You're too kind.

The more I read about the subject, the more reason I see that there is no measurement program available with practically near arbitrary precision in the time/frequency representation. If it's as simple as using the wiki equations, why don't you implement it in REW? It shouldn't take much time, given that you have all the framework done already.

Then try analysing two tones and see what happens!

This is about the general complex phase derative approach:

"For a sinusoidal wave, this definition coincides with the usual frequency. Unfortunately, the instantaneous frequency of the sum of two ordinary sinusoidal waves is the average of their frequencies, which does not coincide with the result of a Fourier analysis.

Hence the caracterization of the instaneous frequency of a signal in a sense that is consistent with the Fourier analysis in simple cases requires other mathematical tools."

Instantanous Frequency of an Analytic Signal
"For a signal that is a pure sinusoid, such as ,equation (13) clearly gives the right answer. When various frequencies are simultaneously present, we can hope that (13) gives a sensible average."

Instantaneous frequency
Again - average.

"Time-varying frequency is a natural occurrence, the mathematical and physical description of which has been evolving for many decades. One description of time-varying frequency is the instantaneous frequency proposed by Gabor, defined as the derivative of the phase of the (analytic) signal. The interpretation of this quantity has been a subject of much investigation. One interpretation arising from time-frequency distribution theory is that instantaneous frequency is the average frequency at each time in the signal. We explore this interpretation in detail, and derive conditions on an arbitrary two-component AM-FM complex signal for which this interpretation is plausible. The situations for which these conditions are met are limited. "

Instantaneous frequency and the conditional mean frequency of a signal
Again - average.

The general approach to solve the problem of being served a single average frequency as the answer, seems to be to filter the input signal. Thereby trying to isolate each of the sinusoids in a complex signal, giving an unique answer for each of them. The filtering can be adaptive and automatic, but it still places restrictions on the input signal that can be analyzed.

"This example illustrates that even for a simple signal, a meaningfull

instantaneous frequency can be obtained only if some restrictive conditions are imposed on the data. "

The Handbook of Data Mining - Google Bøker
More:

http://musicweb.ucsd.edu/~sdubnov/Mu...ClassTalk2.pdf
Here's another one, for sparse sounds:

"Classical time–frequency analysis is based on the amplitude responses of bandpass filters, discarding phase information. Instantaneous frequency analysis, in contrast, is based on the derivatives of these phases. This method of frequency calculation is of interest for its high precision and for reasons of similarity to cochlear encoding of sound. This article describes a methodology for high resolution analysis of sparse sounds, based on instantaneous frequencies. In this method, a comparison between tonotopic and instantaneous frequency information is introduced to select filter positions that are well matched to the signal. Second, a cross-check that compares frequency estimates from neighboring channels is used to optimize filter bandwidth, and to signal the quality of the analysis. These cross-checks lead to an optimal time–frequency representation without requiring any prior information about the signal. When applied to a signal that is sufficiently sparse, the method decomposes the signal into separate time–frequency contours that are tracked with high precision. Alternatively, if the signal is spectrally too dense, neighboring channels generate inconsistent estimates—a feature that allows the method to assess its own validity in particular contexts. Similar optimization principles may be present in cochlear encoding"

Instantaneous frequency decomposition: an applicat... [J Acoust Soc Am. 2005] - PubMed result
And so forth. I find no mention anywhere that the concept of instantaneous frequency is able to describe arbitrary signals. Please provide a link to some reference if you believe this is not the case.

Edit: these are not the only texts I've referenced, just to make that clear. They exemplify the general trend I've seen across many sources.