Python code. Transforms an 8x8 matrix using DCT, quantizes the result, then transforms it back.

dct.py

#!/usr/bin/env python

"""Transforms an 8x8 matrix using DCT,
quantizes the result,
then transforms it back.
"""

from __future__ import division
from math import sqrt, cos, pi, floor

def index(x, y):
    return y * 8 + x


def show(heading, values):
    print heading
    for y in range(8):
        print 'y=%d  ' % y,
        for x in range(8):
            value = values[index(x, y)]
            print '%9.3f' % value,
        print

def showf(heading, func):
    print heading
    for y in range(8):
        print 'y=%d  ' % y,
        for x in range(8):
            value = func(x, y)
            print '%9.3f' % value,
        print

def alpha(u):
    return sqrt(1 / 8) if u == 0 else sqrt(2 / 8)

g = [x - 128 for x in
    52, 55, 61, 66, 70, 61, 64, 73,
    63, 59, 55, 90, 109, 85, 69, 72,
    62, 59, 68, 113, 144, 104, 66, 73,
    63, 58, 71, 122, 154, 106, 70, 69,
    67, 61, 68, 104, 126, 88, 68, 70,
    79, 65, 60, 70, 77, 68, 58, 75,
    85, 71, 64, 59, 55, 61, 65, 83,
    87, 79, 69, 68, 65, 76, 78, 94,
]
show('g', g)

def get_g(x, y):
    return g[index(x, y)]

def get_G(u, v):
    return sum(
        alpha(u) * alpha(v) *
        get_g(x, y) *
        cos(pi / 8 * (x + .5) * u) *
        cos(pi / 8 * (y + .5) * v)
        for y in range(8)
        for x in range(8)
    )

G = [
    get_G(u, v)
    for v in range(8) for u in range(8)
]
show('G', G)

def get_B(u, v):
    v = get_G(u, v)
    # Artificial quantize
    return floor(v)

def get_f(x, y):
    return sum(
        alpha(u) * alpha(v) *
        get_B(u, v) *
        cos(pi / 8 * (x + .5) * u) *
        cos(pi / 8 * (y + .5) * v)
        for u in range(8)
        for v in range(8)
    )

showf('f', get_f)