Howtosignalprocessing
- What is the main difference between DCT and DFT?
- Why DCT is used instead of DFT?
- Is DCT The real part of DFT?
- How to calculate DCT?
What is the main difference between DCT and DFT?
DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common.
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.
Is DCT The 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.
How to calculate DCT?
The DCT Transform Matrix
The two-dimensional DCT of A can be computed as B=T*A*T' . Since T is a real orthonormal matrix, its inverse is the same as its transpose. Therefore, the inverse two-dimensional DCT of B is given by T'*B*T .
