You may try Padé approximant 

http://www.scholarpedia.org/article/Pad%C3%A9_approximant

https://en.wikipedia.org/wiki/Pad%C3%A9_approximant

The simplest way of doing this is...

From the description of the IIR filter find the impulse response. That will be h(n) = [h0, h1, h2, ... h10] (truncated to 10 terms). You do that by applying the difference equation of the IIR to the unit impulse. (The unit impulse is, of course x(n) = [1, 0, 0, 0, .....]).

The FIR approximation you want will be given by the difference equation y(n) = h0*x(n) + h(1)*x(n-1) + h(2)*x(n-2) + ... h(10)*x(n-10).

The more coefficients you use for the FIR, the closest to the behaviour of the IIR you started with.

Mr. Almeida, thank you for your answer. But, I need something like inverse Padé approximation, since I have a rational polynomial (IIR filter) and I want to derive a FIR filter.

Mr. Schlindwein, thank you for your answer. As I stated above, I need an analytical solution for this conversion.

Dear Rafet Şişman! It is impossible to convert IIR filter to FIR filter exactly, we can only approximate IIR filter with FIR model.

The simplest way to do this analytically is to take Fourier transformation of the IIR filter transfer function F(f)

FIR_coefficients[N]=\int\limits_{-f0/2}^{f0/2} F(f) exp[2 pi i N(f/f0)]df,

where f0 is sampling rate, f is frequency.

So, the approximated IIR filter response now reads as

output_of_approximated_IIR[k]=\sum\limits{j} FIR_coefficients[j] X[k-j],

where X[k] is input signal. However, the integrals of the rational function multiplied by exponent in general case are not primitive functions.

To my mind, for practice, the proposed by Prof. Luiz Alberto Luz de Almeida and Prof. Fernando Soares Schlindwein solutions are the best ways for converting IIR filter to FIR filter.

Sincerely,

Daniil D. Stupin