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Fourier analysis provides a mathematical technique to bring out the periodic structures in data or signals, this makes it possible to compress the data by representing it in terms of fewer sinusoids.

Compression

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Compression refers to the process by which information or data is reduced in volume but can ultimately be reproduced in its original, full form. It can be applied in various fields like mathematics, physics, computer science, and engineering. The goal of compression is to reduce the redundancy in stored or communicated data, thus saving on storage space or data transmission capabilities.

What is Compression?

In the broadest sense, compression is the process of reducing the size or volume of a series of data. Compression is utilized across a wide array of disciplines, such as file storage and transfer, image and video processing, and even mathematical theory.

Types of Compression

There are two main types of compression: Lossless and Lossy Compression. Lossless compression allows for the original data to be perfectly reconstructed from the compressed data. This is the basic type of compression in which no data is lost in the process. Lossy compression, on the other hand, only allows an approximation of the original data to be reconstructed and involves a certain degree of loss of information.

Importance of Compression

Compression is crucial in managing large amounts of data, reducing the consumption of expensive resources, such as hard disk space and transmission bandwidth. Without compression, our current usage of digital media and the internet might not be possible.

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Data Storage
A common application of mathematics-based compression is in the field of data storage. By compressing data, you can store more information in a given amount of space.
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Data Transmission
Data transmission in computer networks often depends on the application of compression techniques to reduce the size of data, making it easier and faster to transmit.
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Data Transmission
In data transmission, the compressed data can be sent over a network, which can save bandwidth and reduce transmission time.
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Data Transmission
Compression reduces the volume of information thereby making data transmission more efficient.