SIMULATION OF QUADRATURE MIRROR FILTER

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

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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');

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RESULT:

 Thus the frequency response of quadrature mirror filter for a two channel filter bands was simulated.