Biomimetic Sound Biomimetic Sound Localization Utilizing Localization Utilizing

HeadHead--Related Transfer Related Transfer FunctionsFunctions

RenJase EngineeringRenJase EngineeringDr. Vikram Kapila, Project AdvisorDr. Vikram Kapila, Project Advisor

Mechatronics LaboratoryMechatronics LaboratoryDepartment of Mechanical Engineering, NYU PolytechnicDepartment of Mechanical Engineering, NYU Polytechnic

Funding Provided by the NSF SMART ProgramFunding Provided by the NSF SMART Program

GoalGoal

Our goal is to create:Our goal is to create: an autonomous robot that can, an autonomous robot that can, in a relatively quiet room, in a relatively quiet room, respond to a soundrespond to a sound by rotating and elevating its head by rotating and elevating its head to face the sound source within 5 degrees. to face the sound source within 5 degrees.

This soundThis sound--localization is to be done using:localization is to be done using: Two microphones andTwo microphones and Head Related Transfer FunctionsHead Related Transfer Functions

BackgroundBackground Techniques for Locating SoundTechniques for Locating Sound

InterInter--Aural Time DelayAural Time Delay InterInter--Aural Volume DifferenceAural Volume Difference

But both result in FrontBut both result in Front--Back ambiguities when using Back ambiguities when using only two microphonesonly two microphones

HeadHead--Related Transfer FunctionsRelated Transfer Functions Have been identified as an important biological strategyHave been identified as an important biological strategy Are potentially distinct for all directionsAre potentially distinct for all directions Have been described for humans and other systemsHave been described for humans and other systems

Fourier TransformFourier Transform

Fourier Transform (FT)Fourier Transform (FT) Provides frequency content of complicated timeProvides frequency content of complicated time--domain domain

signalssignals

Transfer FunctionsTransfer Functions

Transfer FunctionTransfer Function Describes the effect of a Describes the effect of a

system on a signal (the system on a signal (the change in magnitude and change in magnitude and phase), such thatphase), such that

Output = TF * InputOutput = TF * Input

HeadHead--Related Transfer Related Transfer Function (HRTF) = Function (HRTF) = Magnitude( FT[Output(t)] Magnitude( FT[Output(t)]

/ FT[Input(t)] )/ FT[Input(t)] )

HeadHead--Related Transfer Function Related Transfer Function (HRTF) Ratios(HRTF) Ratios

[a.k.a “Renjun is a genius.”][a.k.a “Renjun is a genius.”]

A listener does not know the Input signals A listener does not know the Input signals Cannot use Transfer Functions to locate soundsCannot use Transfer Functions to locate sounds

Instead we use HRTF RatiosInstead we use HRTF Ratios = TF_Right / TF_Left= TF_Right / TF_Left = (Output_Right/Input) / (Output_Left/Input)= (Output_Right/Input) / (Output_Left/Input) = Output_Right / Output_Left = Output_Right / Output_Left

Note: Fourier Transforms have been dropped for brevityNote: Fourier Transforms have been dropped for brevity

In this way, the Input is not needed.In this way, the Input is not needed.

Experimental SetupExperimental Setup SigLabSigLab

Creates Input signalCreates Input signal Calculates Fourier TransformCalculates Fourier Transform

AmplifierAmplifier Sound ChamberSound Chamber

SpeakerSpeaker AirAir MicrophonesMicrophones

AmplifierAmplifier SigLabSigLab

Captures Output signalCaptures Output signal Calculates Fourier TransformCalculates Fourier Transform

MatLabMatLab Builds databasesBuilds databases Performs analysisPerforms analysis

Building Databases of HRTF RatiosBuilding Databases of HRTF RatiosExample: 12 positions (30 deg spacing), 5 data per positionExample: 12 positions (30 deg spacing), 5 data per position

Matching MethodsMatching Methods(Minimizing Differences)(Minimizing Differences)

Sound test data is compared to the Database entriesSound test data is compared to the Database entries To find the best match, whichTo find the best match, which Indicates the position of the test soundIndicates the position of the test sound

Least SquaresLeast Squares Quantifies “sameness” using absolute distancesQuantifies “sameness” using absolute distances SUM[ (Test SUM[ (Test –– DatabaseEntry)^2 ]DatabaseEntry)^2 ]

Least Standard DeviationsLeast Standard Deviations Quantifies “sameness” using statistical distancesQuantifies “sameness” using statistical distances SUM[ abs(# STDs Test is from DatabaseEntryMean) ]SUM[ abs(# STDs Test is from DatabaseEntryMean) ]

Matching ResultsMatching Results 12 Positions12 Positions

30 Degree Increments30 Degree Increments Matching Percent Least Matching Percent Least

Squares = 82.67%Squares = 82.67% Matching Percent STD = Matching Percent STD =

98.33%98.33% 36 Positions36 Positions

10 Degree Increments10 Degree Increments Matching Percent STD =Matching Percent STD =

99.86%99.86%

72 Positions72 Positions 5 Degree Increments5 Degree Increments Matching Percent STD=Matching Percent STD=

100%100%

O.K., It’s Not Really That GoodO.K., It’s Not Really That Good

When the “half angles” are tested When the “half angles” are tested {5, 15, 25…} vs. the database of {0, 10, 20, 30…}{5, 15, 25…} vs. the database of {0, 10, 20, 30…}

The rate of matching to a neighboring 10 is onlyThe rate of matching to a neighboring 10 is only

76.26%76.26% No bueno.No bueno.

Adjacent AnalysisAdjacent Analysis We desire a database where each position is most We desire a database where each position is most

similar to its adjacent neighbors.similar to its adjacent neighbors. This would allow us to interpolate.This would allow us to interpolate.

A human HRTF database created at University of A human HRTF database created at University of California, Davis has this property.California, Davis has this property. Analyzing their data revealed a critical angle at which this Analyzing their data revealed a critical angle at which this

property degrades (somewhere between 10 and 30 degrees).property degrades (somewhere between 10 and 30 degrees).

Our 360x5 database exhibits this property for only 58% Our 360x5 database exhibits this property for only 58% of the positions (though our database is currently small)of the positions (though our database is currently small) We have not yet reached the critical angle. Is it > 1?We have not yet reached the critical angle. Is it > 1?

Future DirectionsFuture Directions Phase I: Phase I: CompletedCompleted

Demonstrate conceptDemonstrate concept Develop methodsDevelop methods

Phase II: Build a RobotPhase II: Build a Robot Include ability to adjust head elevationInclude ability to adjust head elevation Automate database construction in 3DAutomate database construction in 3D Create a database with much finer resolutionCreate a database with much finer resolution

Phase III: Phase III: Miniaturize, Miniaturize, Commercialize, and Commercialize, and Get RichGet Rich