Perfect Reconstruction QMF
2.2
2003/01/13
2005/10/04 15:24:57.050 GMT-5
Phil
Schniter
schniter@ee.eng.ohio-state.edu
Adan
Galvan
jago@rice.edu
Phil
Schniter
schniter@ee.eng.ohio-state.edu
perfect reconstruction
QMF
Perfect Reconstruction QMF
The system transfer function for a QMF bank is
T
z
H
0
z
2
H
1
z
2
4
z
-1
P
0
z
2
P
1
z
2
For perfect reconstruction, we need
T
z
z
l
for some
l
,
which implies the equivalent conditions
4
z
-1
P
0
z
2
P
1
z
2
z
l
P
0
z
2
P
1
z
2
1
4
z
l
1
P
0
z
P
1
z
1
4
z
l
1
2
For FIR polyphase filters, this can only be satisfied by
P
0
z
β
0
z
n
0
P
1
z
β
1
z
n
1
where we have
n
0
n
1
l
1
2
and
β
0
β
1
1
4
.
In other words, the polyphase filters are trivial, so that the
prototype filter
H
0
z
has a two-tap response. With only two taps,
H
0
z
cannot be a very good lowpass filter, meaning that the sub-band
signals will not be spectrally well-separated. From this we
conclude that two-channel
It turns out that M-channel
perfect reconstruction QMF banks have more useful responses
for larger values of M.
perfect reconstruction QMF banks exist but are not
very useful.