Approximate the change in perceived gain from applying transfer function to audio signal I have an audio signal that I am applying an analogue transfer function $H(s)$ to. I would like to approximate the change in gain ($\Delta \text{ Gain}$) as perceived by the listener for an arbitrary audio signal sent through the filter $H(s)$.

I was thinking something along the lines of:

$$
\Delta \text{Gain} = \frac {\displaystyle\int_{0}^{\pi} \lvert H(\omega)\rvert d\omega} {\pi}
$$

This is based on an assumption that the formula above gives a sensible approximation of gain across the spectrum by calculating the averaging gain.

Is my thinking sensible or is there some proper theory that will give a better answer that I can refer to?
You want to calculate loudness difference between input and output. 

Loudness depends on the power spectral density of a signal; knowing only the transfer function of your filter is not enough for calculating PSD.

For example, suppose your filter is a lowpass filter, with attenuation 20 dB in the stop band. If your input signal is completely contained below the cutoff frequency, then no perceived gain (input and output are similar), whereas if your input signal is all above the cutoff frequency, then you will perceive a -20dB gain.

Related question on calculating loudness.