# How to estimate filter coefficients of an all-pole system?

Suppose we have measured the frequency response of a system that is known to be all-pole; measuring impulse response is not possible. What are the methods available, if any, to estimate the coefficients of the underlying IIR filter?

EDIT: Frequency response exists only as measured data, so closed mathematical expression is not available, nor is the phase information.

• Does the measured frequency response include phase information? – Olli Niemitalo Sep 17 '15 at 8:27
• Do you have any closed form expression for the frequency response? or you have only samples of the frequency response? – Oliver Sep 17 '15 at 8:47

• 1. restrict how many poles you can have. 2. find out whether your filter is stable for harmonic excitation (poles all within unit circle?), 3. be $y[n] = x[n]*h[n]$ (discrete filter $h$ convoluted with signal $x$), calc the z-transform of both sides of that equation, divide by $X$. 4. inverse z-Transform of $H$ – Marcus Müller Sep 19 '15 at 10:30