# How to quantify phase distortion of a filter specific to a signal?

For example, a EKG input signal is filtered with a known transfer function that does not have linear phase. How do you quantify the phase distortion of the output signal given you have the input? I know that the phase response of the transfer function gives the phase delay at all frequencies but I'm not sure how to make use of this.

• Right now (without reference to phase), how do you quantify the observed distortion ? And what do yo call it ? – Fat32 Dec 7 '19 at 2:24
• Right now I'm just visually observing how the filtered signal deviates from the original... the input signal should be within the pass band. So the distortions I'm seeing are likely due to the phase response of the filter – pproctor Dec 7 '19 at 2:57
• I've added an image to hopefully clarify what I'm after – pproctor Dec 7 '19 at 3:02
• So assuming that the whole signal was within the pass band (of flat unity gain) then any distortion is due to phase shifts and you can quantify it but it won't as simple as a two sinusoid problem, because your real ECG signal will be quite complicated... – Fat32 Dec 7 '19 at 3:11
• Yea the paper is quite old and they used the sinusoids as a proxy for EKG signals. Do you have any suggestions on how to go about quantifying the phase distortion? – pproctor Dec 7 '19 at 3:23

• Dan, group delay variation can be misleading. Take as an example an ideal Hilbert transformer. Apart from $\omega=0$, the magnitude and the the group delay are constant, yet any input signal appears distorted at the output. I think that in general the actually important measure is the deviation of the phase from a linear phase $a\omega$. – Matt L. Dec 8 '19 at 10:46