Generate fractional delay filter based on Thiran approximation
sys
= thiran(tau
, Ts
)
discretizes
the continuoustime delay sys
= thiran(tau
, Ts
)tau
using a Thiran filter
to approximate the fractional part of the delay. Ts
specifies
the sample time.

Time delay to discretize. 

Sample time. 

Discretetime 
Approximate and discretize a time delay that is a noninteger multiple of the target sample time.
sys1 = thiran(2.4, 1) Transfer function: 0.004159 z^3  0.04813 z^2 + 0.5294 z + 1  z^3 + 0.5294 z^2  0.04813 z + 0.004159 Sample time: 1
The time delay is 2.4 s, and the sample time is 1 s. Therefore, sys1
is
a discretetime transfer function of order 3.
Discretize a time delay that is an integer multiple of the target sample time.
sys2 = thiran(10, 1) Transfer function: 1  z^10 Sample time: 1
[1] T. Laakso, V. Valimaki, "Splitting the Unit Delay", IEEE Signal Processing Magazine, Vol. 13, No. 1, p.3060, 1996.