[Mp4-tech] Why only low frequeny is considered in DCT?

[Anup Mankar]

Hi Sagar,
To answer your question, let me take you through the very basic reason
to perform a transform.
1. How does a transform achieve compression?
A. What is compression? Expressing something in the least possible bits.
Take for example, a point in a 2D space. We need to have an component
along the x-axis and a component along the y-axis. Say we need an
integer (32 bits) to store each of these. For simplicity, let's say the
max. component fits within those 32 bits. That makes 64 bits. But if we
twist the axes such that the point lies on the x-axis, we do not need
the component along the y-axis. This is how decorrelation of information
takes place in a transform. But if you observe closely, we have
successfully eliminated the need for the redundant 32 bits and voila,
we've achieved compression.
2. Why the DCT?
A. The Kahrunen-Loeve is one such transform which decorrelates
information without loss, transforming signal information from the
spatial to the frequency domain. But the Markov chain (since we are
working in discrete time) involved needs a lot of processing. Hence we
make use of the poor lossy cousin, the Type II  DCT in real world image
processing, majorly due to it's energy compaction property.
3. Why are the lower frequency components more important?
A. As described in the answer to the 1st question a transform should
ideally allow us to depict the signal information in the least possible
components. The DCT by it's nature compacts the energy of the signal
into the lower frequency components. Since the least frequency is 0, the
DC component is of utmost importance. However the DCT being an
approximation to the KLT, we do get components along the other axes.
Hence even some non-zero frequency components could retain some signal
energy. Hence we perform a zig-zag scan to get the higher energy (low
frequency) components so as to preserve maximum information.
Hope this answers your query.
Regards,
Anup
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