Signal Toolkit - zp2sos

Function File: [sos, g] = zp2sos (z)

Function File: [sos, g] = zp2sos (z, p)

Function File: [sos, g] = zp2sos (z, p, k)

Function File: sos = zp2sos (…)

Convert filter poles and zeros to second-order sections.

INPUTS:

• z = column-vector containing the filter zeros
• p = column-vector containing the filter poles
• k = overall filter gain factor. If not given the gain is assumed to be 1.

RETURNED:

• sos = matrix of series second-order sections, one per row:

   sos = [B1.' A1.'; ...; BN.' AN.']
   

  where B1.' = [b0 b1 b2] and A1.' = [a0 a1 a2] for section 1, etc. See filter for documentation of the second-order direct-form filter coefficients Bi and %Ai, i=1:N.

• g is the overall gain factor that effectively scales any one of the Bi vectors.

If called with only one output argument, the overall filter gain is applied to the first second-order section in the matrix sos.

EXAMPLE:

   [z, p, k] = tf2zp ([1 0 0 0 0 1], [1 0 0 0 0 .9]);
   [sos, g] = zp2sos (z, p, k)

 sos =
    1.0000    0.6180    1.0000    1.0000    0.6051    0.9587
    1.0000   -1.6180    1.0000    1.0000   -1.5843    0.9587
    1.0000    1.0000         0    1.0000    0.9791         0

 g =
     1
 

See also: sos2zp, sos2tf, tf2sos, zp2tf, tf2zp.