I would like to combine multiple sine waves with differing amplitudes, frequencies and phases into a single curve that I can display as a graph. What formula will I need to create the points for the curve?
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- 1$\begingroup$ Depends by what you mean by combine. A linear combination is one possibility: $y(t) = A_1 \cos(\omega_1 t + \phi_1) + A_2 \cos(\omega_2 t + \phi_2) + \ldots $ $\endgroup$Sasha– Sasha2011-08-12 15:20:46 +00:00Commented Aug 12, 2011 at 15:20
- $\begingroup$ A bit of background on the project may be useful: I am working with raw hydrographical data and would like to chart tidal heights over time (e.g. a month). There is a sine wave for each influencing factor (e.g. lunar position, solar position) with their own amplitudes, durations and weights which I would like to aggregate into a single tidal curve. $\endgroup$Mike Poole– Mike Poole2011-08-12 15:36:14 +00:00Commented Aug 12, 2011 at 15:36
- $\begingroup$ Are you hoping to find a simple formula for your final curve? $\endgroup$Unreasonable Sin– Unreasonable Sin2011-08-12 15:45:25 +00:00Commented Aug 12, 2011 at 15:45
- $\begingroup$ Ideally, yes. I will then be able plot the results on a graph. $\endgroup$Mike Poole– Mike Poole2011-08-12 16:34:13 +00:00Commented Aug 12, 2011 at 16:34
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1 Answer
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1 You can start out with just
$a_0 \sin(2\pi f_0 t + \phi_0 ) + a_1 \sin(2\pi f_1 t + \phi_1) + \cdots.$
If there are an infinite number of terms, then they might converge into a recognizable waveform that has an easy description as a function such as a square wave or a triangle wave.
- $\begingroup$ Thanks for the reply. The resulting curve would not be a square wave or triangle wave. The resulting curve would be one which oscillates more on some occasions than others. $\endgroup$Mike Poole– Mike Poole2011-08-12 15:28:44 +00:00Commented Aug 12, 2011 at 15:28