Thiran filters can approximate continuous-time delays that are non-integer multiples of the sampling time (fractional delays). This approximation gives a better matching of the phase shift between the continuous- and the discrete-time system. If there is no fractional part in the delay, then the standard discrete-time delay representation is used.

Inputs

T

A continuous-time delay, given in time units (seconds).

The sampling time of the resulting Thiran filter.

Outputs

sys

Transfer function model of the resulting filter. The order of the filter is determined automatically.

Example

 octave:1> sys = thiran (1.33, 0.5)

 Transfer function 'sys' from input 'u1' to output ...
 
       0.003859 z^3 - 0.03947 z^2 + 0.2787 z + 1
  y1:  -----------------------------------------
        z^3 + 0.2787 z^2 - 0.03947 z + 0.003859 
 
 Sampling time: 0.5 s
 Discrete-time model.
 

 octave:2> sys = thiran (1, 0.5)

 Transfer function 'sys' from input 'u1' to output ...
        1
  y1:  ---
       z^2 
 
 Sampling time: 0.5 s
 Discrete-time model.