# Where Can I Find Helpful Tutorials on Fourier Series?

• cgw
In summary: Free-Engineering-Video-lectures-ltv263-Page1.htmIn summary, the conversation is about finding resources for learning about Fourier series. The conversation includes recommendations for video lectures, websites, and blogs that cover the topic in depth. Some key concepts mentioned include orthogonality, basis states, fast Fourier transform, orthonormal basis, and Hilbert Space. Overall, the conversation is a helpful resource for those looking to understand the math behind Fourier series.
cgw
Looking for Fourier series tutorials or even better video lectures on the subject.

In that vein, can anybody put together a few links to help learn/understand the math behind the Fourier series? Just from eyeballing I'd guess a solid understanding of integration of trigonometric functions, but I'm sure there's more to it.

matticus said:
these video lectures are pretty good, this is the first one but there's tons.

This guy needs some valium!
Glad I don't have lectures with him at 9 on monday mornings

good lecturer though.

By far the only one I saw but I REALLY liked it

http://ocw.mit.edu/OcwWeb/Physics/8-03Fall-2004/VideoLectures/index.htm

11th lecture

The explanation is great. He shows the contribution of every single sin and cos and then shows some vibrations with a computer program which show all the harmonics which contribute to building the periodic function.

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naele said:
In that vein, can anybody put together a few links to help learn/understand the math behind the Fourier series? Just from eyeballing I'd guess a solid understanding of integration of trigonometric functions, but I'm sure there's more to it.

Naele~

Fourier Series is a *special case* of a more general concept. Perhaps some key words you could look up online or in textbooks would be : orthogonality, basis states, fast Fourier transform (FFT), orthonormal basis, maybe even Hilbert Space, or Gram Schmidt, or Legendre polynomials, or Sturm-Liouville.

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I came across these a little while ago:

(I know that Fourier series and the transform itself aren't the same thing, but I thought you might still like the videos)

I watched the whole 30 lecture series and they are very very good. I got so much out of it. Topics covered are Fourier Series, Fourier Transforms, convolutions, how they apply to linear systems in general, sampling, discrete Fourier Transforms, and higher dimensional Fourier Transforms. He also goes into good depth into how distributions like the Dirac Delta function are rigorously defined by Mathematicians. He's a great teacher and explains everything in such a way that it all seems natural. He's also quite funny too. You can download the whole course from iTunes U as well.

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(I know that Fourier series and the transform itself aren't the same thing, but I thought you might still like the videos)

a Fourier transform is like a Fourier series of a periodic function where the period is infinite

A blog post on http://learntofish.wordpress.com/2009/08/28/understanding-the-fourier-transform-intuitively/" .

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matticus said:
these video lectures are pretty good, this is the first one but there's tons.

Wow. And I thought my linear algebra professor flew through material like crazy!

## 1. What is a Fourier Series?

A Fourier Series is a mathematical tool used to represent a periodic function as a sum of sinusoidal functions. It is named after French mathematician Joseph Fourier and is widely used in fields such as signal processing, image processing, and physics.

## 2. Why are Fourier Series important?

Fourier Series are important because they allow us to break down complex functions into simpler components, making it easier to analyze and understand. They also have many practical applications in various fields such as engineering, physics, and mathematics.

## 3. How do you calculate the coefficients of a Fourier Series?

The coefficients of a Fourier Series can be calculated using the Fourier Series formula, which involves integrating the function over one period and multiplying it by the appropriate trigonometric functions. Alternatively, there are also specific formulas for calculating the coefficients of common types of functions such as square waves and sawtooth waves.

## 4. What is the difference between a Fourier Series and a Fourier Transform?

A Fourier Series represents a periodic function as a sum of sinusoidal functions, while a Fourier Transform represents a non-periodic function as a continuous spectrum of sinusoidal functions. In other words, a Fourier Series is used for periodic functions, while a Fourier Transform is used for aperiodic functions.

## 5. Are there any limitations of Fourier Series?

Yes, there are some limitations of Fourier Series. It can only be applied to functions that are periodic, and it may not converge for certain types of discontinuous functions. Additionally, it may not be suitable for analyzing functions with sharp spikes or corners.

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