Digital Signal Processing Reference
In-Depth Information
W
h
[1; 0] = 34g[0]+28g[1]+76g[2]+51g[3]+19g[4]+12g[5]+25g[6]+43g[7]
1
p
W
h
[1; 0] = 34
2
W
h
[1; 1] = 34g[2] + 28g[1] + 76g[0] + 51g[1] + 19g[2] + 12g[3] + 25g[4] + 43g[5]
1
p
1
p
2
W
h
[1; 1] = 28
2
+ 76
W
h
[1; 2] = 34g[4] + 28g[3] + 76g[2] + 51g[1] + 19g[0] + 12g[1] + 25g[2] + 43g[3]
1
p
1
p
2
W
h
[1; 2] = 51
2
+ 19
W
h
[1; 3] = 34g[6] + 28g[5] + 76g[4] + 51g[3] + 19g[2] + 12g[1] + 25g[0] + 43g[1]
1
p
1
p
2
W
h
[1; 3] = 12
2
+ 25
W
h
[1; 4] = 34g[8] + 28g[7] + 76g[6] + 51g[5] + 19g[4] + 12g[3] + 25g[2] + 43g[1]
1
p
2
W
h
[1; 4] = 43
W
h
[1; 5] = 34g[10] + 28g[9] + 76g[8] + 51g[7] + 19g[6] + 12g[5] + 25g[4] + 43g[3]
W
h
[1; 5] = 0:
It should be obvious that any value W
h
[1;n] = 0 when n5. Comparing this to
the lter bank approach, we look at Figure 9.25, which shows a channel from a lter
bank. Keeping in mind that g[0] = a, and g[1] = b, we can trace the signal through
as follows.
y =
340
;
2834
;
7628
;
5176
;
1951
;
1219
;
2512
;
4325
;
043
p
p
p
p
p
p
p
p
p
2
2
2
2
2
2
2
2
2
The output is a down-sampled version of y, so when we eliminate every other value,
