![]() There are two common forms of the Fourier Series, " Trigonometric" and " Exponential." These are discussed below, followed by a demonstration that the two forms are equivalent. In other words he showed that a function such as the one above can be represented as a sum of sines and cosines of different frequencies, called a Fourier Series. In the early 1800's Joseph Fourier determined that such a function can be represented as a series of sines and cosines. We can represent any such function (with some very minor restrictions) using Fourier Series. Since the period is T, we take the fundamental frequency to be ω 0=2π/T. ![]() Contents Statement of the ProblemĬonsider a periodic signal x T(t) with period T (we will write periodic signals with a subscript corresponding to the period). The next page will give several examples. ![]() For now we will consider only periodic signals, though the concept of the frequency domain can be extended to signals that are not periodic (using what is called the Fourier Transform). This page will describe how to determine the frequency domain representation of the signal. ![]() The previous page showed that a time domain signal can be represented as a sum of sinusoidal signals (i.e., the frequency domain), but the method for determining the phase and magnitude of the sinusoids was not discussed.
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