Fourier Series: Square wave approximation using sin wave
In the world of mathematics, few concepts possess the transformative power and versatility of the Fourier series. Named after the French mathematician and physicist Jean-Baptiste Joseph Fourier, this mathematical framework is a cornerstone of modern science and engineering, with applications that span across numerous disciplines.
At its essence, the Fourier series is a profound mathematical tool that allows us to dissect complex, periodic functions into simpler, sinusoidal components. It unravels the hidden melodies within seemingly dissonant waves, revealing a harmonious symphony of fundamental frequencies and amplitudes. In doing so, it offers a unique perspective on the fundamental nature of periodic phenomena, from the vibrations of a guitar string to the intricacies of electromagnetic waves.
The power of the Fourier series lies not only in its ability to deconstruct complex waveforms but also in its capacity to reconstruct them. By summing up these individual sine and cosine waves, we can approximate, and even precisely replicate, complex periodic signals—a capability that underpins countless technologies, from signal processing and image compression to the study of quantum mechanics.
git clone https://github.com/sidx2/fourier-seriescd fourier-seriesindex.html