SIMULATION
OF QUADRATURE MIRROR FILTER
AIM:
To
simulate the frequency response of quadrature mirror for a two
channel filter band.
THEORY:
The
QMF filter is used in the sub-band coding. This filter can be used
for reducing aliasing. This is a multirate digital filter structure
that employes 2 decimeter in signal synthesis section. The low pass
and high pass filters in the analysis section have impulse response
filters (n) and (n) respectively.
Similarly
the low pass filter and high pass filters contained in the synthesis
section have impulse response filters (n) and (n) respectively. To
reduce aliasing the synthesis section have impulse response (n) and
(n) respectively,
(ω)=
(ω)
(ω)=-
(ω-π)
Since
(ω) and (ω)is a mirror image filters
H0(ω)=H(ω)
H1(ω)=H(ω-
π)
G0(ω)=2H(ω)
This
is due to the above design, aliasing effects cancels.
ALGORITHM:
1.
Generate the low pass filter
2.
Generate the high pass filter
3.
Compute the gain response of two filters
4.
Plot the gain response of two filters.
QUADRATURE
MIRROR FILTER:
X(ω)
FILTER
CHARACTERISTICS FOR SUB-BAND CODING
Gain
H0
(ω) H1 (ω)
PROGRAM
####################################################
clc;
clear all;
%generation of complimentary lpf
b1=fir1(50,0.5);
%generation of complimentary hpf
l=length(b1);
for k=1:l
b2(k)=((-1)^k)*b1(k)
end
%computation of gain response of two filters
[H1Z,W]=freqZ(b1,1,256);
H1=abs(H1Z);
g1=20*log10(H1);
[H2Z,W]=freqZ(b2,1,256);
H2=abs(H2Z);
g2=20*log10(H2);
%PLOT OF GAIN RESPONSE OF TWO FILTERS
plot((W*180)/pi,g1,'-',(W*180)/pi,g2,'-');
grid on
xlabel('normalized freq');
ylabel('gain');
#############################################################
RESULT:
Thus
the frequency response of quadrature mirror filter for a two channel
filter bands was simulated.
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