MATLAB: How to filter a signal using Thiran Fractional Delay Filter I have generated a Thrian fractional delay filter using (thiran function) in MATLAB 

h=thiran(0.3,1) 


where 0.3 is the time delay and 1 is the sample time. The output is a discrete time transfer function, the generated filter is all-pass, infinite impulse response (IIR) filter.

The problem is that I could not apply it to a signal x(t). So I would like to know how to filter a signal with the generated thiran filter in MATLAB, what should I use to filter a signal with thiran filter? I can generate thiran filter using (thiran) function and the result will be a discrete time tf, but how to use it to filter a signal. I have tried to use filter, conv and tf functions but they all did not work:

filter and conv functions did not work because they require polynomial coefficients or numerator and denominator coefficients b and a, whereas thiran function generates a discrete transfer function.

[num,den] = tf(d) 


function did not work because it can only convert a filter transfer function which is configured by designfilt function, so in this case d cannot be a thiran filter, d can only be configured by designfilt function
try this: 


h=thiran(0.3,1);
num=  cell2mat(h.Numerator);
denum=cell2mat(h.Denominator);
output=filter(num,denum,x)



Hope that helps