Advantages of dct over 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.

1. What is the difference between DCT and DFT?
2. Why DCT is preferred for image processing?
3. Why DCT is better than FFT?
4. Is DCT faster than DFT?

What is the difference between DCT and DFT?

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 preferred for image processing?

1) The DCT is real-valued instead of complexity (i.e., it involves magnitude and phase) such that it is easier to be implemented. 2) The DCT is more efficient for illumination variation estimation than the DWT. 3) The DCT approach is similar to the homomorphic filtering, which has been used for contrast enhancement.

Why DCT is better than FFT?

The difference between a Discrete Fourier Transform and a Discrete Cosine transformation is that the DCT uses only real numbers, while a Fourier transform can use complex numbers. The most common use of a DCT is compression. It is equivalent to a FFT of twice the length.

Is DCT faster than DFT?

We can say DCT is simpler and faster than DFT and also FFT. DCT is suitable for periodically and symmetrically extended sequence whereas DFT is for periodically extended sequence. Therefore DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry.