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Jhenrique
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Which is the difference between the Fourier integral and Fourier transform? Or they are the same thing!?
Fourier integral:
Fourier integral:
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The Fourier integral is a mathematical tool that is used to represent a periodic function as a combination of sine and cosine waves. It is used in signal processing and other fields to analyze and manipulate signals.
The Fourier transform is a special case of the Fourier integral, where the function being transformed is not necessarily periodic. The Fourier transform allows us to analyze non-periodic signals, while the Fourier integral is specifically for periodic signals.
In signal processing, Fourier transforms are used to convert a signal from its original domain (such as time or space) to a representation in the frequency domain. This allows us to analyze and manipulate signals by their frequency components.
The Fourier transform is calculated using an integral that involves complex numbers and the function being transformed. This integral is known as the Fourier integral and can be solved using mathematical techniques such as integration by parts or the use of tables.
Fourier transforms have many applications in fields such as engineering, physics, and mathematics. Some common applications include signal processing, image processing, data compression, and solving differential equations. They are also used in everyday devices such as cell phones and Wi-Fi routers.