Energy Distribution Measurement
(Release 17 November 2004, for XBAT)
Kathryn A. Cortopassi
SUMMARY
This measurement relies on a number of robust order statistics to characterize signal time / frequency energy distributions. The overall time envelope and frequency spectrum of the signal are explored, as well as its short-time center frequency contour. Three measures of duration / bandwidth are returned, as well as one measure of time / frequency location, and two measures of signal energy symmetry. The shape of the center frequency contour is summarized by four derivative measures and a count of contour inflections. A number of peak measurements are made as well, including generation of a peak frequency contour. These peak measures provide an interesting counterpoint to the more focal robust order-statistic measures.
MEASUREMENT PARAMETER DESCRIPTIONS
|
Parameter
Type
|
Parameter
Name
|
Symbol
|
Description
|
Input Range
|
Units
|
|
Spectrogram
generation
|
FFT Size | N | Size of Fourier transform to use for spectrogram generation | 4 - 65536 | points |
| Data Window Size | L | Size of data block to use for generation of individual spectra in spectrogram | 0 - 1 | fraction of FFT size | |
|
Window Function |
win | Taper function to use for windowing the data blocks for spectrogram generation | see list below* | string value | |
| Window Overlap Size | V | Amount of overlap between current data block and next data block for spectrogram generation | 0 - 1 | fraction of data size | |
|
Spectrogram
denoising
|
Denoising Flag | -- | Flag indicating whether or not to apply spectrogram-based denoising before measurement | 'on' / 'off' | string value |
| Denoising Percentile | PN | Fraction of the spectrogram to threshold to zero if pre-measurement denoising is applied | 0 - 1 | fraction | |
|
Measurement range |
Standard Range Flag | -- | Flag indicating whether to use a standard or signal-specific frequency range for spectrogram bandlimiting and measurement | 'on' / 'off' | string value |
| Low Frequency | F1 | Low end of standard frequency range to use for spectrogram bandlimiting and measurement | 0 - Nyquist | Hz | |
| High Frequency | F2 | High end of standard frequency range to use for spectrogram bandlimiting and measurement | 0 - Nyquist | Hz | |
| Energy Percent | P | Fraction of the total signal energy to use for calculation of the order-statistic measures | 0 - 1 | fraction |
*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
|
Value
Type
|
Value
Name
|
Symbol
|
Order
Statistic
|
Description
|
Units
|
|
Aggregate
Time Envelope
|
Aggregate Power Envelope | -- | -- | Time envelope generated by summing the power values in each short-time power spectrum of the spectrogram | energy vs time |
| Center Time (Q2) | MT | Median | Time that bisects the aggregate envelope so that 50% of the total signal energy lies below MT and 50% lies above; an estimate of signal location in time | sec | |
| P1 Time | P1T | Initial Percentile | Time that partitions the aggregate envelope so that a fraction (1-P)/2 of the total signal energy lies below P1T and (1+P)/2 lies above | sec | |
| P2 Time | P2T | Terminal Percentile | Time that partitions the aggregate envelope so that a fraction (1+P)/2 of the total signal energy lies below P2T and (1-P)/2 lies above | sec | |
| Time Range (IPR) | IPRT | Interpercentile Range | Time span between the initial and terminal percentile values, IPRT = P2T - P1T; an estimate of signal duration | sec | |
| Asymmetry - Envelope | PST | Percentile Skewness | Asymmetry of the interpercentile range relative to the median, PST = (MT-P1T)/IPRT | -- | |
| Concentration - Envelope | CTRT | Concentration | Number of bins (converted to time units) needed to accumulate a fraction P of the total signal energy in the sorted aggregate envelope; an estimate of signal duration | sec | |
| Lower Time | LT | Lower | Smallest time value encountered in the concentration bins | sec | |
| Upper Time | UT | Upper | Largest time value encountered in the concentration bins | sec | |
| Time Spread | LURT | Lower-Upper Range | Time span between the lower and upper values, LURT = UT – LT; an estimate of signal duration | sec | |
| Skew - Envelope | LST | Lower-Upper Skewness | Asymmetry of the lower-upper range relative to the median, LST = (MT-LT)/LURT | -- | |
| Peak Energy - Envelope | -- | -- | Maximum value in the aggregate time envelope | energy | |
| Peak Time | -- | -- | Time of maximum value | sec | |
|
Aggregate
Frequency Spectrum
|
Aggregate Power Spectrum | -- | -- | Frequency spectrum generated by summing the power values in each narrow-band power envelope of the spectrogram | energy vs time |
| Center Frequency (Q2) | MF | Median | Frequency that bisects the aggregate spectrum so that 50% of the total signal energy lies below MF and 50% lies above; an estimate of signal location in frequency | Hz | |
| P1 Frequency |
P1F | Initial Percentile | Frequency that partitions the aggregate spectrum so that a fraction (1-P)/2 of the total signal energy lies below P1F and (1+P)/2 lies above | Hz | |
| P2 Frequency | P2F | Terminal Percentile | Frequency that partitions the aggregate spectrum so that a fraction (1+P)/2 of the total signal energy lies below P2F and (1-P)/2 lies above | Hz | |
| Frequency Range (IPR) |
IPRF | Interpercentile Range | Frequency range between the initial and terminal percentile values, IPRF = P2F - P1F; an estimate of signal bandwidth | Hz | |
| Asymmetry - Spectrum | PSF | Percentile Skewness | Asymmetry of the interpercentile range relative to the median, PSF = (MF-P1F)/IPRF | -- | |
| Concentration - Spectrum |
CTRF | Concentration | Number of bins (converted to frequency units) needed to accumulate a fraction P of the total signal energy in the sorted aggregate spectrum; an estimate of signal bandwidth | Hz | |
| Lower Frequency |
LF | Lower | Smallest frequency value encountered in the concentration bins | Hz | |
| Upper Frequency | UF | Upper | Largest frequency value encountered in the concentration bins | Hz | |
| Frequency Spread |
LURF | Lower-Upper Range | Frequency range between the lower and upper values, LURF = UF – LF; an estimate of signal bandwidth | Hz | |
| Skew - Spectrum |
LSF | Lower-Upper Skewness | Asymmetry of the lower-upper range relative to the median, LSF = (MF-LF)/LURF | -- | |
| Peak Energy - Spectrum |
-- | -- | Maximum value in the aggregate frequency spectrum | energy | |
| Peak Frequency | -- | -- | Frequency of maximum value | Hz | |
|
Median
Frequency Contour
|
Center Frequency Contour | -- | Short-time Medians | Frequency versus time contour generated by finding the median frequency value in each short-time power spectrum of the spectrogram | frequency vs time |
| CF Contour Median Derivative | -- | Median | Median value of the first derivative function of the center frequency contour | Hz/s | |
| CF Contour Average Derivative | -- | -- | Mean of the first derivative function of the center frequency contour | Hz/s | |
| CF Contour Cumulative Absolute Derivative | -- | -- | Sum of the absolute value of the first derivative function of the center frequency contour | Hz/s | |
| CF Contour Average Absolute Derivative | -- | -- | Mean of the absolute value of the first derivative function of the center frequency contour | Hz/s | |
| CF Contour Inflection Count | -- | -- | Number of inflections, or derivative sign changes, in the median frequency contour | count | |
|
Peak
Frequency Contour
|
Peak Frequency Contour | -- | -- | Frequency versus time contour generated by finding the peak frequency value in each short-time power spectrum of the spectrogram | frequency vs time |
| PF Contour Median Derivative | -- | Median (of a non-order statistic contour) | Median value of the first derivative function of the peak frequency contour | Hz/s | |
| PF Contour Average Derivative | -- | -- | Mean of the first derivative function of the peak frequency contour | Hz/s | |
| PF Contour Cumulative Absolute Derivative | -- | -- | Sum of the absolute value of the first derivative function of the peak frequency contour | Hz/s | |
| PF Contour Average Absolute Derivative | -- | -- | Mean of the absolute value of the first derivative function of the peak frequency contour | Hz/s | |
| PF Contour Inflection Count | -- | -- | Number of inflections, or derivative sign changes, in the peak frequency contour | count | |
|
.
|
Time Vector | -- | -- | Time vector for the center and peak frequency contour functions | sec |
|
Spectrogram
|
Total Signal Energy | -- | -- | Sum of all power values in the spectrogram | energy |
| Peak Energy - Spectrogram | -- | -- | Maximum power value in the spectrogram | power | |
| Peak Time - Spectrogram | -- | -- | Time of maximum power value | sec | |
| Peak Frequency - Spectrogram | -- | -- | Frequency of maximum power value | Hz |
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 or event-specific)
2) If indicated, denoise the spectrogram using the following method (after Fristrup & Watkins 1993):
(1) Find the median power value of each narrow-band envelope in the spectrogram, the resulting power spectrum comprising these median values in used as an estimate of the background noise spectrum
(2) Whiten the noise in a copy of the spectrogram by dividing each short-time spectrum by the estimated noise spectrum, and find the specified percentile value, PN, of the whitened spectrogram
(3) Scale the estimated noise spectrum using the percentile value, and subtract the scaled noise spectrum from each short-time spectrum in the original spectrogram; threshold to zero any resulting negative values
3) Extract measures from the denoised time-frequency spectrogram
4) 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 measures from the aggregate power versus time / frequency distributions
5) Generate a center frequency contour by computing the median frequency for each short-time spectrum in the spectrogram, and a peak frequency contour by computing the peak frequency for each short-time spectrum in the spectrogram; extract derivative and inflection measures from the center and peak frequency contours
REFERENCES
Fristrup, K. M. & Watkins, W. A. (1993) Marine animal sound classification. Woods Hole Oceanographic Institution Technical Report WHOI-94-13.