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Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

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DCT (Discrete Cosine Transform) is an N-input sequence x(n) , 0≤n≤N-1 , as a linear transformation or combination of complex exponentials. As a result, the DFT coefficients are in general, complex even if x(n) is real.

Suppose, we try to find out an orthogonal transformation which has N×N structure that expressed a real sequence x(n) as a linear combination of cosine sequence. We already know that −

Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)
And Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

This is possible if N point sequence x(n) is real and even. Thus, Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)  The resulting DFT itself is real and even. These things make it clear that we could possibly device a discrete cosine transform, for any N point real sequence by taking the 2N point DFT of an “Even extension” of sequence.

DCT is, basically, used in image and speech processing. It is also used in compression of images and speech signals.

Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)
Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)
Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)
Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

DCT is defined by,

Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)
Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)
Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

The document Discrete Cosine Transform - Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE) is a part of the Electronics and Communication Engineering (ECE) Course Signals and Systems.
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