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Results tagged with fourier-analysis
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user 157781
The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.
10
votes
2
answers
1k
views
Fourier series of $\log(a +b\cos(x))$?
By numerical computation it seems like, if $a_0 < a_1$:
$$
\begin{multline}
\log({a_0}^2 + {a_1}^2 + 2 a_0 a_1 \cos(\omega t)) = \log({a_0}^2 + {a_1}^2) \\
+ \frac{a_0}{a_1}\cos(\omega t)
- \frac{1}{ …
7
votes
Fourier series of $\log(a +b\cos(x))$?
To apply the solution proposed by @ChristianRemling to the more general case stated in the title you need to do the following:
The formula implies $a > 0$ and $|b| < a$. To solve the problem, we refo …