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jimmy93
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Need help on Fourier series! Been stuck on this questions, it is too tough for me!
What have you been able to do so far?jimmy93 said:
A Fourier series is a mathematical representation of a periodic function as a sum of sinusoidal functions. It is used to decompose a complex function into simpler components, making it easier to analyze and manipulate.
Fourier series have many applications in science and engineering, such as signal processing, image and sound compression, and solving differential equations. Understanding Fourier series allows us to better understand and manipulate these functions for various purposes.
The process for finding the coefficients in a Fourier series involves using the Fourier series formula, which takes into account the function's period and its integral over the period. The coefficients can also be found using orthogonality properties of sine and cosine functions.
In order for a function to have a Fourier series representation, it must be periodic and have a finite number of discontinuities within one period. It must also be square integrable, meaning its integral over one period must converge.
Fourier series are limited to representing periodic functions, so they cannot be used for non-periodic functions. Additionally, the accuracy of the representation depends on the number of terms used in the series, so it may not be suitable for highly complex functions.