cl2tf
Convert coupled allpass lattice to transfer function form
Syntax
[b,a] = cl2tf(k1,k2)
[b,a] = cl2tf(k1,k2,beta)
[b,a,bp] = cl2tf(k1,k2)
[b,a,bp] = cl2tf(k1,k2,beta)
Description
[b,a] = cl2tf(k1,k2) returns
the numerator and denominator vectors of coefficients b and a corresponding
to the transfer function
where H1(z) and H2(z) are
the transfer functions of the allpass filters determined by k1 and k2,
and k1 and k2 are real vectors
of reflection coefficients corresponding to allpass lattice structures.
[b,a] = cl2tf(k1,k2,beta) where k1, k2 and beta are
complex, returns the numerator and denominator vectors of coefficients
b and a corresponding to the transfer function
[b,a,bp] = cl2tf(k1,k2) where k1 and k2 are
real, returns the vector bp of real coefficients
corresponding to the numerator of the power complementary filter G(z)
[b,a,bp] = cl2tf(k1,k2,beta) where k1, k2 and beta are
complex, returns the vector of coefficients bp of
possibly complex coefficients corresponding to the numerator of the
power complementary filter G(z)
Examples
Convert Coupled Allpass Lattice to Transfer Function
tf2cl returns the reflection coeffs
[b,a]=cheby1(10,.5,.4); [k1,k2,beta]=tf2cl(b,a);
Construct the original and the power complementary filter.
[num,den,numpc]=cl2tf(k1,k2,beta); [h,w]=freqz(num,den); hpc = freqz(numpc,den);
Show the frequency response
subplot(211); plot(w./pi,20*log10(abs(h)),'k'); hold on; grid on; plot(w./pi,20*log10(abs(hpc)),'b'); xlabel('Normalized Frequency (x \pi radians/sample)'); ylabel('dB'); legend('Original Filter','Power Complementary Filter',... 'Location','best'); subplot(212); plot(w./pi,unwrap(angle(h)),'k'); hold on; grid on; xlabel('Normalized Frequency (x \pi radians/sample)'); ylabel('Phase (radians)'); plot(w./pi,unwrap(angle(hpc)),'b');
