0:00:14a Q mister chain um a break go
0:00:16up up the ladies and gentlemen my name is challenging light and it's my honour to present to you
0:00:22the design of robust the of a broadband beam formers
0:00:25right the microphone gain in base error of right there is day
0:00:29now during the course of my presentation of first find the problem that
0:00:33we want to solve
0:00:35and then now move
0:00:36to discuss about the array geometry that we use for all beamformer design
0:00:41after that out top some up just the of a broadband beamformer structure use and robust design formulation
0:00:47then out
0:00:48a provide us
0:00:50sign example and finally out close my presentation
0:00:54now in speech acquisition as applications such a
0:00:58teleconferencing and audio surveillance
0:01:02it is likely that the speaker a time was to move around the room
0:01:06you be best if we have a
0:01:08beamformer form that can be steel to the directions of the speaker
0:01:12in order to acquire the speech signal
0:01:15and because we are dealing with a
0:01:16speech signal here which use of rock band we want
0:01:19our be former to have a a frequency invariant property
0:01:23and lastly
0:01:24we want our beamformer to robot
0:01:28to be robust to microphones errors and
0:01:31i the deviation
0:01:32so in other what's these three
0:01:34card to stick is what we are trying to achieve a our design
0:01:39and in these presentations
0:01:41only meet the discussion in the five few more that you as you move and only
0:01:45but it should be not that
0:01:47it can be these design can be easily tend to the knee a few more than
0:01:53not the original tree that we propose here is what we call the spider a i'm alright right
0:01:58basically is the mouth you reading can are right
0:02:05if we can see the that for example
0:02:10michael here for the first all of the zero already
0:02:13and then
0:02:14the microphone at the first three and the next ring we can see that
0:02:18you've form the spiral um
0:02:21and the next one is well so that the reason by would call it
0:02:25the spiral i'm a
0:02:28one of the good properties of this
0:02:31spire i'm i race that's it has
0:02:33uh circular symmetric properties which we we can exploit
0:02:37in order to have a three hundred and sixty degrees during compatibility
0:02:42not the
0:02:43it response of
0:02:45these microphone are rate is given by these equations
0:02:48where the in that
0:02:50C and K
0:02:52we was to the K microphone
0:02:54in the P three
0:02:56and the only got are represent a frequency
0:02:59five represent a as he move and a
0:03:01our P P we present the radius of the P reading a C is the
0:03:06speech of the propagating eighteen
0:03:11now as for the steerable a broadband beamformer structures
0:03:15i'm we are using the farrow structures at each of the microphone
0:03:20so here we can use the for you by bill from the far all structures
0:03:24do not that has
0:03:25the thought here
0:03:27the all main B
0:03:30and the patient is given by these
0:03:32so basically
0:03:33the side here represent the
0:03:36steering and a and a
0:03:38sign met
0:03:39here is the maximum steering range
0:03:41so basically these inspirations
0:03:44is just to scale the
0:03:46theory and a to be we in the range of plus minus the a five for the five
0:03:51farrow structure
0:03:53no do not mean a beam pattern of these
0:03:56beamformer structure is given by these inspiration
0:04:00which can be written compactly in terms of
0:04:03but the form
0:04:05where the back the a a and a
0:04:09C K and and times one long vector
0:04:13wait P C is the number of reading
0:04:15K is the number of microphone re
0:04:17and mine one he's the order of farrow structure
0:04:21and and is the number of
0:04:23for the if a a few of
0:04:27now in print um in print car environment
0:04:30we always has some deviations from the idea more
0:04:34and this
0:04:35deviations can come from
0:04:36a so such as
0:04:38mismatches between microphone elements
0:04:41not i knew characteristic of the microphones
0:04:44positions a those in the microphones
0:04:47elements and also low cost get bring effect
0:04:51if we want to
0:04:53um have uh a robust side of being form of then we need to include
0:04:57some sort of error of modeling into our design
0:05:00so if we include the
0:05:02error modelling into our design then we have
0:05:05oh but to alima response people by D K
0:05:10cut a here
0:05:12we present the gain
0:05:14deviations for each microphone and
0:05:17we present the face deviations for each microphone
0:05:21and if we use these but to my element rest balls then will have
0:05:25the beam paid them with but the element response given by D
0:05:29which we can use then use this
0:05:31in our design
0:05:34now for the robust design we and to optimize the design based on the mean of the deviations
0:05:41which is basically the S but the value you of how a deviation
0:05:46not if we formulate our design in least ways formulation as we have
0:05:51the cost functions people by these
0:05:53what the compute the side we present the desired steering range
0:05:58the tape make a
0:05:59we present the
0:06:00frequency range of interest and the to
0:06:04Y represent present a
0:06:06as a move in of interest
0:06:08and it is well known that
0:06:11these these where cost function can be written in a compact
0:06:14matrix form given by these
0:06:17where the element is
0:06:18uh the matrix
0:06:20chi bet the P
0:06:21but the B and a D is given by these
0:06:26now the mean error terms
0:06:28is given by
0:06:30the matrix
0:06:31you bob L talk and
0:06:34but the tar
0:06:36there are and a into the metric
0:06:39Q you
0:06:40and that the B
0:06:42as you can see here
0:06:43you but with the robust
0:06:46if but with the robust
0:06:48these i'm formulations with do you have this and that
0:06:51form of these ways formulations
0:06:53this mean that this means that to solve this formulations we can still use this then that these squares
0:06:59this i'm at
0:07:01not as and
0:07:02design example suppose that we want to design
0:07:05a being and that can be as a from minus the T six degree tools the T six degree
0:07:11and you has a
0:07:12spectral pass band
0:07:13from two hundred to three thousand and eight hundred uh
0:07:19and you has a fall
0:07:22we've the ring id given by these
0:07:25and for each
0:07:26reading we have four five
0:07:29microphone and the order of fire structure is four and the number of you that the is study two
0:07:36or the microphone gain deviations we use the rally
0:07:40our rally
0:07:41distribution we've sick my was to one and for the slice deviations we use a uniform K
0:07:48we've the actual minus
0:07:50pile but to to pile over two
0:07:54in order to illustrate last the robustness of our design
0:07:57we introduced two types of perturbation
0:08:01to our
0:08:03beam patterns
0:08:04the first but the nations
0:08:06we want to model the bees mismatch between michael
0:08:10so here each of the microphone is more than the as the fifty texts band pass if i a people
0:08:16and then the coefficients of this field those is perturbed by
0:08:19uniform random form random was given by D
0:08:22so as can be seen here the two graph here we represent a
0:08:26frequency response of the microphones where the first
0:08:30the left hand graph represent the microphone case and uh right
0:08:36graph we present the microphone groups delay
0:08:39now each line here
0:08:41give the response of
0:08:43each of the microphone elements used
0:08:46as can be seen from these two graph
0:08:48we can see that
0:08:49for all the michael form in them once we do not have i you
0:08:53microphone characteristic and
0:08:55a microphone elements
0:08:57not match
0:08:58with each other
0:09:01not on top of that
0:09:02we introduced in either the perturbations
0:09:05which is
0:09:06to model the
0:09:07error in the microphone
0:09:10a positions
0:09:12so here
0:09:13the X and Y coding net of all microphone uses
0:09:17is put up with zero-mean gaussian pdf with standard deviation of once same thing we do
0:09:26this for graph shows the beam pattern all sparse are and
0:09:30spectral response of a beamformer
0:09:34the left column here shows the beam pattern them for the non robust design
0:09:39yeah et
0:09:40minus twenty degree and thirty five degree
0:09:44the right
0:09:45hence that here shows the beam pattern for the robust design
0:09:50the a minus twenty green and the five degree
0:09:53not a few comments here
0:09:56for the robust design
0:09:58we can see that
0:10:00the beam pattern
0:10:02you meant tend the properties that we
0:10:04this or we and to design where
0:10:08um why we have a frequency invariance property
0:10:13just do you
0:10:14it is you clear that the as a man being at the directions of
0:10:20the steering and a we she's minus twenty degree his case and
0:10:23the D five degree these case
0:10:26now for the non robust design
0:10:29or the only case do see some
0:10:31beam but then
0:10:32a sum
0:10:34men be at the higher frequency and
0:10:36but and the low frequency and
0:10:39the beam but than just blows out
0:10:41in the presence of perturbation
0:10:45so this clearly shows that i'm the is improvement
0:10:48in the robust design
0:10:53these for beam pattern shows
0:10:55the beam patterns without any perturbation
0:10:58now if the is not that the missions then the non robust design
0:11:03a a a at the left two graphs
0:11:05in the perform better
0:11:07as shown by the more was quite low
0:11:10where for the robust designs
0:11:12we have
0:11:14a be high side not
0:11:16so this is the tradeoff off between
0:11:18have been a lot was
0:11:20a low side and the robust design
0:11:22so in order to achieve
0:11:24robust design we need to trail
0:11:26the side lot level
0:11:28i as
0:11:29compared to the previous slide we can see that for the robust design
0:11:33the beam pattern is maintain
0:11:36in the presence of perturbation
0:11:39now to conclude
0:11:42we have proposed a robust steerable broadband beamformer design
0:11:45and the steering capability is achieved by using the pharaohs if few those structure
0:11:50not the robust
0:11:51formulations is more though using stochastic model
0:11:55and it is optimized for the mean performance
0:11:58and from the design example us
0:12:00it is clearly show that
0:12:02um the robust design achieve the tree
0:12:05i to the that initially we set up to solve
0:12:09it has a steering actually T
0:12:12and it has a frequency variance
0:12:16and lastly it is robust against the perturbations
0:12:20not with these i and my
0:12:23presentation and thank you for your attention
0:12:33use use the mac
0:12:38a case you for in simply we don't and
0:12:41some a question is that the is so i look but you corporate thing to be to to control to
0:12:46the microphone again and and arrow
0:12:48can be a a a a uh a peak move for
0:12:51the the raise
0:12:52for instance here you you use a like a spider of um race where yes
0:12:57but yes S is a a a few cable for linear or
0:13:00no the right
0:13:01yes um this that can be applicable to any other the
0:13:06um array geometry that in that we need to modify is the a response
0:13:12a on the uh original array three that we you uh we design or
0:13:17i guess
0:13:18okay thank you
0:13:27um as you know we the more the average response
0:13:30it could still happen that for some special division of giving and
0:13:34uh a actually there is a a large deviation for the we won
0:13:38you can comment on that and do you also look at worst case optimization performance
0:13:42okay um
0:13:44if the error a D too much from the nominal mean a value of than definitely the you know what
0:13:50think for or if you trim a the mean the average performing sparse specific
0:13:55or additional doing and the is it could go can for the specific variation yeah
0:14:00that a diffusion is very large but still on average is good performance
0:14:03but did you also look at its worst case optimization
0:14:06um we have a look at the worst case
0:14:09a P my stations yet
0:14:10currently we only look
0:14:12look at the mean performance
0:14:15thank you
0:14:18and more questions
0:14:25thank you