sos2cell

Convert second-order sections matrix to cell array

Syntax

cll = sos2cell(sos)

cll = sos2cell(sos,g)

Description

cll = sos2cell(sos) generates a cell array cll containing the coefficients of the filter system described by the second-order section matrix sos.

example

cll = sos2cell(sos,g) also specifies a scale gain g to append in the cell array representation cll of the system specified in sos.

Examples

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Second-Order-Section Cell Array of Elliptic Filter

Open Live Script

Generate a lowpass elliptic filter of order 4 with 0.5 dB of passband ripple and 20 dB of stopband attenuation. The passband edge is 0.6 times the Nyquist frequency. Convert the transfer function to a matrix of second-order sections.

[b,a] = ellip(4,0.5,20,0.6);
m = tf2sos(b,a);

Use sos2cell to convert the 2-by-6 matrix produced by tf2sos into a 1-by-2 cell array, c, of cells. Display the second entry in the first cell of c. Verify that it contains the denominator coefficients of the first second-order section of m.

c = sos2cell(m);
compare = [c{1}{2};m(1,4:6)]

compare = 2×3

    1.0000    0.1677    0.2575
    1.0000    0.1677    0.2575

Input Arguments

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`sos` — Second-order section matrix representation
L-by-6 matrix

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

$sos = [\begin{matrix} b_{01} & b_{11} & b_{21} & 1 & a_{11} & a_{21} \\ b_{02} & b_{12} & b_{22} & 1 & a_{12} & a_{22} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ b_{0 L} & b_{1 L} & b_{2 L} & 1 & a_{1 L} & a_{2 L} \end{matrix}]$

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

$H (z) = g \prod_{k = 1}^{L} H_{k} (z) = g \prod_{k = 1}^{L} \frac{b_{0 k} + b_{1 k} z^{- 1} + b_{2 k} z^{- 2}}{1 + a_{1 k} z^{- 1} + a_{2 k} z^{- 2}} .$

Example: [z,p,k] = butter(3,1/32); sos = zp2sos(z,p,k) specifies a third-order Butterworth filter with a normalized 3 dB frequency of π/32 rad/sample.

Data Types: single | double
Complex Number Support: Yes

`g` — Scale gain
`1` (default) | scalar

Scale gain, specified as a scalar.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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`cll` — Second-order section cell-array representation
row cell array

Second-order section cell-array representation, returned as a row cell array with the following size:

L elements — If g equals 1 or if you do not specify it. Each element of the cell array corresponds to a second order section. For example, the cell array element cll(k) contains the coefficients from the kth section of sos.
```
cll{k} = {sos(k,1:3) sos(k,4:6)}
```
L+1 elements — If g is different from 1. The first element of cll contains the gain specified in g. Each subsequent element of the cell array corresponds to a second order section. For example, the cell array element cll{k+1} contains the coefficients from the kth section of sos.
```
cll{1} = {g 1}
cll{k+1} = {sos(k,1:3) sos(k,4:6)}
```