27. Write a program that implements forward and backward DCT,
using floating-point arithmetic. Run the program on a sample
grayscale image. Since DCT is lossless, the image output by the
program should match the input. Now modify your program so
that it zeroes some of the higher-frequency components, and see
how the output image is affected. How is this different from what
JPEG does?
28. Express DCT(0,0) in terms of the average of the pixel(x,y)s.
29. Think about what functions might reasonably be expected from a
video standard: fast-forward, editing capabilities, random access,
and so on. (See the paper by Le Gall, “MPEG: A video compression
standard for multimedia applications,” given in this chapter’s
Further Reading list, for more ideas.) Explain MPEG’s design in
terms of these features.