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Fourier analysis
The wave patterns produced by the most of sound sources are non-sinusoidal. However, all sound wave patterns have a common important property: they are periodic. So they can be represented as closely as described by the combination of sufficiently large number of sinusoidal waves that form a harmonic series. According to Fourier´s theorem if function y(t) is periodic in time with period T, such that y(t+ T ) = y(t), it can be written as a series of sine and cosine y(t) = Σ(Ansinωnt + Bncosωnt), where the lowest frequency is ω0 = 2π/T. The higher frequencies are integer multiples of the fundamental, and the coefficients An and Bn represent the amplitudes of the various waves.
The simulation helps understanding a harmonic analysis of the wave patterns shown on buttons from the right above. You can construct some very special complex waves by adding to the fundamental the right combination of higher harmonics. In the top box you may see a blue initial signal or red synthesized signal or both together according to your choice. That realizes with help of nearby check box controls. In two below boxes all used harmonics are shown with compatibility values of them amplitudes. The calculated values of amplitude and frequency of fundamental harmonic so as of last from used introduce in output box from right below.
Experiment with different waveforms. With help of the sliders change period Ò, a time controlling patterns features τ and a number of harmonics n.
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