![]() Thus, the signal y(t) can be represented by two (in general infinitely broad) spectra simply by plotting the coefficients A n and B n against n. Where the fundamental frequency f 0 is related to the cycle time T of the function y(t). ![]() The index n in the equations above can be assigned to a specific frequency f n: The set of cosine and sine functions is complete and orthogonal, which guarantees that any periodic function f(t) can be represented, and that the Fourier coefficients are independent of each other. By setting the coefficients A i and B i one can immediately see their effect on the resulting function. The following interactive example shows you how to combine sines and cosines to form a signal y(t). Where the magnitude and the phase angle can be calculated from the Fourier coefficients as follows: Alternatively, the signal y(t) may be described by the magnitudes D n and the phase angles φ n: Is equal to the average amplitude of the signal). The coefficientĪ 0 represents the aperiodic fraction of the signal (i.e. With A n and B n being the Fourier coefficients,Īnd T the cycle time of the function y(t). Any periodic signal y(t) may be constructed from an infinite sum of sine
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