Real

Retrieve DFT coefficients from DCT coefficients

Retrieve DFT coefficients from DCT coefficients
  1. Is DCT real part of DFT?
  2. What is the difference between DFT and DCT?
  3. Why DCT is used instead of DFT?

Is DCT real part of DFT?

DCT is NOT the real part of the DFT rather it is related to the DFT of a symmetrically extended signal/image. The energy of signal/image is packed mostly in only a few DCT coefficients (i.e. only a few significant X(k)'s), hence making DCT very useful for data compression applications.

What is the difference between DFT and DCT?

Like the discrete Fourier transform (DFT), a DCT operates on a function at a finite number of discrete data points. The obvious distinction between a DCT and a DFT is that the former uses only cosine functions, while the latter uses both cosines and sines (in the form of complex exponentials).

Why DCT is used instead of DFT?

> DCT is preferred over DFT in image compression algorithms like JPEG > because DCT is a real transform which results in a single real number per > data point. In contrast, a DFT results in a complex number (real and > imaginary parts) which requires double the memory for storage.

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