0:00:14 | a Q mister chain um a break go |
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0:00:16 | up up the ladies and gentlemen my name is challenging light and it's my honour to present to you |

0:00:22 | the design of robust the of a broadband beam formers |

0:00:25 | right the microphone gain in base error of right there is day |

0:00:29 | now during the course of my presentation of first find the problem that |

0:00:33 | we want to solve |

0:00:35 | and then now move |

0:00:36 | to discuss about the array geometry that we use for all beamformer design |

0:00:41 | after that out top some up just the of a broadband beamformer structure use and robust design formulation |

0:00:47 | then out |

0:00:48 | a provide us |

0:00:50 | sign example and finally out close my presentation |

0:00:54 | now in speech acquisition as applications such a |

0:00:58 | teleconferencing and audio surveillance |

0:01:02 | it is likely that the speaker a time was to move around the room |

0:01:05 | so |

0:01:06 | you be best if we have a |

0:01:08 | beamformer form that can be steel to the directions of the speaker |

0:01:12 | in order to acquire the speech signal |

0:01:15 | and because we are dealing with a |

0:01:16 | speech signal here which use of rock band we want |

0:01:19 | our be former to have a a frequency invariant property |

0:01:23 | and lastly |

0:01:24 | we want our beamformer to robot |

0:01:27 | um |

0:01:28 | to be robust to microphones errors and |

0:01:31 | i the deviation |

0:01:32 | so in other what's these three |

0:01:34 | card to stick is what we are trying to achieve a our design |

0:01:39 | and in these presentations |

0:01:41 | only meet the discussion in the five few more that you as you move and only |

0:01:45 | but it should be not that |

0:01:47 | it can be these design can be easily tend to the knee a few more than |

0:01:53 | not the original tree that we propose here is what we call the spider a i'm alright right |

0:01:58 | basically is the mouth you reading can are right |

0:02:03 | where |

0:02:05 | if we can see the that for example |

0:02:08 | um |

0:02:09 | uh |

0:02:10 | michael here for the first all of the zero already |

0:02:13 | and then |

0:02:14 | the microphone at the first three and the next ring we can see that |

0:02:18 | you've form the spiral um |

0:02:21 | and the next one is well so that the reason by would call it |

0:02:25 | the spiral i'm a |

0:02:27 | now |

0:02:28 | one of the good properties of this |

0:02:31 | spire i'm i race that's it has |

0:02:33 | uh circular symmetric properties which we we can exploit |

0:02:37 | in order to have a three hundred and sixty degrees during compatibility |

0:02:42 | not the |

0:02:43 | it response of |

0:02:45 | these microphone are rate is given by these equations |

0:02:48 | where the in that |

0:02:50 | C and K |

0:02:52 | we was to the K microphone |

0:02:54 | in the P three |

0:02:56 | and the only got are represent a frequency |

0:02:59 | five represent a as he move and a |

0:03:01 | our P P we present the radius of the P reading a C is the |

0:03:06 | speech of the propagating eighteen |

0:03:08 | where |

0:03:11 | now as for the steerable a broadband beamformer structures |

0:03:15 | i'm we are using the farrow structures at each of the microphone |

0:03:20 | so here we can use the for you by bill from the far all structures |

0:03:24 | do not that has |

0:03:25 | the thought here |

0:03:27 | the all main B |

0:03:30 | and the patient is given by these |

0:03:32 | so basically |

0:03:33 | the side here represent the |

0:03:36 | steering and a and a |

0:03:38 | sign met |

0:03:39 | here is the maximum steering range |

0:03:41 | so basically these inspirations |

0:03:44 | is just to scale the |

0:03:46 | theory and a to be we in the range of plus minus the a five for the five |

0:03:51 | farrow structure |

0:03:53 | no do not mean a beam pattern of these |

0:03:56 | beamformer structure is given by these inspiration |

0:04:00 | which can be written compactly in terms of |

0:04:03 | but the form |

0:04:05 | where the back the a a and a |

0:04:08 | ah |

0:04:09 | C K and and times one long vector |

0:04:13 | wait P C is the number of reading |

0:04:15 | K is the number of microphone re |

0:04:17 | and mine one he's the order of farrow structure |

0:04:21 | and and is the number of |

0:04:23 | tech |

0:04:23 | for the if a a few of |

0:04:27 | now in print um in print car environment |

0:04:30 | we always has some deviations from the idea more |

0:04:34 | and this |

0:04:35 | deviations can come from |

0:04:36 | a so such as |

0:04:38 | mismatches between microphone elements |

0:04:41 | not i knew characteristic of the microphones |

0:04:44 | positions a those in the microphones |

0:04:47 | elements and also low cost get bring effect |

0:04:50 | so |

0:04:51 | if we want to |

0:04:53 | um have uh a robust side of being form of then we need to include |

0:04:57 | some sort of error of modeling into our design |

0:05:00 | so if we include the |

0:05:02 | error modelling into our design then we have |

0:05:05 | oh but to alima response people by D K |

0:05:09 | where |

0:05:10 | cut a here |

0:05:12 | we present the gain |

0:05:14 | deviations for each microphone and |

0:05:16 | gamma |

0:05:17 | we present the face deviations for each microphone |

0:05:21 | and if we use these but to my element rest balls then will have |

0:05:25 | the beam paid them with but the element response given by D |

0:05:29 | which we can use then use this |

0:05:31 | in our design |

0:05:34 | now for the robust design we and to optimize the design based on the mean of the deviations |

0:05:41 | which is basically the S but the value you of how a deviation |

0:05:46 | not if we formulate our design in least ways formulation as we have |

0:05:51 | the cost functions people by these |

0:05:53 | what the compute the side we present the desired steering range |

0:05:58 | the tape make a |

0:05:59 | we present the |

0:06:00 | frequency range of interest and the to |

0:06:04 | Y represent present a |

0:06:06 | as a move in of interest |

0:06:08 | and it is well known that |

0:06:11 | these these where cost function can be written in a compact |

0:06:14 | matrix form given by these |

0:06:17 | where the element is |

0:06:18 | uh the matrix |

0:06:20 | chi bet the P |

0:06:21 | but the B and a D is given by these |

0:06:26 | now the mean error terms |

0:06:28 | is given by |

0:06:30 | the matrix |

0:06:31 | you bob L talk and |

0:06:33 | B |

0:06:34 | but the tar |

0:06:35 | and |

0:06:36 | there are and a into the metric |

0:06:39 | Q you |

0:06:40 | and that the B |

0:06:42 | as you can see here |

0:06:43 | you but with the robust |

0:06:45 | sorry |

0:06:46 | if but with the robust |

0:06:48 | these i'm formulations with do you have this and that |

0:06:51 | form of these ways formulations |

0:06:53 | this mean that this means that to solve this formulations we can still use this then that these squares |

0:06:59 | this i'm at |

0:07:01 | not as and |

0:07:02 | design example suppose that we want to design |

0:07:05 | a being and that can be as a from minus the T six degree tools the T six degree |

0:07:11 | and you has a |

0:07:12 | spectral pass band |

0:07:13 | from two hundred to three thousand and eight hundred uh |

0:07:19 | and you has a fall |

0:07:21 | reading |

0:07:22 | we've the ring id given by these |

0:07:25 | and for each |

0:07:26 | reading we have four five |

0:07:29 | microphone and the order of fire structure is four and the number of you that the is study two |

0:07:35 | now |

0:07:36 | or the microphone gain deviations we use the rally |

0:07:40 | our rally |

0:07:41 | distribution we've sick my was to one and for the slice deviations we use a uniform K |

0:07:47 | a |

0:07:48 | we've the actual minus |

0:07:50 | pile but to to pile over two |

0:07:54 | in order to illustrate last the robustness of our design |

0:07:57 | we introduced two types of perturbation |

0:08:01 | to our |

0:08:02 | um |

0:08:03 | beam patterns |

0:08:04 | the first but the nations |

0:08:06 | we want to model the bees mismatch between michael |

0:08:10 | so here each of the microphone is more than the as the fifty texts band pass if i a people |

0:08:15 | talk |

0:08:16 | and then the coefficients of this field those is perturbed by |

0:08:19 | uniform random form random was given by D |

0:08:22 | so as can be seen here the two graph here we represent a |

0:08:26 | frequency response of the microphones where the first |

0:08:30 | the left hand graph represent the microphone case and uh right |

0:08:36 | graph we present the microphone groups delay |

0:08:39 | now each line here |

0:08:41 | give the response of |

0:08:43 | each of the microphone elements used |

0:08:46 | as can be seen from these two graph |

0:08:48 | we can see that |

0:08:49 | for all the michael form in them once we do not have i you |

0:08:53 | microphone characteristic and |

0:08:55 | a microphone elements |

0:08:56 | ah |

0:08:57 | not match |

0:08:58 | with each other |

0:09:01 | not on top of that |

0:09:02 | we introduced in either the perturbations |

0:09:05 | which is |

0:09:06 | to model the |

0:09:07 | error in the microphone |

0:09:10 | a positions |

0:09:12 | so here |

0:09:13 | the X and Y coding net of all microphone uses |

0:09:17 | is put up with zero-mean gaussian pdf with standard deviation of once same thing we do |

0:09:25 | now |

0:09:26 | this for graph shows the beam pattern all sparse are and |

0:09:30 | spectral response of a beamformer |

0:09:34 | the left column here shows the beam pattern them for the non robust design |

0:09:39 | yeah et |

0:09:40 | minus twenty degree and thirty five degree |

0:09:44 | the right |

0:09:45 | hence that here shows the beam pattern for the robust design |

0:09:50 | the a minus twenty green and the five degree |

0:09:53 | not a few comments here |

0:09:56 | for the robust design |

0:09:58 | we can see that |

0:10:00 | the beam pattern |

0:10:02 | you meant tend the properties that we |

0:10:04 | this or we and to design where |

0:10:08 | um why we have a frequency invariance property |

0:10:12 | and |

0:10:13 | just do you |

0:10:14 | it is you clear that the as a man being at the directions of |

0:10:20 | the steering and a we she's minus twenty degree his case and |

0:10:23 | the D five degree these case |

0:10:26 | now for the non robust design |

0:10:29 | or the only case do see some |

0:10:31 | beam but then |

0:10:32 | a sum |

0:10:34 | men be at the higher frequency and |

0:10:36 | but and the low frequency and |

0:10:39 | the beam but than just blows out |

0:10:41 | in the presence of perturbation |

0:10:45 | so this clearly shows that i'm the is improvement |

0:10:48 | in the robust design |

0:10:51 | no |

0:10:53 | these for beam pattern shows |

0:10:55 | the beam patterns without any perturbation |

0:10:58 | now if the is not that the missions then the non robust design |

0:11:02 | even |

0:11:03 | a a a at the left two graphs |

0:11:05 | in the perform better |

0:11:07 | as shown by the more was quite low |

0:11:10 | where for the robust designs |

0:11:12 | we have |

0:11:14 | a be high side not |

0:11:16 | so this is the tradeoff off between |

0:11:18 | have been a lot was |

0:11:20 | a low side and the robust design |

0:11:22 | so in order to achieve |

0:11:24 | robust design we need to trail |

0:11:26 | the side lot level |

0:11:28 | i as |

0:11:29 | compared to the previous slide we can see that for the robust design |

0:11:33 | the beam pattern is maintain |

0:11:35 | even |

0:11:36 | in the presence of perturbation |

0:11:39 | now to conclude |

0:11:42 | we have proposed a robust steerable broadband beamformer design |

0:11:45 | and the steering capability is achieved by using the pharaohs if few those structure |

0:11:50 | not the robust |

0:11:51 | formulations is more though using stochastic model |

0:11:55 | and it is optimized for the mean performance |

0:11:58 | and from the design example us |

0:12:00 | it is clearly show that |

0:12:02 | um the robust design achieve the tree |

0:12:05 | i to the that initially we set up to solve |

0:12:08 | namely |

0:12:09 | it has a steering actually T |

0:12:12 | and it has a frequency variance |

0:12:15 | properties |

0:12:16 | and lastly it is robust against the perturbations |

0:12:20 | not with these i and my |

0:12:23 | presentation and thank you for your attention |

0:12:30 | questions |

0:12:33 | use use the mac |

0:12:38 | a case you for in simply we don't and |

0:12:41 | some a question is that the is so i look but you corporate thing to be to to control to |

0:12:46 | the microphone again and and arrow |

0:12:48 | can be a a a a uh a peak move for |

0:12:51 | the the raise |

0:12:52 | for instance here you you use a like a spider of um race where yes |

0:12:57 | but yes S is a a a few cable for linear or |

0:13:00 | no the right |

0:13:01 | yes um this that can be applicable to any other the |

0:13:06 | um array geometry that in that we need to modify is the a response |

0:13:11 | functions |

0:13:12 | a on the uh original array three that we you uh we design or |

0:13:17 | i guess |

0:13:18 | okay thank you |

0:13:27 | um as you know we the more the average response |

0:13:30 | it could still happen that for some special division of giving and |

0:13:34 | uh a actually there is a a large deviation for the we won |

0:13:38 | you can comment on that and do you also look at worst case optimization performance |

0:13:42 | okay um |

0:13:43 | if |

0:13:44 | if the error a D too much from the nominal mean a value of than definitely the you know what |

0:13:50 | think for or if you trim a the mean the average performing sparse specific |

0:13:55 | or additional doing and the is it could go can for the specific variation yeah |

0:14:00 | that a diffusion is very large but still on average is good performance |

0:14:03 | but did you also look at its worst case optimization |

0:14:06 | um we have a look at the worst case |

0:14:09 | a P my stations yet |

0:14:10 | currently we only look |

0:14:12 | look at the mean performance |

0:14:15 | thank you |

0:14:18 | and more questions |

0:14:25 | thank you |