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zheng89120
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If you are given part of a period of a Function, what rules would you apply to draw out the full function, so that it converges as quickly as possible as a Fourier series?
thanks
thanks
zheng89120 said:If you are given part of a period of a Function, what rules would you apply to draw out the full function, so that it converges as quickly as possible as a Fourier series?
thanks
A Fourier series is a mathematical representation of a periodic function as a sum of sine and cosine functions with different amplitudes and frequencies.
The purpose of a Fourier series is to approximate a periodic function with a simpler combination of trigonometric functions, making it easier to analyze and manipulate.
The rules for convergence of a Fourier series state that the series will converge to the original function if the function is continuous and piecewise smooth, and if the series satisfies certain conditions such as the Dirichlet conditions.
The Dirichlet conditions are a set of criteria that a function must satisfy in order for its Fourier series to converge. These conditions include the function being periodic, having a finite number of discontinuities, and having a finite number of extrema within a given interval.
No, a Fourier series can only converge to a periodic function. If a non-periodic function is to be approximated, it must first be made periodic by extending it periodically outside of its original domain.