0:00:13alright right sorry for the delay
0:00:16so uh that that some of it's and as a as we use it
0:00:20uh it may be described as follows and a sum of the elements of a some services
0:00:24that's out the such
0:00:26that uh
0:00:26sounds that would give an design a physical properties
0:00:29you also over it extended region
0:00:32oh and and not the for such a a and of the elementary sound was is is this is the
0:00:38fifty six to a lot the care that is installed
0:00:41no all of the power
0:00:42and a because a of a circle of uh
0:00:45two uh one point five meters that ideas
0:00:49and so it practice these uh uh elementary sound sources what
0:00:52uh that a lot because of the we you rather speak about the secondary sources because
0:00:57is certain locations you assume properties that are are difficult to to source it to a
0:01:03a discrete a lot to get what spatial extent
0:01:07and if you are familiar with a work you might to be where how much appreciate the state each and
0:01:13even more important the transparency of an analytical approach you
0:01:17the most uh a uh double double but that's not a weighted and this was proposed by that backup
0:01:21then that one variant of the ambisonics sonics approach
0:01:25according to that in
0:01:26and also the spectral of in like that that the the but which is a
0:01:30and extension of the so said set to a lower in there a race
0:01:34and i i was be a particularly about but local sound it's and
0:01:38and we use that a local of that to this is a good and you as as you have already
0:01:42learned than the previous talks
0:01:43um a practical implementation of some fields and that this system don't work perfectly but perfectly
0:01:49physical physical
0:01:50but um you can achieve
0:01:53a a a a low the increase of the course of the physical occurs
0:01:56this is what we
0:01:57so a local self
0:02:00so quick uh
0:02:02introduction to the mathematical formulation
0:02:05so these on the analytical approach is they typically assume a and and and an acoustically transparent
0:02:10continuous distribution
0:02:12of these elementary sources which are referred to as a second or so
0:02:17and then you can establish what we don't listen to a this is
0:02:21um which
0:02:22at that was the following
0:02:24we assume a a continuous distribution
0:02:26uh of taking small system the
0:02:29you you all maybe a
0:02:30and the the led to the function G represents the spatial that the transfer function of these second or sources
0:02:36so for example a one who or a similar or
0:02:39so so a school
0:02:41a a a a a a or six so of the complex
0:02:44a directivity T
0:02:45and X not um um represents a position on the secondary source distribution X positions space
0:02:53and and you that the for this transfer function because it may be interpreted as a a green function
0:02:59and and then
0:03:00the a the of the crime stick for each of which is individual for a a a source and if
0:03:05few integrate great with this continuous distribution
0:03:08the result of is
0:03:09the is see it
0:03:11and S
0:03:12so examples for um such as as a to the things are
0:03:17these are the the most different want on the left side you have a cycle
0:03:20distribution and closing the target model
0:03:23and a not on the right hand side you have an example for uh
0:03:27for the situation when only since is a a a like a typical be or result of plane is designed
0:03:32as a a a a a circular distribution
0:03:35and a to uh the problem and so a a uh uh for the moment is that usually you do
0:03:39not want how to how what's some you most if you drive you all speakers or the secondary sources and
0:03:44the specific
0:03:46you were rather want to
0:03:47to know how to drive the second or sources and all those that that is is a six of the
0:03:51walls so you will want to a educate S
0:03:55and calculate that of the
0:03:57there are two methods to do this
0:03:59one is the X is it yeah yeah solutions to this one but um so you you can transform this
0:04:05a i put it into a the um the spatial frequency domain
0:04:09which is a which is the domain exactly that is on the geometry of the of the second or sources
0:04:14you shows good at the start from knicks expansion or wave number maybe or a similar
0:04:19and then this in one turns into uh a multiplication which can use of these uh for the driving signal
0:04:25than inverse transform in order to the a
0:04:29this signal that have to implement
0:04:30i this is what a it is a specific or something formation
0:04:34a does it also has that it is
0:04:38and and i i have a i'm having a technical problem
0:04:48and of it and that seems to be a problem with this design it
0:05:36and and
0:05:47sorry again
0:06:10yeah hmmm
0:06:14and a
0:06:15maybe re
0:06:59and sorry yeah right can i have it my computer i'm quite sure that i
0:08:14i don't
0:08:17i'm very sorry
0:08:29thank you for pitch
0:08:31me and the are trying to to these include it is explicit solution is an implicit missing
0:08:36we a you want um exploit the has
0:08:39but i
0:08:40i i i have
0:08:43and where you exploit the physical relationship between the sound in of volume
0:08:47and uh and this something at the ball all real this volume which is for example described by the case
0:08:53of and once my ready to goes
0:08:55in order to to a derive of the time function from a description of the desired sound
0:09:00it's you don't to explicitly so
0:09:04and this is done with fit in this is and all this that was also a sort of a
0:09:10so for this in a and we want to uh this is it with a linear a speaker rate is
0:09:15explicit solution and then as and this is equation
0:09:18given as i think about from minus infinity to T
0:09:22yeah although i don't we assume a a secondary sources
0:09:26a a yeah X axis
0:09:28and then um then you can into a an interpret this is this equation as a convolution along a
0:09:36a X is
0:09:36and so for this someone was that the was zero
0:09:40which relates to a more quantities and wave number domain
0:09:43which you can then you use the um it were in this as a a a a a a with
0:09:47respect to X
0:09:48which you can use a rewrite
0:09:51and and uh to to to solve for the by signal and then you of for both
0:09:55had transform over to
0:09:57finally obtain a
0:09:58but then we can i think of obviously he's of abilities of such a linear a are um
0:10:03are are limited and you have to reference
0:10:05this thing is that's all
0:10:07to to a line
0:10:08and this is and you want look at where it is correct
0:10:10and you
0:10:12and that that is a that that's probably in most cases
0:10:16so that looks as follows
0:10:18if we want to read we're guess fact way which is shown
0:10:22yeah the source located at
0:10:24as you cross section two or something
0:10:27we are and one right hand side we assume pointing is distribution of uh uh model
0:10:32is just look the next section
0:10:34and we synthesized this um
0:10:36and and then it what's quite but but for any frequency you can imagine
0:10:42so that's why point to the from what was on that data of course and feeling in a be we
0:10:46we can assume a continuous distribution but in practice
0:10:49it will run like this
0:10:51so we have
0:10:52uh uh uh discrete distribution of of a finite number of uh of speakers
0:10:58and uh and you have a before that this to two
0:11:02in a very see
0:11:02for example they anything less
0:11:05and what we do in order to describe
0:11:08we don't assume a discrete distribution of secondary sources but we assume a continuous distribution that is excited at is
0:11:15me points that need to be some a
0:11:17not the the secondary so
0:11:19but the driving function
0:11:21yeah a that is that all these i go back
0:11:24on be into the relations we have a uh we have a
0:11:28exploit in be continuous case stay still value
0:11:32and a and B for i want to um
0:11:34describe the the consequence of the spatial sampling of what to work with excursion and to you be something of
0:11:40a time domain signal which are
0:11:42a probably all familiar with
0:11:43yeah yeah that is a a a a a a a week because it i do this i can i
0:11:47Z are emphasized a relation
0:11:50a relations which uh
0:11:52"'cause" it
0:11:54so let us to having a a a a a a a a a a time of my think and
0:11:58the with um and uh
0:12:00symmetric uh um a spectrum
0:12:03and so typically of like a lot to uh and the only think that and used on this something use
0:12:09i'm of a signal
0:12:10a repetitions of the spectrum of and this is
0:12:13a period of repetitions
0:12:16depends on on the vol
0:12:18and able to reconstruct a
0:12:20this is a you know i i i i don't have to to in order to
0:12:23to extract the based
0:12:26and is a discrete uh signal
0:12:29which contains a than for you one only if there um
0:12:33the you need
0:12:34signal is it's
0:12:37and with a a a a a a a a and you can
0:12:39indeed achieve a perfect
0:12:42i see
0:12:45i i had uh emphasise that in high domain mean yeah it's and time and something we used to be
0:12:50the repetitions time
0:12:52it away
0:12:53and a no pass filter is then used in order to interpolate these discrete
0:12:57time a signal
0:12:59it back to continuous time
0:13:01in of something this is that the different because space is more nation and time
0:13:06can can a proof that station something need to repetition
0:13:10as base frequency domain
0:13:11but in which for print is a representation of space frequency domain that depends on the geometry of the a
0:13:17second or so
0:13:19is to using you have some examples of me i don't know the are
0:13:22a a a a a a listed here
0:13:24and we will uh and that is a uh uh and i'm a a a range and then uh obtained
0:13:30from digits wave that will be
0:13:31and these are of just cannot get what it is is the way
0:13:34to circle
0:13:36and then in in a in a with a spatial or something such than the is data transfer functions as
0:13:41a secondary sources as they use of a is discrete signal into
0:13:45continuous space
0:13:46and we have a a a a a a a is a sum
0:13:49yeah investigations of one
0:13:51a for example how a lot bigger
0:13:53he's a in order to record to the uh
0:13:56to derive right a a a a and type to go
0:14:00and a like
0:14:02the continuous time function in this is a specific wave number of uh the way
0:14:07looks like this and if me
0:14:10we obtain a reputation
0:14:12it do it at a over there
0:14:15so we now consider a and an or you use a lot of a uh uh uh you know
0:14:22spatial frequencies because the higher one are then
0:14:25and and in here by G
0:14:27directive given of because
0:14:28and i and you get out of a
0:14:30and and and read only send
0:14:32so we see an of C
0:14:34there is no and interference of the different different spectrum to show that the above
0:14:39a wrong
0:14:40nine hundred hertz
0:14:41these uh rubber this winter fee
0:14:44so if we look at the sum but the synthesized
0:14:46it looks as follows on that and side of the continuous distribution
0:14:49and on the right hand side of discrete distribution
0:14:52with a lot because they single
0:14:53twenty sent
0:14:54at a time but
0:14:56you don't see any considerable difference
0:14:58between two
0:14:59if we go higher are two nine hundred for we see
0:15:02some some
0:15:03on the way
0:15:04and we go even higher
0:15:06then we have a
0:15:07indeed double
0:15:08a a sort of the from
0:15:10no at this and not my uh and
0:15:15we are we're going to back to it the later
0:15:17now the uh uh we are of course not forced to to use some stuff continued it got up to
0:15:22five five
0:15:23we could E
0:15:25a a just a a a a a with the meeting
0:15:27i i and by
0:15:28a i all the unwanted a specific or to zero of that's just one line because of an implementation
0:15:35and if we then a sum of this timing function
0:15:37these repetitions do not over that
0:15:39and leave
0:15:40our based and uh i'm for all
0:15:43and if we then look at the uh you want something
0:15:46again this is the design a result the perfect we've got in B C and D
0:15:50that in the set of of a a of this uh a a and B Y axes
0:15:55there are indeed very soon
0:15:57but uh uh of course a a a a a a to the locations of this far away from the
0:16:02we uh uh we have to uh
0:16:05we have a
0:16:06well one uh
0:16:08the of it i
0:16:11uh a result
0:16:12and since we achieve a low which is in a a curve as C we this is one of the
0:16:18of course he's not increase of a course come at the cost of a
0:16:22for a an increase of the duration as well
0:16:25of course you not forced to to do this band but an an imitation a symmetric you can do also
0:16:30a the method pretty good
0:16:31to the we can see
0:16:33then the
0:16:34the uh uh uh a as it do not overlap i
0:16:38and then
0:16:39these the region to region of increase the C can be you and was the city
0:16:45and my might yeah i want to mention that all is not that that i i uh a uh a
0:16:50a a lot of the shown
0:16:51are what equipment to like
0:16:56to that one so we we consider this situation
0:16:58and try to improve it
0:17:00so i quickly compute
0:17:02in order not to uh use it too much or with the you
0:17:05the problem of that this can be elegantly for data by a to the great
0:17:10as it and i'm very transparent the formation in terms of their limitations
0:17:15no this cannot be implemented in practice we have to use a discrete
0:17:18um a discrete arrangement of secondary sources which
0:17:21can to but are different
0:17:23a local increase of for um
0:17:26uh a C can be achieved by appropriate
0:17:28spatial and
0:17:30and this is and what we do
0:17:33as a result
0:17:34and we have presented a similar to and not exactly the same but that compared them for um
0:17:40for a circular arrangements
0:17:42a secondary source
0:17:43and uh i can you know
0:17:45the only thing or or or or do you think that the working one at the moment and this is
0:17:49something i want to do
0:17:51is that
0:17:53you cannot be used
0:17:54the of but there's a big difference uh uh two in the way a some it looks like in a
0:18:00and the way a it sounds like a when when you it
0:18:03so you cannot be to come simulation or something so like
0:18:06and this is what we are what
0:18:08at the moment to see you to exploit a static still
0:18:11see if it's really
0:18:13three for or or not
0:18:15thank you much
0:18:49yeah yeah some an and some relationship between uh the a a uh
0:18:55spectrum of us all and the the
0:18:59lee or the properties of
0:19:02the space
0:19:03i guess go back to this frequency domain illustration
0:19:08is this one
0:19:10so uh in that case
0:19:11the E
0:19:14zero you know uh everything
0:19:16a the energy of around zero a frequency corresponds to a components of the sound for travelling a regular
0:19:23to this uh to the secondary source
0:19:25your from that means if quickly
0:19:26i go back again
0:19:28if we can the energy of the percent
0:19:30there is a a is a sum that
0:19:32yeah um
0:19:34almost at a particular
0:19:36to of the second source distribution and a re
0:19:41you and not in a a a a a a shift so like change the region
0:19:45what we the energy in the space we can to domain is
0:19:49the synthesized so
0:19:53we see a
0:20:29a a good point
0:20:32i would assume that a a a uh is complex valued it to as a couple
0:20:40so far i but at uh if a if it is this a correct
0:20:44you agree
0:20:45no make is that something maybe michael or more quickly uh uh uh uh is up the G