Waveform Quantization and Compression - Digital Signal Processing: Fundamentals and Applications - page 522

For comprehensive coverage of the topics on DCT, see Li and Drew (2004), Nelson (1992),
Saywood (2000), and Stearns (2003).

11.4.2 Modified Discrete Cosine Transform
In the previous section, we observed how a 1D-DCT is adopted for coding a block of data. When we
apply the 1D-DCT to audio coding, we first divide the audio samples into blocks and then transform
each block of data with DCT. The DCT coefficients for each block are quantized according to the bit
allocation scheme. However, when we decode DCT blocks, we encounter edge artifacts at boundaries
of the recovered DCT blocks, since DCT coding is block based. This effect of edge artifacts produces
periodic noise and is annoying in the decoded audio. To solve for such a problem, the windowed
MDCT has been developed (described in Pan, 1995; Princen and Bradley, 1986). The principles are
illustrated in Figure 11.14 . As we shall see, the windowed MDCT is used in MPEG-1 MP3 audio
coding.
We describe and discuss only the main steps for coding data blocks using the windowed MDCT
(W-MDCT) based on Figure 11.14 .

N /2 N /2 N /2

A B C

N

N

Encoding
stage

50% overlap
with window h(n)

A

A B

W-MDCT

B

C

W-MDCT

W-MDCT

A_MDCT B_MDCT C_MDCT

W-IMDCT 50% overlap

with window f(n)

W-IMDCT

W-IMDC T

A

A B

BC

Decoding
stage

50%
overlap
add

50%
overlap
add

50%
overlap
add

Recovered A Recovered B Recovered C

FIGURE 11.14

Modified discrete cosine transform (MDCT).