The DCT exhibits the “energy compaction property”, meaning that for many signals only the first few DCT coefficients have significant magnitude. Zeroing out the other coefficients leads to a small reconstruction error, a fact which is exploited in lossy signal compression (e.g. JPEG compression).
The example below shows a signal X and two reconstructions (X20 and X15) from the signal’s DCT coefficients. The signal X20 is reconstructed from the first 20 DCT coefficients, X15 is reconstructed from the first 15 DCT coefficients. It can be seen that the relative error of using 20 coefficients is still very small (~0.1%), but provides a five-fold compression rate.
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