(Release 17 November 2004, for XBAT)
Kathryn A. Cortopassi

SUMMARY

This measurement extracts a frequency versus time (FM) contour, in a specified frequency range, for the given signal. It uses an autoregressive (AR) process model (Kay & Marple 1981) to make estimates of the signal's frequency content over short-time periods, and then a Viterbi-based tracking algorithm (Forney 1973) to connect those estimates into a single smooth frequency contour. Multiple frequency estimates are typically returned for each shorttime period depending on the harmonic structure of the signal. The tracking algorithm connects one estimate from each time interval, returning the best overall contour by minimizing a penalty function based on contour deviation and smoothness (i.e., contour first and second derivatives). Estimates of signal duration, bandwidth, frequency location, and spectral entropy are made using a robust, order statistic based, energy distribution measurement (see the section on this site describing Robust Signal Measurement). AR frequency estimates are made only over the estimated signal duration. A number of summary measurements are returned, which characterize the shape of the estimated FM contour. In addition, the measurement uses the AR model to estimate the first two characteristic frequencies for the signal as a whole.

MEASUREMENT PARAMETER DESCRIPTIONS

*Window list: 'Bartlett-Hann'; 'Bartlett'; 'Blackman'; 'Blackman-Harris'; 'Bohman'; 'Flat Top'; 'Gaussian'; 'Hamming'; 'Hann'; 'Nuttall Blackman-Harris'; 'Parzen de la Valle-Poussin'; 'Rectangular'; 'Triangular'

MEASUREMENT VALUE DESCRIPTIONS

BRIEF DESCRIPTION OF MEASUREMENT PROCEDURE

1) Generate a time-frequency power spectrogram using the specified spectrogram parameters, and bandlimit the spectrogram using the frequency range indicated (standard (F1SPC - F2SPC) or event-specific)

2) Generate an aggregate power versus time envelope by summing the power values in each short-time spectrum of the spectrogram, and an aggregate power versus frequency spectrum by summing the power values in each narrow-band envelope of the spectrogram; extract bandwidth and duration measures from the aggregate power versus time and frequency distributions using the specified energy fraction, P

3) Generate a new aggregate power versus frequency spectrum over the duration measured above, and calculate its Shannon entropy and maximum possible entropy

4) Starting from the original time waveform, use an AR process model with the parameters specified to make a series of estimates (using the time resolution and overlap specified) of the signal's short-time frequency content. Consider estimates only over the duration measured above, and only over the frequency range (F1AR - F2AR) specified. Using a Viterbi-based tracking algorithm, find the best path through the available frequency estimates (which minimizes first and second derivative penalties), to generate an FM contour for the signal.

5) Smooth the extracted FM contour, and summarize its shape by measuring its start, end, etc. frequencies, derivatives, and inflexion count as described

6) Starting from the original time waveform, and using only the duration measured above, estimate the entire signal's frequency content using the AR model. Consider estimates only over the frequency range (F1AR - F2AR) specified. Return the first and second frequency estimates (in ascending order).

REFERENCES

Forney, G. D., Jr. (1973) The Viterbi algorithm. Proceedings of the IEEE, 61(3):268 - 278.

Kay, S. M. & Marple, S. L., Jr. (1981) Spectrum analysis—A modern perspective. Proceedings of the IEEE, 69(11):1380 - 1419.