# Summation of multiple sine wave

Discussion in 'General Electronics Chat' started by misrasomendra, Aug 12, 2014.

1. ### misrasomendra Thread Starter New Member

Aug 12, 2014
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Hi there,

I had looked this on the internet, but could not find. I found the resultant equation for amplitude and phase for addition of 2 sine wave of different amplitude and phase shift.

But what will be the equations to find the amplitude and phase is we are adding multiple sine wave say 3 or 4 having different amplitude and phase shift?

Regards,

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
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782
Are all the sinewaves at the same frequency?

3. ### misrasomendra Thread Starter New Member

Aug 12, 2014
7
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May or may not be, I want a general equation.

Regards,

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
The concept of resulting equivalent phase & amplitude is only meaningful when the sinusoids have the same frequency. Two sinusoids at different frequency have continuously varying phase displacement relative to one another.

5. ### misrasomendra Thread Starter New Member

Aug 12, 2014
7
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Ok. So what will be the equations for same frequency.

Regards,

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
Do you expect to do this using trigonometric relationships, vector addition or complex numbers?

Aug 12, 2014
7
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Regards,

8. ### MrAl Well-Known Member

Jun 17, 2014
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432
Hi,

Why not just do them in pairs, ie two at a time?

Aug 12, 2014
7
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Regards,

10. ### phantomzz New Member

Sep 26, 2013
18
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You could represent each sine wave as a vector and find the resultant.

As for signals of different frequencies you can use an inverse Fourier transform to obtain the resulting wave as a function of time....although I am not sure how to incorporate phase into that....

11. ### misrasomendra Thread Starter New Member

Aug 12, 2014
7
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Can you tell me a source where I can find how to do that?

Regards,

12. ### phantomzz New Member

Sep 26, 2013
18
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If you have the eqn for summation of 2 sine waves you could do what Mr Al recommended. It becomes time consuming for lots of sine waves so it would be better to use a computer to that end.

If you want to learn about vector addition you can use an engineering mathematics book. It should also cover Fourier Transforms and IFT, although if you want an application specific understanding you should pick up a Signals and Systems book.

I would recommend Signals and Systems by Oppenheim and Wilsky. Be warned though this is a heavily mathematical subject so you need to have a good grasp on calculus and more importantly not be intimidated by all the math. Spend time on it, stick to it and you will understand it eventually.

13. ### misrasomendra Thread Starter New Member

Aug 12, 2014
7
0
Thanks for all the input.

Regards,