What Are the Benefits of Using Discrete Cosine Transform?

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The Discrete Cosine Transform (DCT) converts a sequence of real numbers into a set of coefficients that represent the original data in a more compact form. This transformation is particularly beneficial for data compression, as it helps reduce the amount of information needed to represent a signal while preserving essential features. DCT is widely used in image and audio compression formats, such as JPEG and MP3, due to its ability to minimize redundancy. Additionally, it enhances the efficiency of data transmission and storage. Overall, utilizing DCT leads to improved performance in various applications by optimizing data representation.
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The N real numbers x0, ..., xN-1 are transformed into the N real numbers X0, ..., XN-1 according to one of the formula by DCT.

I would ask what is the benefit and why should we do that?
 
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