# Tagged Questions

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### What is the formula for single frequency generation function obtained from FFT?

What is the correct formula of a function that generates specific tone from fourier transform? I thought that having: transformata - an array with FFT of a source sample. v = transformata[freq] - ...
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### Fourier Series Approximations of Functions

From a few examples of smooth functions, discontinuous functions and continuous functions which have a 'kink' (i.e. $|x|$ where left and right limits disagree)... I've seen that the fourier series ...
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### How to extend a given function to an odd function with period 2 (Fourier Series)

This is the question. f(x) = 7x^2 + 4 I want to know how to extend the above fuction to become a odd function with period 2.
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### Fourier Series of what appears to be a sawtooth series

Find the Fourier series of $$f(x)=\begin{cases} x-[x] \quad &\text{if x is not an integer} \\ \frac{1}{2} \quad &\text{if x is an integer} \end{cases}$$ ...
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### Representing series $f(t)= \frac{\pi c^2}{l^2} \sum_{n=1}^\infty \frac{ n }{\omega_n}\cos(\omega_nt)$ as a Dirac comb function.

Consider the function $$f(t)= \frac{\pi c^2}{l^2} \sum_{n=1}^\infty \frac{ n }{\omega_n}\cos(\omega_nt)$$ where $\omega_n= \sqrt{(\frac{n \pi c}{l})^2-(\frac{r_0}{2})^2}.$ If we neglect the term ...
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### Relations between complex functions satisfying a specific condition

What is the relation between the following two complex functions: $$g(\theta)=\sum_n x[n]\ y[n]\ e^{in\theta}$$ and $$f(\theta)=\sum_n \left(x[n]\pm i\sqrt{1-x[n]^2}\right)\ y[n]\ e^{in\theta}$$ ...
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### expansion for $1-|t|$

Let $f$ be a continuous function on $\mathbb{R}$ with compact support with exactly one maximum. Form the functions $$f_{m,k}(x)=f^m\left(x-\frac{k}{2^m}\right)$$ I am wondering if one can expand ...
We know that the Fourier Series $$s(x)=\sum_{k\neq0}\frac{1}{k}\exp\left(2\pi ik x\right)$$ corresponds to the sawtooth function, $s(x)=\left\{x\right\} -\frac{1}{2}$. Suppose that ...