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

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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

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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.

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

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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

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Properties of best basis functions

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Comparison with Wavelet functions

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Bat sonar echo localization (Simulated) Time in microSec

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

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Conventional Time/Freq analysis

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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

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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.)

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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

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Bat sonar echo localization (Simulated) Time in microSec

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

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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

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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.

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Time series plot of 98 consecutive clicks (File R0606C09)

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Fourier plots of the clicks (File R0606C09)

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Time-frequency representations (File R0606C09)

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

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

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

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

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

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

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Fourier plots of the clicks R0606C16

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Time-frequency representations R0606C16

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

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

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

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

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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

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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

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