We all know that if you have an even function you have only cosine terms and an odd function only sine. When the function is neither even nor odd you get both, or do you?calculate. Once the Fourier series is calculated you just add the dc part back in again. Therefore functions of this sort should also have no cosine terms either just like odd functions. Not seen this in books for some reason.
This suddenly struck me. Suppose you have
f(x)=sin(x) - this is odd since f(-x) = -f(x)
f(x)=sin(x)+1 is neither even nor odd. Now f(-x) ne -f(x)
But this is just a dc level shift.
Could you not therefore apply this to function of this sort. Ones that kind of look odd but have different amplitudes in the negative half cycle. Just adjust the dc level (add or subtract) to zero and then it becomes odd. Then no cosine terms to
We all know that if you have an even function you have only cosine terms
and an odd function only sine.
When the function is neither even nor odd you get both, or do you?
This suddenly struck me. Suppose you have
f(x)=sin(x) - this is odd since f(-x) = -f(x)
f(x)=sin(x)+1 is neither even nor odd. Now f(-x) ne -f(x)
But this is just a dc level shift.
We all know that if you have an even function you have only cosine terms and an odd function only sine. When the function is neither even nor odd you get both, or do you?
This suddenly struck me. Suppose you have
f(x)=sin(x) - this is odd since f(-x) = -f(x)
f(x)=sin(x)+1 is neither even nor odd. Now f(-x) ne -f(x)
But this is just a dc level shift.
Could you not therefore apply this to function of this sort. Ones that kind of look odd but have different amplitudes in the negative half cycle. Just adjust the dc level (add or subtract) to zero and then it becomes odd.
f(x) = odd(f(x)) + even(f(x))
We all know that if you have an even function you have only cosine terms and an
odd function only sine.
When the function is neither even nor odd you get both, or do you?
This suddenly struck me. Suppose you have
f(x)=sin(x) - this is odd since f(-x) = -f(x)
f(x)=sin(x)+1 is neither even nor odd. Now f(-x) ne -f(x)
But this is just a dc level shift.
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