matlab filtering from laplace transfer function

[bigmike500]

i have an array of time domain data (20000 samples), that i need to filter using this transfer function to wieght the data, however i am having problems as it is in the laplace transform, below

74.128s + 698.654
H(s) = ----------------------------
1.5s^2 + 73.458s + 1663.423

as my maths is pretty appalling i need help in converting this transfer function from the s domain to the time domain in matlab and also how to to impliment the actual filtering. Thanks in advance for any help given.
Mike

 

[VisiGoth]

Can you skip the convertion to the time domain and go directly to your requirements of implementing the filter?
You can map s to z using the built in MATLAB functions and use a ration of polynomials in z (IIR form) to implement the function. If your sample rate is very different (i.e. 10X greater) than your lowest frequency pole or zero, then you should consider a state space or delta domain implementation instead of a direct z form.