 'source' is switched on. The state 'on-off-on-off', with a switch, will transmit/carry useful binary information as with Morse Code etc. The amount of information governs the bandwidth occupied by a signal. It is worth while discussing this in terms of Radio Transmissions although it applies for all non-continuous waves. I find the optical equivalent less approachable - except for optical communications, of course.

If a radio wave is 'modulated', it can carry a signal. With amplitude modulation the ( eg low frequency square wave) modulating signal produces a string of symmetrical 'sidebands' above and below the carrier frequency.

A 'photograph' of the RF waveform will be the same over the whole of a signal path. The speed of the information (group velocity) will be the same as the speed of the carrier wave the relationships between all the components of the RF signal will be the same.

But if there's any form of dispersion, the various sidebands will lose their original phase relationship; they arrive at different times and the demodulated waveform may be distorted significantly.

This is termed 'Group Delay Distortion' and is usually caused by the various filters are used to restrict the channel width and in the receiver. It shows the difference in Wave and Group transit time (from Δω and Δk across the bandwidth), rather than the absolute transit time (from ω and k) which is often impossible to measure in practice.

But the absolute transmission time is usually of no consequence; it's the variation of transmission time that counts. Your 'perfect' analogue TV pictures are good (enough) at all distances and on all channel frequencies.