actually a and introduction and the will um so some part of the motivation was already given by D so um head related transfer functions or impulse response characterise the was a from source measure for example from a loudspeaker the years of a i mean that really or us and uh is your microphones and these functions are known that they are of course students angle uh dependence was you for example would take you had uh i if a and they also to some extent at distance so for example to use to situation gets free does me to does of course a big difference in and uh H T S if you know want the set up something like for example of a well what will auditory environment then uh it would be nice to have a database of hrtf covering all potential positions but like to have a which was also and of course the measurement of such a database is a quite tedious files so people can up with the idea of if you know for example of the hrtf a a set for all incidence angles for one distance how can you compute or syntactically we create a yes different this is and that these techniques are on a range extra for and of course that some techniques which uh uh uh based on psychoacoustic and some based and physical assumptions and i will uh are physically degraded of course and the past the a lot of uh stuff has been done here uh for example uh uh at for it to such a can measure a must you also circle so it's quite natural to sing yeah that the could expand them into spherical harmonics it's not that straightforward as one would assume you need to exploit you the prosody uh of a big the creation or to do so and then you can expand on the uh data set terms of so if a spherical harmonics and spherical hankel function of of the form uh range one problem image of a person in the context of very from one is that if you have a uh a not very dense sent think for it or even if bits on forty but like this is coded weekly data sets then you these methods are quite prone to numerical instability okay a stuff and that's of course some uh "'cause" but a class of texas based on the uh idea of uh what will acoustics and i will go to detail a time and the idea here is that you can X uh interpret yeah data set as of what will also be carry of course if you would take all speaker had a a a and it room that's the same have a loud speakers and of the come back to that so uh if you have a for example and hrtf a set which just examples here quite costly for the straight you have a right i H the F and we have all of these and yeah so if you can that this as an ensemble of lots because what will of course be oh uh the data then this is an speaker if you know for for instance want to have a H T F's from and the difference source of the distance like like from yeah uh what you can do is uh you can think but this we can interpret this as and what will uh so some what will some system so you have a a T yes three percent a lot i rate drive this what's will loudspeaker read by an appropriate a in signal which as oh so at first sight one saying oh uh uh and some um this is the head of the that's not a but or by the take and that's only partly true uh uh and this context play role course if you for example have scattering the head but the source but real source or uh synthesized sound correctly yeah doesn't care or something comes it's easy for them of course the sample synthesis introduces some errors you and the overall uh syntactic hrtf is then given from as the transfer function from the work clothes all over the end right this that so in a minute how was looks in mathematics so uh that's the two dimensional case here so uh assuming that we have taking measurements on a circle around to is not that that's not a free field case so don't hrtf and it's on of is this you typically start with a continuous diffusion or so called secondary so but kind of this continuous loudspeaker that you wait right few into all over all you use a a the end up pressure at all points yeah and uh to be is assume that you have a point source located of point source someone a whole model for you second a resource that's given by the so if we now want to load the uh do you pressure at the left and right yeah it's straightforward forward to replace the queens funk a the uh a two data transfer function the cost data transfer function is if a measure it was a lot people also to from from a point source to one of the S so it's quite straightforward to like and the overall transfer function is them from the source U S as a total for a you have to take yeah just case that to driving function uh should of course a and what was also has to be driven by a to work well but the region transfer um so for i can that the continuous phase of course you have to sample saying so you have a a sent here and uh in this case of course it's not extract any on you have some kind of approximation and on your space sending it the well you will need and just say me for send data sets for what then driving function and let them right H and of course like always and sampling you may get uh spatial at yes and and of a come back so a of no i didn't talk about the technique used to calculate a drive functions and the construct a takes around uh which we term a sound field synthesis techniques takes that of techniques uh at at least it this is of a sound field was was not extend the every using an ensemble law so physical synthesis this is that as the basic assumption of sort that synthesis and well known approach here of for example a few synthesis you you compensated by the sonics the spectral do method and a number of them are debate for and but you can use use all of these approaches here not to voice for more less i we can of a few synthesis for some reason that see later so a very brief introduction to but if it's and this is uh if you want to know more about because in this is i would like to do a you to the paper is to time train a have a make some this is is based on an approximation of the synthesis so if you have yeah a sound field of the but will solve can can approximate this by this integral over a oh is so face yeah we are you want to synthesized a sound field and you have a as at which is a window function you have a directional gradient a some of you false that's the gradient direction of all the vector and in for so this part is right from a function a takes care that only part of the because i used and synthesis and typically that hot a the but at all propagate into the action of the but was um some properties of a it's of this is uh just summarise here that are some minor deviation you to be in both approximations a estimation yeah that's some for few assumption but it so for a very low frequencies and nearby by sources it's has some minor deviation if is this is typically a model based approach which means that you have some models for you but was also but good in our context yeah so plain based on sources i have some lakes or you and uh just calls and as we a back and i'm minute later or you can have source inside to the thing every so called and a very important fact for this paper is that and a if it's in this is allows for very efficient implementation using a pretty for the ring of the but was source signal and in the for the out so you and really meant to the time T the time domain be efficiently and is in a and in as they no regularization so um some pictures just the depict would make it and is is going in this cost you i simple it a political what will uh system this is uh uh close and hrtf dataset this five five sampling that one meter so it can see for but will one source but at three meters for one thing about see C you just synthesized correctly so as to oh that it is and a four is we can see C yeah that's the spatial aliasing a so some for things happen you spain um that's being some so some on the uh certain properties of spatial aliasing and uh from him a basic and for typical of a synthesis set might be perceived will be to spatial aliasing in the however if a synthesis all some systems also not sense of was that high number oh back to focus or since that even want first thing than the context of uh spatial something and a focused source is of uh that's the kind of a if you can generate a such techniques uh i if if it's and also but you for was you if you to two a focus and so if a if you converges the just point and directors off and that is focus point we have the few a more as a point so and and uh an interesting property is that if you increase the frequency still give it to cut outs have four khz you can see that uh the area which is a it is an scenario to too small small it is in free around the sensor or point focus source and he can four eight khz we are a i mean to be a inside this is a but a uh so if you that feel was all spatial um and lot a property which is important uh i set already didn't do this in every has limited so need if you the low the focus point has probably propagation direction or whatever change propagation gaze direction by changing but all speakers to use in this example of it is also side oh so uh you to but to use uh in terms of spatial that is the and in the following of show results which are related to focus source this has to be used on the one hand at is and is not particular about and on the other hand this is this this and if you H T F to so interesting because uh H H G T S a change from dramatically for sources which are close to that this so for two or three meters the a story a we by what to go for example half a meter or you you trying to see as the changes that what brought so that's quite interesting eighteen since if you so yeah a some results uh the how to the it that that a straightforward uh uh use the time domain implementation of but it's and this is so just some waiting and a with the so that really straightforward a little more tricks a a and that things about both oh have a this this create realisation of the bit i'm going to a more detail no what if a if you want to and thing you have that that yeah is that you're spatial exactly and also the distance but also front of you to some button and and S um a systematic and to if it is to come back in a minute and uh for evaluation and used a love we uh a data set of H um range uh you can also and it shows some results from you so this is you one this is that in is not uh from and source denoted i yeah or note to uh uh uh uh this uh to use "'em" S and if you consider that case is that you have a a S and homes on the plane uh this is a a a a so for the how the man oh the you the issues would assume that uh the also because would you look at a of you in if we dimensional space that's not the case for or something plane and you know i'm about so that lot that around you and the also some physically error and physically motivated has nothing to do with that so um and you have some systematic and deviation or shown but no yeah for example if you have the you have a plane wave travelling from the from uh from up to down you can see a course a and B the polls years three you this well like to have it oh we have a if the and example a this site here he that is some and to to uh uh "'kay" should not assume of the head so uh yeah compensate for that's score important if you would not do so and level difference i i feel a uh wrong and i D is are very well for you uh for perception of you here co four so some results um that's is the one of the age of them related impulse responses that uh for for a four each other a using uh and a data P a one and and C quite nice a a a a a a a major data set of how how meter yeah and see some the or here there are a mind a and if you listen to the data set yeah most so the question for uh that's well for and a direct used the control level difference um results it is well known that the i'll likely be used for you by also so for example yeah right the line and yeah you do line shows to measure data sets for for a good you and for how you can see that i i E increases what we want and uh using a whole except at at and also see that uh uh i i be also increases almost a low to we measured one of a me to just did he is missus might you to the fact that the or measurements that all speaker for half the measurements some you the fact center yeah well so it's also known that for nearby source is the low frequency response of the system from increase in low frequencies from source is that's shown here so that again the dashed line the the measurement a red fine i X one point at three the how i mean you one the a made of one mean you can see we can model yeah use low frequency increases the and also the overall all frequency one uh a the little of course there's some issue sure i so some in oh i see that the application of so so but will wave field synthesis a matrix relation but especially especially are correct results the the form you know you're and and uh for for for of the for all the distances is that the false also works get some spatial aliasing artifacts a question as for a C there are and that's not it in number and the number they and the small realisation no involvement must in in the but we might in that case it that's very low and big city and you can also use although the what was models and point sources right so i this is if you sources and if you like to hear how it sounds than a mode some this in a lot more form inside i'm sources yeah are very minor differences between them and hi um i'm that some way to increase the uh speech at is we can see it can use multiple make it this is a present that this is the last week and the S oh a four and of course uh would be very interest taking a uh if you to fixed using to models have i some this i a and for oh actually a i i i i oh oh one oh and that my yeah yeah oh i yeah i i well oh well i i no yeah and is not not to ring for calculating you ones so if you have a data a measure one and we meeting uh you can have for example assume that the data set for however that's quite a different you can really here do this uh and a a and then the think examples can really here that there's a big difference with we we don't have a really here a coming close so and otherwise it would have to matter all this this this which is uh take a oh that's the main make sure i play a they well oh no yeah or i house yeah yeah yeah and yeah hmmm so right where where yeah uh_huh yeah that that's also the reason why we and because of you know that very must yeah that's small was the way to do it or or or or also here are already that a spherical harmonics and uh and that's how and the you it's a more correct yeah okay okay