How does the DCT (Discrete Cosine Transform) help to compress sound (or any wave-like data)? According to the DCT transform there are N input values and N output values as a result. Where is the compression achieved and how?
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Think about the sequence 1,2,3,4,5,.. It will not compress using LZ (zip) at all because there is zero repetition. Now encode the sequence as differences: 1,1,1,1,1,… Zip will compress it 99% now. Every algorithm detects a certain pattern well. DCT helps to encode the data into a format that is well compressible.