ABSTRACT
Orthogonality and cyclic convolution structure are two interesting
properties of many transforms that allow complete recovery of a
signal from its version in the transform domain. In this chapter, we
start by visiting some very fundamental requirements of a transform
with these properties and naturally formulate the discrete Fourier
transform (DFT) and the number theoretic transform (NTT). We
then highlight the fastest way to realize the DFT using the NTT
and develop the discrete cosine transform (DCT), integer cosine
transform (ICT) with the kernel (1,2,1) in H.264/HEVC standards
and our most recently suggested kernel (5,7,3) for video coding.
We shall also discuss our recent work on using DCT techniques
for fast and quality super-resolution videos. We have a strategy on
using academic research results to underpin industrial research and
development, which aremostly related tomodern video surveillance
with big data and Internet of things. With this strategy in mind, we
will end the chapter with brief ideas on new trends and future hi-
tech applications.
