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No. Assuming you want ∞ to mean infinity, beware of involving it in any equation. If you want it to mean something else, use another symbol.Similarly t' can mean t + Δt or anything else you define it as, and σ is usually reserved for standard deviation, unless you define it as something else. Always begin with your definitions, so people know what you are talking about. As my navigation instructor used to say "start from where you are, then you won't get lost before you take off". When you have landed, tell the passengers where you are - i.e. what you have demonstrated by your mathematics. Maths is the way we plot our course from one physical observation to another!And remember cos^{2}x + sin^{2}x = 1. This is a great help in checkng your equations and graphs.For what it's worth, white light is a continuous spectrum. You can't generate it from the harmonics of a single frequency.

, and yes infinite was infinite.

I want to explain that x is a continuous linearity of time, and i want to explain that Y is a single time wave but the distance between the troths are random .

Quote from: Thebox on 02/12/2015 12:14:55, and yes infinite was infinite. in which case the equations are meaningless. QuoteI want to explain that x is a continuous linearity of time, and i want to explain that Y is a single time wave but the distance between the troths are random .Then just say "y(t) is random". There's nothing more you can say or do about it, mathematically or physically.There's a difference between "white noise", which is random and has an infinite spectrum of constant power density, and white light, which has a limited spectrum defined by the response of the human eye to electromagnetic radiation. You might be interested in autocorrelation functions as a means of expressing randomness, but I don't see any relevance to white light.