sos2tf

R2026b

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

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.

[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

Transfer Function Representation of a Second-Order Section System

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

sos — Second-order section representation

matrix

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

$$\text{sos}=\left[\begin{array}{cccccc}{b}_{01}& b_{11}& b_{21}& 1& a_{11}& a_{21}\\ b_{02}& b_{12}& b_{22}& 1& a_{12}& a_{22}\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ b_{0L}& b_{1L}& b_{2L}& 1& a_{1L}& a_{2L}\end{array}\right]$$

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

$$H(z)=g{\displaystyle \prod _{k=1}^L{H}_k}(z)=g{\displaystyle \prod _{k=1}^L\frac{b_{0k}+b_{1k}{z}^{-1}+b_{2k}{z}^{-2}}{1+a_{1k}{z}^{-1}+a_{2k}{z}^{-2}}}.$$

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

g — Overall system gain

real scalar

Overall system gain, specified as a real scalar.

Data Types: double

Output Arguments

b, a — Transfer function coefficients

row vectors

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:

$$H(z)=\frac{B(z)}{A(z)}=\frac{b_1+b_2{z}^{-1}+\cdots +b_{n+1}{z}^{-n}}{a_1+a_2{z}^{-1}+\cdots +a_{m+1}{z}^{-m}}.$$

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™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The sos2tf function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced before R2006a

R2026b: Use thread-based environments

You can use sos2tf in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.