The discrete cosine transform (DCT) helps separate the image into parts (or spectral sub-bands) of differing importance (with respect to the image's visual quality). The DCT is similar to the discrete Fourier transform: it transforms a signal or image from the spatial domain to the frequency domain .
From Book: "Introduction to digital audio coding and standards"
The Fourier Transform is the basic tool for converting a signal from its representation in time x(t) into a corresponding representation in frequency X(f).
For sin, cos signal, Notice that the Fourier Transform has components only at frequencies equal to positive and negative f0. This is a general property of periodic functions.
Notice that great deal of data reduction associated with representing this signal, as opposed to having to store its value at every point in time x(t).
Few words of my understanding:
At a period of time, instead of record the value at every time point, we record thefrequency of waves that composite the signal. According to the frequency information, we can calculate the value of signal at a certain time of point.
Mapping time to frequency is in fact a trade of memory space and calculation time.
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