Learn about fourier series, trigonometrical fourier series

Thread starter seema283k
Start date Aug 18, 2009
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Fourier Fourier series Series

In summary, a Fourier series is a mathematical representation of a periodic function as a sum of sine and cosine functions. It is used to analyze and approximate periodic functions in various fields. The difference between a Fourier series and a trigonometrical Fourier series is that the latter is specifically used to represent a function with a period of 2π. To calculate a Fourier series, the coefficients of the sine and cosine functions must be found. These coefficients can be found using different methods such as the Fourier coefficients formula or Euler's formula. Fourier series have various real-world applications, including signal processing and data compression. However, they may have limitations when representing functions with sharp corners or discontinuities and may not converge for some types of functions, resulting in

Aug 18, 2009

seema283k

sir please give me a good way to learn about Fourier series, trigonometrical Fourier series.
explain the term by examples and by 3-d figure and imagination

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Aug 26, 2009

foxjwill

Have you tried your local university's library?

Aug 26, 2009

HallsofIvy

Science Advisor

Homework Helper

This is probably not a good place for a complete course!

1. What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function as a sum of sine and cosine functions with different amplitudes and frequencies. It is used to analyze and approximate periodic functions in fields such as mathematics, physics, and engineering.

2. What is the difference between Fourier series and trigonometrical Fourier series?

A Fourier series is a general term for any series made up of sine and cosine functions. On the other hand, a trigonometrical Fourier series specifically refers to a Fourier series that is used to represent a periodic function with a period of 2π.

3. How is a Fourier series calculated?

A Fourier series is calculated by finding the coefficients of the sine and cosine functions that, when added together, will approximate the given periodic function. These coefficients can be found using various methods, such as the Fourier coefficients formula or the Euler's formula.

4. What is the importance of Fourier series in real-world applications?

Fourier series have a wide range of applications in various fields, including signal processing, image analysis, and data compression. They allow us to break down complex periodic functions into simpler components, making it easier to analyze and manipulate them.

5. What are some limitations of Fourier series?

While Fourier series can accurately represent most periodic functions, they may not be able to accurately represent functions with sharp corners or discontinuities. Additionally, they may not converge for some types of functions, resulting in an inaccurate representation.