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cl2tf

Convert coupled allpass lattice to transfer function form

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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 vectors of coefficientsbandawhenk1andk2are real vectors.b是向量的系数corresponding to the numerator of the transfer function H(z).a是向量的系数corresponding to the denominator of the transfer function H(z).k1andk2are real vectors corresponding to denominators of the allpass filtersH1(z)andH2(z). This is provided in the transfer function:

H ( z ) = B ( z ) / A ( z ) = 1 2 [ H 1 ( z ) + H 2 ( z ) ]

[b,a] = cl2tf(k1,k2,beta)returns the vectors of coefficientsbandacorresponding to the numerator and denominator, respectively, of the transfer functionH(z), wherek1,k2, andbetaare complex vectors.

H ( z ) = B ( z ) / A ( z ) = 1 2 [ − ( β ¯ ) ⋅ H 1 ( z ) + β ⋅ H 2 ( z ) ]

[b,a,bp] = cl2tf(k1,k2)also returns the vectorbpof real coefficients corresponding to the numerator of the power-complementary filterG(z), wherek1andk2are real vectors.

G ( z ) = B p ( z ) / A ( z ) = 1 2 [ H 1 ( z ) − H 2 ( z ) ]

[b,a,bp] = cl2tf(k1,k2,beta)also returns the vector of coefficientsbpof possibly complex coefficients corresponding to the numerator of the power complementary filterG(z), wherek1,k2, andbetaare complex.

G ( z ) = B p ( z ) / A ( z ) = 1 2 j [ − ( β ¯ ) ⋅ H 1 ( z ) + β ⋅ H 2 ( z ) ]

Examples

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Open Live Script

Compute the reflection coefficient usingtf2clfunction.

[b,a] = cheby1(10,.5,.4); [k1,k2,beta] = tf2cl(b,a);

Construct the original and the power-complementary filters.

[num,den,numpc] = cl2tf(k1,k2,beta); [h,w] = freqz(num,den); hpc = freqz(numpc,den);

Plot the frequency response.

subplot(211) plot(w./pi,20*log10(abs(h)),'k') holdon; gridon; 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') holdon; gridon; xlabel('Normalized Frequency (x \pi radians/sample)'); ylabel('Phase (radians)'); plot(w./pi,unwrap(angle(hpc)),'b')

Figure contains 2 axes objects. Axes object 1 with xlabel Normalized Frequency (x \pi radians/sample), ylabel dB contains 2 objects of type line. These objects represent Original Filter, Power Complementary Filter. Axes object 2 with xlabel Normalized Frequency (x \pi radians/sample), ylabel Phase (radians) contains 2 objects of type line.

Input Arguments

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Reflection coefficients corresponding to allpass lattice structure ofH1(z), specified as a real- or complex-valued vector.

Data Types:single|double
Complex Number Support:Yes

Reflection coefficients corresponding to allpass lattice structure ofH2(z), specified as a real- or complex-valued vector.

Data Types:single|double
Complex Number Support:Yes

Complex scalar of magnitude 1.

Data Types:single|double
Complex Number Support:Yes

Output Arguments

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Coefficients of the numerator of the transfer functionH(z), returned as a real- or complex-valued vector.

Data Types:double
Complex Number Support:Yes

Coefficients of the denominator of the transfer functionH(z), returned as a real- or complex-valued vector.

Data Types:double
Complex Number Support:Yes

Coefficients of the numerator of the power-complementary filterG(z), returned as a real- or complex-valued vector.

Data Types:double
Complex Number Support:Yes

References

[1] Mitra, Sanjit Kumar, and James F. Kaiser, eds.Handbook for Digital Signal Processing. New York: Wiley, 1993.

[2] Vaidyanathan, P. P. Multirate Systems and Filter Banks . Prentice-Hall Signal Processing Series. Englewood Cliffs, N.J: Prentice Hall, 1993. CloseDeleteEdit

Extended Capabilities

Version History

Introduced in R2011a

See Also

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