cell2sos

Convert second-order sections cell array to matrix

Syntax

sos = cell2sos(cll)

[sos,g] = cell2sos(cll)

Description

sos = cell2sos(cll) generates a matrix sos containing the coefficients of the filter system described by the second-order section cell array cll.

[sos,g] = cell2sos(cll) also returns the scale gain g.

Examples

Second-Order Sections from Cell Array Input

Generate a 3-by-1 cell array of 1-by-2 cell arrays of 1-by-3 row vectors. Convert it to a matrix of second-order sections.

cll = {{[3 6 7] [1 1 2]} 
       {[1 4 5] [1 9 3]}
       {[2 7 1] [1 7 8]}};
sos = cell2sos(cll)

sos = 3×6

     3     6     7     1     1     2
     1     4     5     1     9     3
     2     7     1     1     7     8

Input Arguments

cll — Second-order section cell-array representation

cell

Second-order section cell-array representation, specified as a cell array.

For a filter system with L sections, specify cll using this structure:

• Cell array with L elements — For unity-gain filter systems. Each element of the cell array corresponds to a second-order section. The kth cell array element of cll

  cll{k} = {[b_0k b_1k b_2k] [1 a_1k a_2k]}

  contains the coefficients from the kth second-order-section of the filter system H(z):

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

• Cell array with L+1 elements — If the gain of the filter system is different from 1. The first element of cll contains the system gains at the numerator (g_n) and at the denominator (g_d). Then, the function appends each element of the cell array for the corresponding second-order section.

  The first and the k+1th cell array element of cll

  cll{1} = {g_n g_d}
  cll{k+1} = {[b_0k b_1k b_2k] [1 a_1k a_2k]}

  contain the system gain and the coefficients from the kth second-order section of the filter system H(z), respectively, such that:

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

Example: cll = {{[2 4 2] [6 0 2]} {[3 3 0] [6 0 0]}} specifies the second-order-section coefficients of a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample in the cell array format.

Example: cll = {{7 5} {[2 4 2] [6 0 2]} {[3 3 0] [6 0 0]}} specifies the second-order-section coefficients of a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample and scalar gain value of 7/5 = 1.4, represented in the cell array format.

Data Types: double
Complex Number Support: Yes

Output Arguments

sos — Second-order section representation

L-by-6 matrix

Second-order section representation, returned as an L-by-6 matrix, where L is the number of second-order sections. The matrix

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

represents the second-order sections of H(z):

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

g — Scale gain

1 (default) | scalar

Scale gain, returned as a scalar.

• If you specify cll as a cell array with L elements for a filter system with L sections, the cell2sos function returns g as 1.

• If you specify cll as a cell array with L+1 elements for a filter system with L sections, the cell2sos function returns g as g = g_n/g_d, where g_n and g_d come from the first element of cll.

Tips

• You can use cll = sos2cell(sos) to perform the reverse operation of sos = cell2sos(cll).

Version History

Introduced before R2006a