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can anyone please tell me how can I compute the period of this signal? enter image description here

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    Recall that both $\sin(x)$ and $\cos(x)$ have period $2\pi$ – 2017-01-22
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    The period of a linear combination of periodic functions is the Least Common Multiple of their periods. – 2017-01-22
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    yeah, but can you explain for example how should I compute it for this one? – 2017-01-22

1 Answers 1

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$x(t)=1-2\sin(4\pi t) + 6\cos (9\pi t +\frac{\pi}{3} + c)$

If F(x)=sin(ax + c) then period of F(x) is $\dfrac{2\pi}{a}$

So period of $\sin(4\pi t)$ is $\dfrac{2\pi}{4\pi}=\dfrac 12$ and period of $\cos (9\pi t +\frac{\pi}{3} + c)$ is $\dfrac{2\pi}{9\pi}=2/9$

So by taking LCM of both (sin and cos function periods) gives 2 as period of $x(t)$