>>7812092 I should clarify: generally you look at just the fourier series when you don't particularly care about the phase. If you also care about the phase, you'd more likely use the fourier transform. Some math majors might get angry at me for this explanation, but as a EE that's how I like to think about it.
>>7812615 well it would happen if the frequency were different, which is almost always the case... except here.
Take another look at the formula. A sine and a cosine are just the same function shifter by 90° right? the coefficients in front of them are just tuning parameters saying how much closer to a sine or to a cosine the function is. If phi=0, you get a regular sin. All the weight is put on the sine part. If phi increases, you get something closer to a cos, and more weight is put on the cos part. So another way to see it is to consider the shift as a weight given to each function basically.
>>7812659 Thanks, this makes sense, I'm just too used to seeing different frequencies. Could I just ask one last question? As far as I understood I can use Fourier transform on a periodic function (let's say a piano note) to switch between time (direct) and frequency (inverse) domain. But how do I use it? Let's say I have the value of the air pressure in a point in function of the time (real value), but the Fourier transform uses complex numbers, doesn't it? Do I just set the imaginary part to 0 and call it done or did I get it wrong?
>>7812099 I'm a math major and yes we do get "angry". Just in case anyone is interested, there's a major difference between a Fourier series and a transform. The series works with periodic functions or with discrete functions defined for all n. The transform works with integrable functions in the whole real line (or real plane, or whatever you're dealing with).
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