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Unformatted text preview: 11.01.1 Chapter 11.01 Introduction to Fourier Series In general, curve fitting interpolation through a set of data points can be done by a linear combination of polynomial functions, with based functions 1, . ,......., , 2 m x x x In this chapter, however, trigonometric functions such as ), ( cos ),...... 2 ( cos ), ( cos , 1 nx x x and ) ( sin ),......, 2 ( sin ), ( sin nx x x will be used as based functions. In the former, the unknown coefficients of based functions can be found by solving the associated linear simultaneous equations (where the number of unknown coefficients will be matched with the same number of equations, provided by a set of given data points). In the latter, however, the unknown coefficients can be efficiently solved (by exploiting special properties of trigonometric functions) without requiring solving the expensive simultaneous linear equations (more details will be explained in Equation 6 of Chapter 11.05). Introduction The following relationships can be readily established, and will be used in subsequent sections for derivation of useful formulas for the unknown Fourier coefficients, in both time...
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- Spring '08