N. Intrator N. Neretti T. Nguyen Y. Chen Q. Huynh R. Coifman I. Cohen Waveform Design and Decomposition for Biosonar YALE UNIVERSITY

Long 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 kHz band, adjusting repetition-rate and duration to the momentary conditions of the task in hand.

Time-Frequency Plane: Tilings Time Dirac Fourier Wavelet Wavelet Packet Frequency Windowed Fourier

The Uncertainty Principle  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: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 functions

Comparison with Wavelet functions

Bat sonar echo localization (Simulated) Time in microSec

Dolphin vs. Broad Band sonar Total time 100microSec Amplitude Continuous wavelet analysis

Conventional Time/Freq analysis

Fundamental 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 from 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 localization Echo can be measured at this frequency Echo can be measured at this frequency Echo can also be measured here Time in microSec

Bat sonar echo localization (Simulated) Time in microSec

Click Classification using Time Frequency Analysis Thanks to Maryam Saleh and Juda Jacobson Told you… and don’t make a mistake next time

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

Time series plot of 98 consecutive clicks (File R0606C09)

Fourier plots of the clicks (File R0606C09)

Time-frequency representations (File R0606C09)

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

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

Dendrogram of the projections of R0606C09 onto the PCs (time-frequency)

Scatter plots for time-frequency analysis (using PCs: PC1 vs PC2-15) R0606C09

Scatter plots for Fourier analysis (using PCs: PC1 vs PC2-15) R0606C09

Time series plot of 98 consecutive clicks R0606C16 Note: the first three clicks were not used in the creation of the PC’s!

Fourier plots of the clicks R0606C16

Time-frequency representations R0606C16

Dendrogram of the projections of R0606C16 onto the T/F PC’s

Dendrogram of the projections of this file onto the Fourier PC’s R0606C16

Scatter plots for T/F analysis (PC1 vs PC2-15) R0606C16

Scatter plots for Fourier analysis projections (PC1 vs PC2-15) R0606C16

Preliminary 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 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