alright right sorry for the delay and so uh that that some of it's and as a as we use it uh it may be described as follows and a sum of the elements of a some services that's out the such that uh sounds that would give an design a physical properties you also over it extended region oh and and not the for such a a and of the elementary sound was is is this is the fifty six to a lot the care that is installed no all of the power and a because a of a circle of uh two uh one point five meters that ideas and so it practice these uh uh elementary sound sources what uh that a lot because of the we you rather speak about the secondary sources because is certain locations you assume properties that are are difficult to to source it to a a discrete a lot to get what spatial extent and and if you are familiar with a work you might to be where how much appreciate the state each and even more important the transparency of an analytical approach you the most uh a uh double double but that's not a weighted and this was proposed by that backup then that one variant of the ambisonics sonics approach uh according to that in and also the spectral of in like that that the the but which is a and extension of the so said set to a lower in there a race and i i was be a particularly about but local sound it's and and we use that a local of that to this is a good and you as as you have already learned than the previous talks um a practical implementation of some fields and that this system don't work perfectly but perfectly physical physical but um you can achieve a a a a low the increase of the course of the physical occurs this is what we so a local self so quick uh introduction to the mathematical formulation so these on the analytical approach is they typically assume a and and and an acoustically transparent continuous distribution of these elementary sources which are referred to as a second or so and then you can establish what we don't listen to a this is equation um which at that was the following we assume a a continuous distribution uh of taking small system the you you all maybe a and the the led to the function G represents the spatial that the transfer function of these second or sources so for example a one who or a similar or like so so a school a a a a a a or six so of the complex a directivity T and X not um um represents a position on the secondary source distribution X positions space and and you that the for this transfer function because it may be interpreted as a a green function and and then the a the of the crime stick for each of which is individual for a a a source and if few integrate great with this continuous distribution the result of is the is see it and S so examples for um such as as a to the things are these are the the most different want on the left side you have a cycle distribution and closing the target model and a not on the right hand side you have an example for uh for the situation when only since is a a a like a typical be or result of plane is designed as a a a a a circular distribution and a to uh the problem and so a a uh uh for the moment is that usually you do not want how to how what's some you most if you drive you all speakers or the secondary sources and the specific you were rather want to to know how to drive the second or sources and all those that that is is a six of the walls so you will want to a educate S and calculate that of the there are two methods to do this one is the X is it yeah yeah solutions to this one but um so you you can transform this a i put it into a the um the spatial frequency domain which is a which is the domain exactly that is on the geometry of the of the second or sources you shows good at the start from knicks expansion or wave number maybe or a similar and then this in one turns into uh a multiplication which can use of these uh for the driving signal than inverse transform in order to the a this signal that have to implement i this is what a it is a specific or something formation a does it also has that it is but so and and i i have a i'm having a technical problem and of it and that seems to be a problem with this design it can right number and and oh or great we sorry again and um should i sure most yeah hmmm really and a maybe re i okay what and sorry yeah right can i have it my computer i'm quite sure that i like i i oh i oh and vol oh that or i oh that's i oh oh i or yes okay i don't i'm very sorry thank you for pitch so me and the are trying to to these include it is explicit solution is an implicit missing we a you want um exploit the has but i i i i have that's and where you exploit the physical relationship between the sound in of volume and uh and this something at the ball all real this volume which is for example described by the case of and once my ready to goes in order to to a derive of the time function from a description of the desired sound it's you don't to explicitly so a equation and this is done with fit in this is and all this that was also a sort of a accelerated so for this in a and we want to uh this is it with a linear a speaker rate is explicit solution and then as and this is equation i given as i think about from minus infinity to T yeah although i don't we assume a a secondary sources a a yeah X axis and then um then you can into a an interpret this is this equation as a convolution along a X a X is and so for this someone was that the was zero which relates to a more quantities and wave number domain which you can then you use the um it were in this as a a a a a a with respect to X which you can use a rewrite and and uh to to to solve for the by signal and then you of for both had transform over to finally obtain a but then we can i think of obviously he's of abilities of such a linear a are um are are limited and you have to reference this thing is that's all to to a line and this is and you want look at where it is correct and you and that that is a that that's probably in most cases so that looks as follows if we want to read we're guess fact way which is shown and yeah the source located at as you cross section two or something we are and one right hand side we assume pointing is distribution of uh uh model is just look the next section and we synthesized this um and and then it what's quite but but for any frequency you can imagine so that's why point to the from what was on that data of course and feeling in a be we we can assume a continuous distribution but in practice it will run like this so we have uh uh uh discrete distribution of of a finite number of uh of speakers and and uh and you have a before that this to two in a very see for example they anything less and what we do in order to describe we don't assume a discrete distribution of secondary sources but we assume a continuous distribution that is excited at is me points that need to be some a not the the secondary so but the driving function yeah a that is that all these i go back on be into the relations we have a uh we have a exploit in be continuous case stay still value and a and B for i want to um describe the the consequence of the spatial sampling of what to work with excursion and to you be something of a time domain signal which are a probably all familiar with yeah yeah that is a a a a a a a week because it i do this i can i Z are emphasized a relation a relations which uh "'cause" it so let us to having a a a a a a a a a a time of my think and the with um and uh symmetric uh um a spectrum and so typically of like a lot to uh and the only think that and used on this something use i'm of a signal a repetitions of the spectrum of and this is a period of repetitions depends on on the vol and able to reconstruct a this is a you know i i i i don't have to to in order to to extract the based all and is a discrete uh signal which contains a than for you one only if there um the the you need signal is it's and with a a a a a a a a and you can indeed achieve a perfect that two i see so i i had uh emphasise that in high domain mean yeah it's and time and something we used to be the repetitions time it away and a no pass filter is then used in order to interpolate these discrete time a signal it back to continuous time in of something this is that the different because space is more nation and time so can can a proof that station something need to repetition as base frequency domain but in which for print is a representation of space frequency domain that depends on the geometry of the a second or so is to using you have some examples of me i don't know the are a a a a a a listed here and we will uh and that is a uh uh and i'm a a a range and then uh obtained from digits wave that will be and these are of just cannot get what it is is the way to circle and then in in a in a with a spatial or something such than the is data transfer functions as a secondary sources as they use of a is discrete signal into continuous space and we have a a a a a a a is a sum yeah investigations of one a for example how a lot bigger he's a in order to record to the uh to derive right a a a a and type to go and a like so no the continuous time function in this is a specific wave number of uh the way looks like this and if me some we obtain a reputation which it do it at a over there so we now consider a and an or you use a lot of a uh uh uh you know spatial frequencies because the higher one are then and and in here by G directive given of because and i and you get out of a and and and read only send so we see an of C there is no and interference of the different different spectrum to show that the above a wrong nine hundred hertz these uh rubber this winter fee so if we look at the sum but the synthesized it looks as follows on that and side of the continuous distribution and on the right hand side of discrete distribution with a lot because they single twenty sent at a time but you don't see any considerable difference between two if we go higher are two nine hundred for we see some some on the way and we go even higher then we have a indeed double a a sort of the from no at this and not my uh and uh we are we're going to back to it the later now the uh uh we are of course not forced to to use some stuff continued it got up to five five we could E a a just a a a a a with the meeting i i and by a i all the unwanted a specific or to zero of that's just one line because of an implementation and if we then a sum of this timing function these repetitions do not over that and leave our based and uh i'm for all and if we then look at the uh you want something again this is the design a result the perfect we've got in B C and D that in the set of of a a of this uh a a and B Y axes there are indeed very soon but uh uh of course a a a a a a to the locations of this far away from the right we uh uh we have to uh we have a well one uh the of it i uh a result and since we achieve a low which is in a a curve as C we this is one of the so of course he's not increase of a course come at the cost of a for a an increase of the duration as well of course you not forced to to do this band but an an imitation a symmetric you can do also a the method pretty good to the we can see then the the uh uh uh a as it do not overlap i and then these the region to region of increase the C can be you and was the city direct and my might yeah i want to mention that all is not that that i i uh a uh a a a lot of the shown are what equipment to like to to that one so we we consider this situation and try to improve it so i quickly compute in order not to uh use it too much or with the you the problem of that this can be elegantly for data by a to the great as it and i'm very transparent the formation in terms of their limitations no this cannot be implemented in practice we have to use a discrete um a discrete arrangement of secondary sources which can to but are different a local increase of for um uh a C can be achieved by appropriate spatial and limitation and this is and what we do as a result and we have presented a similar to and not exactly the same but that compared them for um for a circular arrangements a secondary source and uh i can you know the only thing or or or or do you think that the working one at the moment and this is something i want to do size is that you cannot be used the of but there's a big difference uh uh two in the way a some it looks like in a simulation and the way a it sounds like a when when you it so you cannot be to come simulation or something so like and this is what we are what at the moment to see you to exploit a static still see if it's really three for or or not thank you much i i i oh yeah and and i oh i yeah oh oh so yeah yeah some an and some relationship between uh the a a uh space spectrum of us all and the the lee or the properties of the space i guess go back to this frequency domain illustration i right is this one so uh in that case the E um zero you know uh everything a the energy of around zero a frequency corresponds to a components of the sound for travelling a regular to this uh to the secondary source your from that means if quickly i go back again if we can the energy of the percent there is a a is a sum that yeah um properties almost at a particular to of the second source distribution and a re yeah you and not in a a a a a a shift so like change the region what we the energy in the space we can to domain is wrote the synthesized so i we see a one you me i oh and oh a oh where um a a good point yeah but i would assume that a a a uh is complex valued it to as a couple so yeah so far i but at uh if a if it is this a correct you agree no make is that something maybe michael or more quickly uh uh uh uh is up the G a oh hmmm yeah yeah and i i i