Skip to content
View jonas1ara's full-sized avatar
45 followers · 93 following

Achievements

Achievement: Pull SharkAchievement: StarstruckAchievement: YOLOAchievement: Quickdraw

Achievements

Achievement: Pull SharkAchievement: StarstruckAchievement: YOLOAchievement: Quickdraw

Highlights

  • Pro

Block or report jonas1ara

Block user

Prevent this user from interacting with your repositories and sending you notifications. Learn more about blocking users.

You must be logged in to block users.

Please don't include any personal information such as legal names or email addresses. Maximum 100 characters, markdown supported. This note will be visible to only you.
Report abuse

Contact GitHub support about this user’s behavior. Learn more about reporting abuse.

Report abuse
jonas1ara/README.md

I'm Jonas Lara

A mathematician

Fourier series, a poem ...

The Fourier series is a branch of Fourier analysis that aims to decompose a periodic function into a sum of exponentials (or trigonometric functions) with different frequencies and magnitudes, in this particular demonstration, we are defining $f(t)$ to be a periodic complex function with $t\in[0, 1]$

Represent $f(t)$ as a sum of exponential functions rotating at frequencies of $0, 1, -1, 2, -2, ...$ rotations per $t$:

$$ f(t) = \dots + c_{-2}e^{-2\cdot 2\pi it} + c_{-1}e^{-1\cdot 2\pi it} + c_{0}e^{0\cdot 2\pi it} + c_{1}e^{1\cdot 2\pi it} + c_{2}e^{2\cdot 2\pi it} + \dots $$

Taking the integral of the function across its domain:

$$ \int_0^1 f(t) dt $$

Expanding $f(t)$ in terms of its Fourier series:

$$ \int_0^1 f(t) dt = \int_0^1 (\dots + c_{-1}e^{-1\cdot 2\pi it} + c_{0}e^{0\cdot 2\pi it} + c_{1}e^{1\cdot 2\pi it} + \dots)dt $$

Distributing the definite integral:

$$ \int_0^1 f(t) dt = \dots + \int_0^1c_{-1}e^{-1\cdot 2\pi it}dt + \int_0^1c_{0}e^{0\cdot 2\pi it}dt + \int_0^1c_{1}e^{1\cdot 2\pi it}dt + \dots $$

Blog

If you are interested in computer science topics, you may be interested in my blog: jonas1ara.net

Popular repositories Loading

  1. 73 73 Public

    The 73 most useful LeetCode problems implemented in C, C++, C# and F#

    C# 116 9

  2. IPN-CS IPN-CS Public

    Ciencias de la computación impartidas en la Unidad Profesional Interdisciplinaria de Ingeniería Campus Tlaxcala (Linux)

    C 21 5

  3. Numerical-methods-fs Numerical-methods-fs Public

    Fsharp makes it easy to use numerical methods

    F# 20 2

  4. Windows.devs Windows.devs Public archive

    Customize Windows 10 with FHD Backgrounds and Fluent Design File Explorer, Powershell 7 preview, Azure CLI, CMD and WSL (Debian, Ubuntu, Kali) with Docker and ... .NET 5

    11 3

  5. dotFiles dotFiles Public

    dotFiles for work with .NET from terminal (Windows, Linux and Mac) 🖥️

    PowerShell 3 1

  6. NNs-Cpp NNs-Cpp Public

    Implementación de una red neuronal (perceptron) en C usando el dataset MNIST para reconocer números escritos a mano

    C 3