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

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should

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yeah hmmm

really

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okay

what

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like

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and

vol

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that

or

i

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i

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i

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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