Why is that when i change my phase angle, the amplitude changes in sin and cos functions in Matlab?

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Nina 2013-10-31

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评论： sixwwwwww 2013-11-1

I am doing simple tests trying to get back the amplitude and phase angle from fft, when i have

x = A*sin(2*pi*t*f) + B*cos(2*pi*t*f), where A = B = 1, I get the correct amplitude back which is sqrt(2) but when i add some phase angle to them, it changes, why is that? Thank you all very much!

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Answer 1

sixwwwwww 2013-10-31

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编辑：sixwwwwww 2013-10-31

Dear Nina, values for sin and cos varies between -1 and 1 so when you add two sinusoidal functions(as you are doing) then at some point they are in phase and there amplitudes add up and at some points they are out of phase and there amplitudes are subtracted. So that's the reason of getting amplitudes other than expected. If you take 'fft' of one of these functions then you will get expected answer individually but in combine effect situation will be different. Maybe following link is also helpful for further explanation:

http://www.acs.psu.edu/drussell/demos/superposition/superposition.html

I hope it explains the reason. Good luck!