Can I Determine the Fourier Series of |sin x|?

In summary, a Fourier series is a mathematical representation of a periodic function as the sum of sine and cosine functions. It is important because it has practical applications in various fields and allows us to analyze complex functions. It differs from a Fourier transform in that it is used for periodic functions and can be calculated through integrals or complex analysis. The applications of Fourier series include signal processing, data analysis, and solving differential equations in fields such as physics, engineering, and mathematics.
  • #1
Tomp
27
0
Homework Statement
f(x) = |sin x|, -pi < x < pi, f(x) = f(x + 2pi)

Determine the Fourier series of f(x)

The attempt at a solution
I am unsure how to evaluate an integral with absolute signs in it, however, I am wondering if I could reduce the bounds to 0<x<pi and and f(x) = sin x and assume an even function extension (cosine extension). When I sketch these I obtain the same graph.

Am I able to do this?
 
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  • #2
Yes.
 
  • #3
vela said:
Yes.

:) Thank you
 

FAQ: Can I Determine the Fourier Series of |sin x|?

What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function as the sum of sine and cosine functions. It allows us to break down a complex function into simpler components and analyze its behavior.

Why is Fourier series important?

Fourier series is important because it has many practical applications in fields such as signal processing, engineering, physics, and mathematics. It helps us understand and model complex phenomena and solve differential equations.

What is the difference between a Fourier series and a Fourier transform?

A Fourier series is used to represent a periodic function, while a Fourier transform is used to represent a non-periodic function. The Fourier transform is also more general and can be applied to a wider range of functions.

How do you calculate a Fourier series?

The coefficients of a Fourier series can be calculated using integrals or complex analysis techniques. The process involves finding the amplitude and phase of each sine and cosine function that make up the series.

What are the applications of Fourier series?

Fourier series has many applications, including signal processing, image and sound compression, data analysis, and solving differential equations. It is also used in fields such as physics, engineering, and mathematics to model and understand complex phenomena.

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