Digital signals lab – final exercise

[Paige C]

‘Can you find phi such that sin(theta+phi) = cos(theta)?’

I know that phi = pi/2 because maths, but wondering how we would get this just from the notebook – are you wanting us to set one of the phase shifts to pi/2 and notice that its plot is now a cosine wave, or is there some other result that I’m missing?

[Catherine Lai]

Hi Paige,

You’re not missing anything! The thing to take away is that the difference between cosine and sine waves of the same frequency (and amplitude) can be characterised by a 90 degree (pi/2) phase shift.

The idea was to either try different phase shifts until you get something that looks like a cosine wave or to derive this based on the fact that one period is equivalent to 2pi (and you know cosine start at the positive peak of the wave so 1/4 into the sine wave cycle). But, yes, you might just know it as a mathematical identity!

cheers,
Catherine

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