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I'm trying to solve the following: \begin{equation} A \cos(2\pi f t + \theta_1) + B \cos(2\pi f t + \theta_2) = D\cos(?f?\theta) \end{equation}

I just need to know the correct value of D, the value of frequency and delta is not important since it is non-coherent.

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    $\begingroup$ Link Search for "arbitrary phase shift"... $\endgroup$
    – mateC
    Commented Jan 21, 2019 at 10:20

1 Answer 1

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$$A\cos(2\pi f+\theta_1)+B\cos(2\pi f+\theta_2)=C\cos(2\pi f+\theta_3)$$

where

$$C=|u|\quad\textrm{and}\quad \theta_3=\arg\{u\}$$

with

$$u=Ae^{j\theta_1}+Be^{j\theta_2}$$

The constant $C$ can be written as

$$C=\sqrt{A^2+2AB\cos(\theta_1-\theta_2)+B^2}$$

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