Waveform Quantization and Compression - Digital Signal Processing: Fundamentals and Applications - page 524

2 n 1

n þ 2 f hðN n 1 Þf ðnÞh ¼ 0 (11.36)

Here, we choose the following simple function for the W-MDCT:

f ðnÞ¼hðnÞ¼ sin p

N ðn þ 0 : 5 Þ

(11.37)

Equation (11.37) must satisfy the conditions described in Equations (11.35) and (11.36) . This will be
left for an exercise in the Problems section at the end of this chapter. The MATLAB functions
wmdcth() and wimdctf() relate to this topic and are listed in Programs 11.14-11.5 in section ( 11.7 ) .
Now, let us examine the W-MDCT in Example 11.11.

EXAMPLE 11.11
Given the data 1, 2, 3, 4, 5, 6, 4, 5 .,
a. determine the W-MDCT coefficients for the first three blocks using a block size of 4;
b. determine the first two overlapped subblocks, and compare the results with the original data sequence using
the W-MDCT coefficients in (a).
Solution:
a. We divided the first two data blocks using the overlapping of 2 samples:
First data block: 1 2 34
Second data block 3456
Third data block: 5 645
We apply the W-MDCT to get
>> wmdct([1 2 3 4])
ans ¼ 1.1716 3.6569
>> wmdct([3456])
ans ¼8.0000 7.1716
>> wmdct([5 6 4 5])
ans ¼4.6569 18.0711
b. The results from W-IWDCT are as follows:
>> x1¼wimdct([1.1716 3.6569])
x1 ¼0.5607 1.3536 1.1465 0.4749
>> x2¼wimdct([-8.0000 7.1716])
x2¼1.8536 4.4749 2.1464 0.8891
>> x3¼wimdct([-4.6569 -18.0711])
x3 ¼2.8536 6.8891 5.1820 2.1465
Applying the overlap and add, we have
>> [x1 0 0 0 0]þ [00x200]þ [0000x3]
ans ¼ -0.5607 1.3536 -3.0000 4.0000 5.0000 6.0000 5.1820 2.1465

The first two recovered subblocks contain the values 3, 4, 5 6, which are consistent with the input data.

Figure 11.15 shows coding of speech data we.dat using the DCT transform and W-MDCT trans-
form. To be able to see the block edge artifacts, the following parameters are used for both DCT and
W-MDCT transform coding: