N. IntratorN. Neretti

T. NguyenY. Chen

Q. Huynh

R. CoifmanI. Cohen

Waveform Design and Decomposition

for Biosonar

www.physics.brown.edu/users/faculty/intrator/darpa/

YALEYALEUNIVERSITY

Long Term GoalsLong Term Goals

Understand the type of changes in multiple clicks

Understand the strategy in changing clicks Understand its usefulness for object

detection and discrimination

• Understand how dolphins integrate information from multiple clicks• Understand image clutter strategies • Develop needed signal processing and info theory

Big brown bats emit trains of brief FM sounds in the 20-100 kHz band, adjusting repetition-rate and duration to the momentary conditions of the task in hand.

Time-Frequency Plane: TilingsTime-Frequency Plane: Tilings

Time

Dirac Fourier

Wavelet

Wavelet Packet

Frequency

Windowed Fourier

The Uncertainty The Uncertainty PrinciplePrinciple

A signal cannot be localized arbitrarily well both in time/position and in frequency/momentum.

There exists a lower bound to the Heisenberg’s product:

t f 1/(4)

Improving on this bound would result in sonars with better temporal resolution at a given frequency range f = 10kHz, t = 50 sec ~ 10cm

Properties of best basis functionsProperties of best basis functions

Comparison with Wavelet functionsComparison with Wavelet functions

Bat sonar echo localization Bat sonar echo localization (Simulated)(Simulated)

Time in microSec

Dolphin vs. Broad Band sonarDolphin vs. Broad Band sonar

Total time 100microSecTotal time 100microSec

Am

plit

ude

Am

plit

ude

Continuous wavelet analysis

Continuous wavelet analysis

Conventional Time/Freq analysisConventional Time/Freq analysis

Fundamental Research QuestionsFundamental Research Questions

Data Representation

• Is the more detailed Time/Frequency analysis robust

Due to the very short time of the pulse, can a detailed

representation be estimated

Data Analysis

• Is the signal generation of Dolphins robust up to such

details

• Can we gain more information from this detailed

representation

Mine structure reconstruction Mine structure reconstruction from Dolphin clicksfrom Dolphin clicks

Methodology• Time/Frequency analysis using continuous wavelet transform• Image processing to improve temporal resolution – wave types separation (potentially beyond the limit imposed by the uncertainty principle) • Slice reconstruction from multiple angle pings• Dolphin data was collected at SPAWAR by Dr. Patrick Moore

Manta cross section Section reconstruction (Hi freq.)

Echo localizationEcho localization

Echo can be measuredat this frequency

Echo can be measured at this frequency

Echo can also be measured here

Time in microSec

Bat sonar echo localization Bat sonar echo localization (Simulated)(Simulated)

Time in microSec

Click Classification using Time Click Classification using Time Frequency AnalysisFrequency Analysis

Thanks to Maryam Saleh and Juda Jacobson

Told you…and don’t make a mistake next time

GoalsGoals

• Asses the relevance of Time/Frequency analysis to dolphin clicks• Asses the robustness of the of dolphin clicks to the details of the time frequency analysis

• Can we gain more information from this detailed

representation

• Study the click sequence structure

• Study variability due to task and other environmental

conditions

Time/Frequency analysisTime/Frequency analysis

Allows a detailed analysis of the click where the timelocation of each frequency component is displayed.The clicks above show some tilt in time when goingFrom low to high frequencies. X axis is time in microseconds, Y axis freq. in Mhz.

Time series plot of 98 consecutive clicksTime series plot of 98 consecutive clicks (File R0606C09)(File R0606C09)

Fourier plots of the clicks Fourier plots of the clicks (File R0606C09)(File R0606C09)

Time-frequency representations Time-frequency representations (File (File

R0606C09)R0606C09)

15 Fourier PC’s generated from 1360 15 Fourier PC’s generated from 1360 clicks (Rake Saline)clicks (Rake Saline)

15 Time/Freq PC’s generated from 1360 15 Time/Freq PC’s generated from 1360 clicks (Rake Saline) clicks (Rake Saline)

Dendrogram of the projections of Dendrogram of the projections of R0606C09R0606C09 onto the PCs (time-frequency)onto the PCs (time-frequency)

Scatter plots for time-frequency analysis Scatter plots for time-frequency analysis (using PCs: PC1 vs PC2-15) (using PCs: PC1 vs PC2-15) R0606C09R0606C09

Scatter plots for Fourier analysis (using Scatter plots for Fourier analysis (using PCs: PC1 vs PC2-15) PCs: PC1 vs PC2-15) R0606C09R0606C09

Time series plot of 98 consecutive clicksTime series plot of 98 consecutive clicks R0606C16R0606C16

Note: the first three clicks were not used in the creation of the PC’s!

Fourier plots of the clicksFourier plots of the clicks R0606C16R0606C16

Time-frequency representationsTime-frequency representations R0606C16R0606C16

Dendrogram of the projections of Dendrogram of the projections of R0606C16R0606C16 onto the T/F PC’sonto the T/F PC’s

Dendrogram of the projections of this file Dendrogram of the projections of this file onto the Fourier PC’s onto the Fourier PC’s R0606C16R0606C16

Scatter plots for T/F analysis Scatter plots for T/F analysis (PC1 vs PC2-15) (PC1 vs PC2-15) R0606C16R0606C16

Scatter plots for Fourier analysis projections Scatter plots for Fourier analysis projections (PC1 vs PC2-15) (PC1 vs PC2-15) R0606C16R0606C16

Preliminary conclusionsPreliminary conclusions

The detailed time/frequency analysis appears to be relevant to dolphin signals

The dolphin is generating a collection of signals that can not be explained by a (single) signal + noise model

First clicks are very different than last ones (Need to match with Ted’s results)

There is interesting cluster structure of the clicks in high dimension

Future directionsFuture directions

The detailed time/frequency analysis appears to be relevant to dolphin signals

The dolphin is generating a collection of signals that can not be explained by a (single) signal + noise model

First clicks are very different than last ones (Need to match with Ted’s results)

There is interesting cluster structure of the clicks in high dimension