The Discrete Cosine Transform (DCT)
The Fourier transform and the DFT are designed for processing complex-valued signals, and they always produce a complex-valued spectrum even in the case where the original signal was strictly realvalued. The reason is that neither the real nor the imaginary part of the Fourier spectrum alone is sufficient to represent (i.e., reconstruct) the signal completely. In other words, the corresponding cosine (for the real part) or sine functions (for the imaginary part) alone do not constitute a complete set of basis functions.
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