Howtosignalprocessing
- What is the main difference between DCT and DFT?
- How do the properties of DFT and DCT compare?
- Why DCT is used instead of DFT?
- What is the relation between DCT and FFT?
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.
How do the properties of DFT and DCT compare?
The difference between the two is the type of basis function used by each transform; the DFT uses a set of harmonically-related complex exponential functions, while the DCT uses only (real-valued) cosine functions.
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.
What is the relation between DCT and FFT?
Relationship between DCT and FFT
DCT (Discrete Cosine Transform) is similar to the DFT since it decomposes a signal into a series of harmonic cosine functions. DCT is actually a cut-down version of the Fourier Transform or the Fast Fourier Transform (FFT): Only the real part of FFT (less data overheads).
