sos2tf

Convert digital filter second-order section data to transfer function form

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Syntax

[b,a] = sos2tf(sos)
[b,a] = sos2tf(sos,g)

Description

[b,a] = sos2tf(sos) returns the transfer function coefficients of a discrete-time system described in second-order section form by sos.

example

[b,a] = sos2tf(sos,g) returns the transfer function coefficients of a discrete-time system described in second-order section form by sos with gain g.

Examples

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Compute the transfer function representation of a simple second-order section system.

sos = [1  1  1  1  0 -1; -2  3  1  1 10  1];
[b,a] = sos2tf(sos)
b = 1×5

    -2     1     2     4     1


a = 1×5

     1    10     0   -10    -1

Input Arguments

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Second-order section representation, specified as a matrix. sos is an L-by-6 matrix

sos=[b01b11b211a11a21b02b12b221a12a22⋮⋮⋮⋮⋮⋮b0Lb1Lb2L1a1La2L]

whose rows contain the numerator and denominator coefficients bik and aik of the second-order sections of H(z):

H(z)=g∏k=1LHk(z)=g∏k=1Lb0k+b1kz−1+b2kz−21+a1kz−1+a2kz−2.

Example: [2 4 2 6 0 2;3 3 0 6 0 0] specifies a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

Data Types: double
Complex Number Support: Yes

Overall system gain, specified as a real scalar.

Data Types: double

Output Arguments

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Transfer function coefficients, returned as row vectors. b and a contain the numerator and denominator coefficients of H(z) stored in descending powers of z:

H(z)=B(z)A(z)=b1+b2z−1+⋯+bn+1z−na1+a2z−1+⋯+am+1z−m.

Algorithms

sos2tf uses the conv function to multiply all of the numerator and denominator second-order polynomials together. For higher order filters (possibly starting as low as order 8), numerical problems due to round-off errors may occur when forming the transfer function.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

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Introduced before R2006a

Signal Processing Toolbox Documentation

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