Transforms to and from the Frequency Domain - Digital Video and Audio Broadcasting Technology - page 102

The DCT is the algorithm at the core of the JPEG and MPEG image
compression (digital photography and video) in which an image is trans-
formed two-dimensionally block by block into the frequency domain and
compressed block by block. It is of particular importance that the block
edges cannot be recognized in the image after its decompression (no dis-
continuities at the edges).
The discrete cosine transform does not supply the coefficients in the
frequency domain in pairs, i.e. separated according to real and imaginary
parts and does not provide any information about the phase, only about the
amplitude. Neither does the amplitude characteristic correspond directly to
the result of the DFT. But this type of frequency transform is adequate for
many applications and is also possible in both directions (Inverse Discrete
Cosine Transform - IDCT) (Fig. 6.10.).
In principle, of course, there is also a Discrete Sine Transform (Fig. 6.9)
where it is attempted to duplicate a time domain signal by the superposi-
tion of pure sinusoidal signals.
Fig. 6.11. Fourier Transform of a single squarewave pulse
Fig. 6.12. Fourier Transform of a periodic squarewave pulse