It's a useful principle but not often used by name.
White noise has an infinite spectrum, think of it as infinitesimally spaced components across a frequency range extending from zero to as high as you can manage. The interesting things are the overall amplitude template, and the pattern (if any) of the phases of all those components. White means the amplitudes are flat, and the phases are randomly scattered.
All non-repetitive signals give spectra of infinitesimally spaced components. By choosing the template of the amplitudes of those components and the pattern of their phases, we can make any wave shape we can imagine. (Fourier)
If we make the waveform repetitive, then the spectrum simplifies, leaving only components at the repetition frequency and its harmonics. The amplitude template and phase pattern remains.
So the non-repetitive waveform case is just the repetitive one with the repetition frequency set to zero.
One interesting cousin of white noise happens if we keep the infinite number of infinitesimally spaced spectral components and order the phases into a regular pattern.
We wind up with a waveform which tends towards a zero width spike of infinite amplitude Mathematicians call this a Dirac Function
From an engineering point of view, Dirac functions are a bit of a problem. You hit something with an infinite force but for zero time? did it move? Angels, pinhead. pinhead, angels. So arbitrarily the amplitude-time product is assigned as 1 for a Dirac impulse.
Green's functions describe the behaviour of something described by differential equations (like most circuits, filters, transmission lines, control systems etc etc) if it gets hit by one of those Dirac spikes. You can play about with the results and get either the impulse response of the system, or the amplitude and phase versus frequency response.
Play the game backwards and you can take the frequency/phase response of a system and you can calculate its impulse response. This is great for finding the impulse response of something that would have been destroyed if you hit it with a real impulse.
And there's that white noise bit. You could feed noise into something and correlate it with the things response to that noise. This will give you the impulse response and you can trade that into the frequency response.
There's another relative to white noise and Dirac impulses, THe step function (Heaviside function, yes, him! he got around a bit.) this also has infinitesimally-spaced frequency components, but a different zero freq value and a different phase pattern) So you can play the same game with these as with the Dirac. Once you know the full frequency/phase response, you can calculate how your circuit or whatnot will behave when hit with a perfectly fast step of voltage.
If you want to test bridges, nuclear power stations and other things that would get in the papers if you wrecked them, you can apply gentle noise, measure the response and calculate what stresses would be created if you hit it with something more dramatic.
There is one small fly in the ointment:
It all assumes the system is linear. Which means that if you apply several signals at once (added together) the response will be the sum of all the responses to each of those signals individually. This is calles 'superposition'
The interchangeability of all these ways of looking at essentially the same thing is so common and so everyday that it's a crying shame Green doesn't get credited.
Never thought I'd explain that little lot in an audiophoolery thread. It's the very antithesis of audiophoolery saying that you can measure one thing and calculate everything else and invoke theoretical signals which are impossible in practice. It leaves nowhere for the golden eardrums to hide AND it's mathematically provable!
Thanks for the local knowledge, David. Somewhere I'd like to visit.
David