- #1
iScience
- 466
- 5
actually have two questions:
here we have a Fourier series..
$$f(t) = \sum c_k e^{2\pi ikt}$$ (c is complex)
if we're trying to express a real function via Fourier series, and we do it the following way..
Impose condition: $$\overline{c_k} = c_{-k}$$
$$f(t) = \sum\limits_{k= -n}^n c_k e^{2\pi ikt}$$
then, although the constants would become real, wouldn't the exponents go to zero? why not?
could someone give me more of an intuitive understanding for the "orthogonality" of sine functions? i know the integral definition, but how exactly does this integral dictate what can & can't be expressed in terms of what (ie could you relate the integral definition to the classical sense of the word 'orthogonal')
here we have a Fourier series..
$$f(t) = \sum c_k e^{2\pi ikt}$$ (c is complex)
if we're trying to express a real function via Fourier series, and we do it the following way..
Impose condition: $$\overline{c_k} = c_{-k}$$
$$f(t) = \sum\limits_{k= -n}^n c_k e^{2\pi ikt}$$
then, although the constants would become real, wouldn't the exponents go to zero? why not?
could someone give me more of an intuitive understanding for the "orthogonality" of sine functions? i know the integral definition, but how exactly does this integral dictate what can & can't be expressed in terms of what (ie could you relate the integral definition to the classical sense of the word 'orthogonal')
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