![]() ) are needed to approximate the function this is because of the symmetry of the function. As before, only odd harmonics (1, 3, 5.There is no discontinuity, so no Gibb's overshoot.Even with only the 1st few harmonics we have a very good approximation to the original function. Conceptually, this occurs because the triangle wave looks much more like the 1st harmonic, so the contributions of the higher harmonics are less. The amplitudes of the harmonics for this example drop off much more rapidly (in this case they go as 1/n 2 (which is faster than the 1/n decay seen in the pulse function Fourier Series (above)).As you add sine waves of increasingly higher frequency, the approximation gets better and better, and these higher frequencies better approximate the details, (i.e., the change in slope) in the original function.Note: this is similar, but not identical, to the triangle wave seen earlier. ![]() If x T(t) is a triangle wave with A=1, the values for a n are given in the table below (note: this example was used on the previous page). During one period (centered around the origin) The periodic pulse function can be represented in functional form as Π T(t/T p). The Fourier series expansion for a square-wave is made up of a sum of odd harmonics, as shown here using MATLAB.
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