IEEE Circuits and Systems Magazine - Q4 2022 - 61

(for HD video) or H.265 (for Ultra HF/4k video). When we
capture video on our phones, watch TV, Netflix, Amazon
video, or make a Zoom or Teams call, we use these
formats, which are all DCT-based. Today, almost 80%
of all data traffic on the Internet is on video streams
in those formats. Ahmed et al.'s [2] original DCT work
was also an inspiration for designing DCT variants and
extensions, such as the modified discrete cosine transform
(MDCT) and lapped transforms (LTs), with overlapping
basis functions that improve compression and
reconstruction quality for images and audio. Essentially
all modern digital audio formats, such as MP3, WMA,
and AAC, are based on these digital variants. The JPEG
XR image format also uses one of those variants and
is used extensively by hundreds of millions of people,
as it is integrated with all Microsoft Office applications.
Moreover, compressed domain image and video
processing which leverages the DCT coefficients, their
residues along with other information like block coding
modes, motion vectors have offered a completely
new paradigm for algorithm development courtesy the
unique DCT properties.
References
[1] J. W. Cooley and J. W. Tukey, " An algorithm for the machine calculation
of complex Fourier series, " Math. Comput., vol. 19, no. 90,
pp. 297-301, 1965.
[2] N. Ahmed, T. Natarajan, and K. Rao, " Discrete cosine transform, "
IEEE Trans. Comput., vol. C-23, no. 1, pp. 90-93, Jan. 1974.
[3] N. Ahmed, " How I came up with the discrete cosine transform, " Digit.
Signal Process., vol. 1, no. 1, pp. 4-5, Jan. 1991.
[4] M. D. Flickner and N. Ahmed, " A derivation for the discrete cosine
transform, " Proc. IEEE, vol. 70, no. 9, pp. 1132-1134, Sep. 1982.
[5] S. A. Martucci, " Symmetric convolution and the discrete sine
and cosine transforms, " IEEE Trans. Signal Process., vol. 42, no. 5,
pp. 1038-1051, May 1994.
[6] J. Mukhopadhyay, Image and Video Processing in the Compressed
Domain. Boca Raton, FL, USA: CRC Press, 2011.
[7] J. Makhoul, " A fast cosine transform in one and two dimensions, "
IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-28, no. 1,
pp. 27-34, Feb. 1980.
Manish Okade (okadem@nitrkl.ac.in), (Senior Member,
IEEE) is an Assistant Professor of electronics and communication
engineering at the National Institute of Technology,
Rourkela, India.
Jayanta Mukherjee (jay@cse.iitkgp.ac.in), (Senior Member,
IEEE) is a Professor of computer science and engineering
at the Indian Institute of Technology Kharagpur, India.
Interview (continued from page 5)
I do not agree when sometimes people say we have no
prejudices, when you can cite example after example of
things that wouldn't have happened if it wasn't for such
a prejudice. So I hope this will change, and I think we
have to work at it because unless we work at it, change
will not come.
Question 8: You are on board of director of Enhancing
Diversity in Graduate Education (EDGE). What role does
this organization play?
Prof. Daubechies: I have worked with EDGE for many
years. At first, I have been on the periphery, and now on
the board. EDGE has helped young women, especially
women from disadvantaged backgrounds who are interested
in mathematics, to persist in mathematics. Even
if their background may be less prepared than others,
EDGE helps them with workshops, special activities,
and a network that gives them both moral and mathematical
support. The success rate of young people
who came through EDGE and then went on to PhDs in
mathematics is very high, which is very impressive.
EDGE now also has a program that is not aimed only at
women but at underrepresented mid-career fellows. It
fourth QuartEr 2022
is a really remarkable program and I think it's the same
idea again - but now for other groups in which we see
underrepresentation in STEM, like people of color and
African Americans, to an even more dramatic extent
than for women. There are young people who have talent,
and we should encourage them if they have the inclination
to become STEM professionals. That's why I'm
proud of my son, because at his school, 95% are black
or Hispanic. Having a positive, fun math teacher can be
life changing.
Question 9: What is your own definition of " success " , or
do you consider one of your past roles to be " success " ?
Prof. Daubechies: Things that make me most proud is
being a member of the community. If my students later
say that they really appreciate my mentorship and they
felt that I made a difference for them for the better, that
is what I find most successful. I now have the next generation.
My son has two small children and asked me to
help. I am actually taking a week off next week to be a
grandma, which also makes me feel very proud. I think
the feeling that I have a meaningful role in people's lives
gives me the greatest sense of accomplishment.
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