Consider a linear, time-invariant system. Noisy measurements of the magnitude and phase associated with the frequency response of the system are available over some dense generally non-uniform grid of frequencies.
I need to use these measurements to estimate group delay. Direct approximation of the derivative of phase via successive differences in the phase measurements is extremely noisy.
Some form of smoothing seems appropriate (e.g., spline smoothing). If I know the maximum rate of change of group delay as a function of frequency, how can I incorporate that side-information into a smoothing procedure? More generally, is anyone aware of other techniques (beyond fitting the frequency response measurements to some rational filter model and computing group delay from the associated parametric model)?