- #1
Umabel
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Does anyone know a good site that covers the Fourier series/transform and its uses?
Understand Fourier Transforms: A Comprehensive Guide
- Thread starter Umabel
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In summary, the conversation discusses the topic of Fourier series/transform and its multiple uses. It is mentioned that there are too many uses to be covered by one website, and the concept of duality between functions on a group and functions on the dual group is brought up. The conversation concludes with the suggestion to start searching and reading different websites or going to a library for further knowledge.
- #2
mathwonk
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its uses are too many to be covered by one site. the idea is to look at the duality between functions on a group such as R, and functions on the dual group, in this case the circle.
It has hugely many uses including generalizations to analysis of sheaves on abelian varieties and their dual varieties.why not just start searching and reading the sites you find? or go to the "library" (a building at your school where knowledge is stored in print in "books").
It has hugely many uses including generalizations to analysis of sheaves on abelian varieties and their dual varieties.why not just start searching and reading the sites you find? or go to the "library" (a building at your school where knowledge is stored in print in "books").
- #3
Umabel
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Good idea. I thought it was broad...just not THAT broad. Thanks alot. 
FAQ: Understand Fourier Transforms: A Comprehensive Guide
What is a Fourier Transform?
A Fourier Transform is a mathematical technique used to analyze signals or functions that vary over time or space. It decomposes a signal into its individual frequency components, allowing for a better understanding of the underlying patterns and characteristics.
Why are Fourier Transforms important?
Fourier Transforms are important because they are used in many scientific and engineering fields, including signal processing, image and sound analysis, and quantum mechanics. They also allow for a deeper understanding of the behavior and properties of complex systems.
How is a Fourier Transform calculated?
A Fourier Transform is calculated by taking a signal and breaking it down into its individual frequency components using a mathematical formula called the Fourier Series. This involves converting the signal from the time domain to the frequency domain, where it can be represented as a sum of sinusoidal functions.
What is the difference between a Fourier Transform and a Fourier Series?
A Fourier Transform is a continuous version of the Fourier Series, which is a discrete version. A Fourier Series breaks down a signal into a finite number of frequency components, while a Fourier Transform can handle signals with an infinite number of frequency components. Additionally, a Fourier Series is used for periodic signals, while a Fourier Transform can be applied to non-periodic signals as well.
How are Fourier Transforms used in image processing?
In image processing, Fourier Transforms are used to analyze the spatial frequency content of an image, which can reveal important information about its features and structure. They are also used in image filtering and compression techniques, as well as in the creation of 2D and 3D images from multiple 1D signals.