Fouriertunnus
Fouriertunnus, also known as Fourier's theorem or Fourier's series, is a fundamental concept in mathematics and physics, named after the French mathematician Joseph Fourier. It states that any periodic function can be represented as a sum of sine and cosine functions, or equivalently, as a sum of complex exponentials. This theorem is crucial in various fields, including signal processing, heat transfer, and quantum mechanics.
The Fourier series is expressed as:
f(t) = a0/2 + ∑ [an * cos(nωt) + bn * sin(nωt)],
where f(t) is the periodic function, ω is the angular frequency, and an and bn are the Fourier
Fouriertunnus has several important properties:
1. Linearity: The Fourier series of a linear combination of functions is the same linear combination of
2. Orthogonality: The sine and cosine functions used in the series are orthogonal, meaning they are independent
3. Convergence: The Fourier series converges to the original function at points where the function is continuous
The Fourier transform, an extension of the Fourier series, is used to analyze non-periodic functions. It converts