ca2tf

Convert coupled allpass filter to transfer function form

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Syntax

[b,a]=ca2tf(d1,d2)
[b,a]=ca2tf(d1,d2,beta)
[b,a,bp]=ca2tf(d1,d2)
[b,a,bp]=ca2tf(d1,d2,beta)

Description

[b,a]=ca2tf(d1,d2) returns the vector of coefficients b and the vector of coefficients a corresponding to the numerator and the denominator of the transfer function

H(z)=B(z)/A(z)=12[H1(z)+H2(z)]

d1 and d2 are real vectors corresponding to the denominators of the allpass filters H1(z) and H2(z).

[b,a]=ca2tf(d1,d2,beta) where d1, d2 and beta are complex, returns the vector of coefficients b and the vector of coefficients a corresponding to the numerator and the denominator of the transfer function

H(z)=B(z)/A(z)=12[−(β¯)⋅H1(z)+β⋅H2(z)]

[b,a,bp]=ca2tf(d1,d2), where d1 and d2 are real, returns the vector bp of real coefficients corresponding to the numerator of the power complementary filter G(z)

G(z)=Bp(z)/A(z)=12[H1(z)−H2(z)]

[b,a,bp]=ca2tf(d1,d2,beta), where d1, d2 and beta are complex, returns the vector of coefficients bp of real or complex coefficients that correspond to the numerator of the power complementary filter G(z)

G(z)=Bp(z)/A(z)=12j[−(β¯)⋅H1(z)+β⋅H2(z)]

Examples

Create a filter, convert the filter to coupled allpass form, and convert the result back to the original structure (create the power complementary filter as well).

[b,a]=cheby1(10,.5,.4);

 

[d1,d2,beta]=tf2ca(b,a);

% tf2ca returns the denominators of the allpasses

[num,den,numpc]=ca2tf(d1, d2,beta);

% Reconstruct the original filter plus the power complementary one

[h,w,s]=freqz(num,den);

 

hpc = freqz(numpc,den);

 

s.plot = 'mag';

 

s.yunits = 'sq';

 

freqzplot([h hpc],w,s);

% Plot the mag response of the original filter and the power complementary one

Examples

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Open Live Script

Create a filter, convert the filter to coupled allpass form, and convert the result back to the original structure (create the power complementary filter as well).

[b,a]=cheby1(10,.5,.4);
 [d1,d2,beta]=tf2ca(b,a);

tf2ca returns the denominators of the allpass filters

[num,den,numpc]=ca2tf(d1, d2,beta);

Plot the magnitude response of the original filter and the power complementary one.

fvtool(num,den,numpc,den,'Analysis','magnitude','MagnitudeDisplay',...
    'Magnitude Squared')

Extended Capabilities

See Also

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Introduced in R2011a

DSP System Toolbox Documentation
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