![]() ![]() ![]() This indicates that comparatively few terms yield a good approximation. Note that the amplitude of the harmonics decreases progressively as the order of the harmonics increases. According to the principle of superposition, the total response is the sum of the responses produced by each term. Each term is considered a separate source. Ω = 2¶/T = The fundamental angular frequency, or 2π times the frequency of the original periodic wave.Įach frequency component (or term) of the response is produced by the corresponding harmonic of the periodic waveform. Given the mathematical theorem of a Fourier series, the period function f(t) can be written as follows:į(t) = A 0 + A 1cosωt + A 2cos2ωt + … + B 1sinωt + B 2sin2ωt + …Ī 0 = The DC component of the original wave.Ī 1cosωt + B 1sinωt = The fundamental component (has the same frequency and period as the original wave).Ī ncosnωt + B nsinnωt = The n th harmonic of the function. This permits further analysis and allows you to determine the effect of combining the waveform with other signals. It permits any nonsinusoidal period function to be resolved into sine or cosine waves, possibly an infinite number, and a DC component. Fourier Analysis is a method of analyzing complex periodic waveforms. ![]()
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