# Appropriate model for IIR filter to compare with spectral ratios

A quick, basic question. I have measured spectral ratios - comparing a measured signal to an 'ideal' signal. I am fitting a specific, simple IIR filter to that data for transfer functions. So, if I'm using normalized power spectral density ratios (i.e., $S_{s1}\sigma_{s2}^2/S_{s2}\sigma_{s1}^2$, $\sigma^2$ is variance) would I use the equation

$$T = \frac{1}{\sqrt{1+\left(\frac ff_c\right)^2}}\quad\text{or}\quad T = \frac{1}{1+\left(\frac ff_c\right)^2}$$

with $f_c$ being the cutoff frequency.

• It depends on the order of the low pass filter you are trying to model. Have you considered expressing your transfer function with poles as in $T=\frac{1}{(s-p_1)(s-p_2)(s-p_3)...}$?, (where s is $j(2\pi f)$ to describe the frequency response) For an IIR specifically it would be in units of $T=\frac{1}{(z-p_1)(z-p_2)(z-p_3)...}$ where z is the unit circle to describe the frequency response ($z=e^{j2\pi n/N}$) where n goes from 0 to N-1. – Dan Boschen Mar 10 '17 at 17:44