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We have the following expression:

if:

v(t)=Vrf.sin(Wrf.t)+Vlo.sin(Wlo.t);

then:

v^2(t)=(Vrf.sin(Wrf.t)+Vlo.sin(Wlo.t))^2

which is then simplified to:

v^2(t)=Vrf^2.(1+cos(2.Wrf.t))+Vlo^2.(1+cos(2.Wlo.t))+2.Vrf.Vlo.(cos((Wrf-Wlo).t)+cos((Wrf+Wlo).t));

The purpose of this kind of simplification is to have 'sin' and 'cos' terms of power of one from a trigonometric function, consisting 'sin' and 'cos' of any power.

The question is that how can I perform the simplification of higher order of v(t) ( v(t)^n ) into terms of 'sin' and 'cos' of power of one in Matlab?

edition added: Looking for specific simplification codes in symbolic Matlab!

A. Donda
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Majid Rafei
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  • Check out the formulas [here](http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Power-reduction_formula). Just program them into your matlab file. – Nemesis Mar 31 '15 at 10:49
  • Thanks for the link. But I am looking for a kind of simplification in Matlab for symbolic representations! – Majid Rafei Mar 31 '15 at 11:02
  • So you want to use the symbolic toolbox and results should still be symbolic functions? Will your input be always a 2-tone signal (i.e. with two frequencies) or are more tones possible? – Nemesis Mar 31 '15 at 11:20
  • Yes, I want to use symbolic Matlab, and it should be considered that v(t) is equal to a.sin(w1.t)+b.sin(w2.t)+c.sin(w3.t)+... in general, and I am looking for the simplification of v(t) in any power ( v(t)^n ) – Majid Rafei Mar 31 '15 at 11:29

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