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# ss2sos() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

### Alternatives / See Also

### Reference

ss2sos converts a state-space representation of a given digital filter to an equivalent second-order section representation.[sos,g] = ss2sos(A,B,C,D) finds a matrix sos in second-order section form with gain g that is equivalent to the state-space system represented by input arguments A, B, C, and D. The input system must be single output and real. sos is an L-by-6 matrixsos=[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[sos,g] = ss2sos(A,B,C,D,iu) specifies a scalar iu that determines which input of the state-space system A, B, C, D is used in the conversion. The default for iu is 1. [sos,g] = ss2sos(A,B,C,D,'order') and [sos,g] = ss2sos(A,B,C,D,iu,'order') specify the order of the rows in sos, where 'order' is'down', to order the sections so the first row of sos contains the poles closest to the unit circle'up', to order the sections so the first row of sos contains the poles farthest from the unit circle (default)The zeros are always paired with the poles closest to them.[sos,g] = ss2sos(A,B,C,D,iu,'order','scale') specifies the desired scaling of the gain and the numerator coefficients of all second-order sections, where 'scale' is'none', to apply no scaling (default)'inf', to apply infinity-norm scaling'two', to apply 2-norm scalingUsing infinity-norm scaling in conjunction with up-ordering minimizes the probability of overflow in the realization. Using 2-norm scaling in conjunction with down-ordering minimizes the peak round-off noise.Note Infinity-norm and 2-norm scaling are appropriate only for direct-form II implementations.sos = ss2sos(...) embeds the overall system gain, g, in the first section, H1(z), so that H(z)=∏k=1LHk(z)Note Embedding the gain in the first section when scaling a direct-form II structure is not recommended and may result in erratic scaling. To avoid embedding the gain, use ss2sos with two outputs.

[sos,g] = ss2sos(A,B,C,D)[sos,g] = ss2sos(A,B,C,D,iu)[sos,g] = ss2sos(A,B,C,D,'order')[sos,g] = ss2sos(A,B,C,D,iu,'order')[sos,g] = ss2sos(A,B,C,D,iu,'order','scale')sos = ss2sos(...)

State-space system must have only one input.