# Fourier series wave-equation Definition and 4 Discussions

In mathematics, a Fourier series () is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. With appropriate weights, one cycle (or period) of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). As such, the summation is a synthesis of another function. The discrete-time Fourier transform is an example of Fourier series. The process of deriving weights that describe a given function is a form of Fourier analysis. For functions on unbounded intervals, the analysis and synthesis analogies are Fourier transform and inverse transform.

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1. ### I Electronics experiment boards -- What experiment can I do with these?

I recently got these electrical experiment boards to do some experiments but I am new to doing experiments with such boards. Can someone help? Thanks in advance https://ibb.co/zXTbNby https://ibb.co/tDjKrV0 https://ibb.co/JdCTgqY https://ibb.co/DDkGjbp
2. ### Evaluate Fourier series coefficients and power of a signal

Homework Statement Derive the expression for coefficients of Fourier series in exponential form for the sequence of rectangular pulses (with amplitude A, period T and duration θ) shown in this image: Derive the expression for signal power depending on the coefficients of Fourier series...
3. ### Solving Coefficient not using Fourier Series coefficient

Given the Laplace's equation with several boundary conditions. finally i got the general solution u(x,t). One of the condition is that: u(1,y)=y(1-y) After working on this I finally got: ∑An sin(π n y )sinh (π n) = y(1-y) However, i was asked to find An, by not using Fourier series...
4. ### Fourier series solution of wave equation

Homework Statement Suppose a horizontally stretched string is heavy enough for the effects of gravity to be significant, so that the wave equation must be replaced by ##u_{tt} = c^2u_{xx} - g## where ##g## is the acceleration due to gravity. The boundary conditions are ##u(0,t) = u(l,t) = 0##...