Signal Processing Toolbox

tf2zpk

Convert transfer function filter parameters to zero-pole-gain form

Syntax

• [z,p,k] = tf2zpk(b,a) 
  

Description

tf2zpk finds the zeros, poles, and gains of a discrete-time transfer function.

Note    You should use tf2zpk when working with transfer functions expressed in inverse powers (1 + z-1 + z-2), which is how transfer functions are usually expressed in DSP. A similar function, tf2zp, is more useful for working with positive powers (s2 + s + 1), such as in continuous-time transfer functions.

[z,p,k] = tf2zpk(b,a) finds the matrix of zeros z, the vector of poles p, and the associated vector of gains k from the transfer function parameters b and a:

• The numerator polynomials are represented as columns of the matrix b.
• The denominator polynomial is represented in the vector a.

Given a single-input, multiple output (SIMO) discrete-time system in polynomial transfer function form

you can use the output of tf2zpk to produce the single-input, multioutput (SIMO) factored transfer function form

The following describes the input and output arguments for tf2zpk:

• The vector a specifies the coefficients of the denominator polynomial A(z) in descending powers of z.
• The ith row of the matrix b represents the coefficients of the ith numerator polynomial (the ith row of B(s) or B(z)). Specify as many rows of b as there are outputs.
• The zero locations are returned in the columns of the matrix z, with as many columns as there are rows in b.
• The pole locations are returned in the column vector p and the gains for each numerator transfer function in the vector k.

Examples

Find the poles, zeros, and gain of a Butterworth filter:

• [b,a] = butter(3,.4);
  [z,p,k] = tf2zpk(b,a)
  z =
    -1.0000          
    -1.0000 + 0.0000i
    -1.0000 - 0.0000i
  
  p =
     0.2094 + 0.5582i
     0.2094 - 0.5582i
     0.1584          
  
  k =
      0.0985
  

See Also

sos2zp, ss2zp, tf2sos, tf2ss, tf2zp, zp2tf

tf2zp

tfe