# Method to Decompose Modulation Series

Given a signal $$\sin\left(\frac{2\pi}{\sin(2\pi/Tx)x}\right)+n$$ (where n is noise) is there a way to isolate and decompose the number, frequency, and causal (carrier-modulator) order of the oscillators (here 2)?

(Similar to How do I find amplitude modulation effects in natural signals but more formal).

• The equation you gave seems to be constant. Can you clarify what the signal is? – MBaz Oct 30 '16 at 2:05
• @MBaz Sorry, I forgot x. Also added a noise parameter to the signal. (Random fluctuations are expected.) – user16743 Oct 30 '16 at 10:41
• Are you sure $x$ appears in the denominator? That is unusual. Could you also include the statistics of $n$ (distribution,mean, etc)? – MBaz Oct 30 '16 at 15:58
• @MBaz What I'm trying to illustrate is a function f(x)=sin(2pi/Tx) where the input x is essentially the same function f(x), but with a different value for T. (One sine wave oscilator modulating another sine wave... generalized to n sine waves) I would assume that the noise is poisson distributed. Alternatively, the noise can be reduced by averaging multiple segments of similar signals (common mode rejection) or it can be treated as a residual (and simply ignored for an 'ideal' analytical solution). – user16743 Oct 30 '16 at 16:04
• @MBaz My maths is not so good. Sorry about that. – user16743 Oct 30 '16 at 16:08