0:00:13actually a and introduction
0:00:15and the will um
0:00:18some part of the motivation was already given by D
0:00:21so um head related transfer functions or impulse response
0:00:25characterise the was
0:00:27a from source
0:00:30for example from a loudspeaker
0:00:31the years of a i mean that really
0:00:34or us and uh is your microphones
0:00:37these functions are known that they are of course
0:00:40students angle uh dependence was you for example would take you had uh i if a and they also to
0:00:46some extent at distance
0:00:49for example to use to situation gets free does me to does of course a big difference in and uh
0:00:55H T S
0:00:56if you know want the set up something like for example of a well what will auditory environment
0:01:01then uh
0:01:02it would be nice to have a database of hrtf covering all potential positions but like to have a which
0:01:08was also
0:01:09and of course the measurement of such a database is a quite tedious files
0:01:14so people can up with the idea of
0:01:16if you know
0:01:17for example of the hrtf a a set for all incidence angles for one distance
0:01:22how can you
0:01:24compute or
0:01:25syntactically we create a yes different
0:01:28this is
0:01:29and that
0:01:30these techniques are on a range extra for
0:01:33and of course that some techniques which uh
0:01:35uh uh based on psychoacoustic and some based and physical
0:01:39assumptions and i will uh are physically degraded
0:01:44of course and the past the a lot of uh stuff has been done here uh for example uh
0:01:50at for it to such a can measure a must you also circle
0:01:54so it's quite natural to sing yeah that the could expand them into spherical harmonics
0:01:58it's not that straightforward as one would assume you need to exploit you the prosody uh of a big the
0:02:04creation or to do so
0:02:05and then you can expand on the uh data set
0:02:08terms of so if a spherical harmonics and
0:02:10spherical hankel function of of the form
0:02:13uh range
0:02:15one problem image of a person in the context of very from one is that if you have a uh
0:02:20a not very dense sent think for it or even if bits on forty but like this is coded weekly
0:02:24data sets
0:02:25then you these methods are quite prone to numerical instability
0:02:29okay a stuff and that's of course some
0:02:34but a class of texas based on the uh
0:02:37idea of uh what will acoustics and i will go to detail a time
0:02:41and the idea here is that you can X
0:02:43uh interpret
0:02:44yeah data set as of what will also be carry
0:02:46of course if you would take all speaker
0:02:48had a a a and it room that's the same
0:02:52a loud speakers
0:02:55and of the come back to that
0:02:56so uh if you have a for example and hrtf a set which just examples here
0:03:01quite costly
0:03:02for the straight you have a right i H the F and we have all of these
0:03:08so if you can that this as an ensemble of lots because what will of course be oh
0:03:14uh the data
0:03:15then this is an speaker
0:03:17if you know for for instance
0:03:19want to have a H T F's from and
0:03:21the difference source of the distance
0:03:23like like from yeah
0:03:24uh what you can do is uh
0:03:27you can think
0:03:28but this we can interpret this as and what will uh
0:03:31so some what will some system
0:03:33so you have a a T yes three percent a lot i rate
0:03:36drive this
0:03:37what's will loudspeaker read
0:03:38by an appropriate a in signal
0:03:41which as
0:03:44so at first sight one saying
0:03:46uh uh and some um this is the head of the that's not
0:03:49a but or by the take
0:03:51and that's
0:03:51only partly true uh uh and this context
0:03:54play role
0:03:56if you for example have
0:03:57scattering the head but the source but real source
0:04:02synthesized sound correctly
0:04:05yeah doesn't care or something comes
0:04:08it's easy for them
0:04:11of course the sample synthesis introduces some errors
0:04:16and the overall uh syntactic hrtf is then given from as the transfer function from the work clothes all over
0:04:22the end
0:04:25so in a minute how was looks in mathematics
0:04:28so uh that's the two dimensional case here so uh assuming that we have taking measurements
0:04:33on a circle around to is not that
0:04:37that's not a free field case so don't hrtf
0:04:40and it's on of is this you typically start
0:04:42with a continuous
0:04:43diffusion or
0:04:45so called secondary so
0:04:46but kind of this continuous loudspeaker
0:04:49that you wait
0:04:51few into all over all
0:04:53you use a a the end up
0:04:56at all points
0:04:58and uh to be is assume that you have a point source located of point source someone a whole model
0:05:04for you second a resource that's given by the
0:05:07so if we now want to load the uh
0:05:10do you pressure at the left and right yeah
0:05:12it's straightforward forward to replace the queens funk
0:05:14a the uh a two data transfer function
0:05:17the cost data transfer function is
0:05:19if a measure it was a lot people also to
0:05:21from from a point source
0:05:23to one of the S
0:05:25so it's quite straightforward to
0:05:28and the overall transfer function is them from the source U S as a total for a you have to
0:05:33take yeah just case that to driving function
0:05:35uh should of course
0:05:37a and what was also has to be driven by a to work well
0:05:41but the region
0:05:44um so for i can that the continuous phase of course you have to sample saying so you have a
0:05:49a sent here
0:05:51and uh in this case of course
0:05:53it's not
0:05:54extract any on you have
0:05:55some kind of approximation
0:05:57and on your space sending it the well
0:05:59you will need and just
0:06:00say me for send data sets
0:06:03for what
0:06:04then driving function
0:06:06and let them right
0:06:08and of course like always and sampling you may get uh
0:06:13spatial at yes and and of a come back
0:06:16so a of no i didn't talk about the technique used to calculate a drive functions and the construct a
0:06:22takes around
0:06:23uh which we term a sound field synthesis techniques takes that of techniques
0:06:27at at least it this is of a sound field
0:06:29was was not extend the every using an ensemble law
0:06:33physical synthesis this is that as the
0:06:35basic assumption of sort that synthesis
0:06:37and well known approach here of for example a few synthesis
0:06:41you you compensated by the sonics
0:06:43the spectral do method and a number of them are debate
0:06:48and but you can use use all of these approaches here
0:06:51not to
0:06:53for more less
0:06:54i we can of a few synthesis for some reason that see
0:06:59so a very brief introduction to but if it's and this is uh
0:07:02if you want to know more about because in this is i would like to do a you to the
0:07:05paper is to time
0:07:08a have a make some this is is based on an approximation of the synthesis
0:07:12so if you have yeah
0:07:13a sound field of the but will solve
0:07:15can can approximate this by
0:07:17this integral over a
0:07:19oh is so face
0:07:21yeah we are you want to synthesized
0:07:23a sound field and
0:07:24you have a
0:07:24as at
0:07:26which is a window function you have a directional gradient
0:07:29a some of you
0:07:31false that's the
0:07:32gradient direction of all the vector
0:07:34and in
0:07:36so this part is right from
0:07:38a function a
0:07:39takes care that only part of the because i used
0:07:42and synthesis
0:07:43and typically that hot
0:07:45the but at all
0:07:46propagate into the action of the
0:07:48but was
0:07:50um some properties of a it's of this is uh just summarise here that are some minor deviation
0:07:55you to be in both approximations a
0:07:58estimation yeah that's some
0:07:59for few assumption
0:08:01but it so for a very low frequencies and nearby by sources it's
0:08:04has some
0:08:05minor deviation
0:08:07if is this is typically a model based approach which means that you have some models for you but was
0:08:11but good in our context yeah
0:08:13so plain based on sources
0:08:15i have some lakes or you and uh just
0:08:19as we a back and i'm minute later or you can have source inside to the thing every so called
0:08:24and a very important fact
0:08:26for this paper is that
0:08:27and a if it's in this is allows for very efficient implementation using a pretty for the ring of the
0:08:32but was source signal and in the for the out
0:08:35so you and really
0:08:36meant to the time T the time domain be efficiently
0:08:39and is in a and in as they no regularization
0:08:44so um some pictures just the depict would make it and is is going in this cost you i simple
0:08:49it a political what will uh system
0:08:52this is uh uh close and hrtf dataset this
0:08:55five five sampling
0:08:56that one meter
0:08:58so it can see for but will one source
0:09:00but at three meters
0:09:01for one thing about
0:09:02see C you just synthesized
0:09:04correctly so as to
0:09:06oh that it is
0:09:07and a four is we can see
0:09:10C yeah that's the
0:09:11spatial aliasing a so some
0:09:13for things happen
0:09:17um that's being some so some on the uh certain properties of spatial aliasing and uh from him a basic
0:09:23and for typical of a synthesis set
0:09:25might be perceived will be to spatial aliasing in
0:09:30if a synthesis all some systems also not sense of was that high
0:09:37oh back to focus or since that even want first thing than the context of uh
0:09:41spatial something
0:09:42and a focused source is of
0:09:45that's the kind of a if you can generate a such techniques uh i
0:09:49if if it's and also
0:09:50but you
0:09:51for was you if you to two a focus and so if a if you converges
0:09:56just point and directors off
0:09:58and that is focus point
0:10:00we have the few
0:10:01a more as a point so
0:10:04and and uh an interesting property is that if you increase the frequency still give it to cut outs have
0:10:09four khz
0:10:10you can see that uh
0:10:12the area which is a it is an scenario to too small small it is in free around the sensor
0:10:17or point focus source
0:10:19and he can four eight khz
0:10:21we are
0:10:23a i mean to be a inside
0:10:25this is a
0:10:26but a uh
0:10:27so if you that
0:10:29feel was all spatial
0:10:31um and lot a property which is important uh i set already didn't do this in every has limited so
0:10:36need if you
0:10:37the low the focus point has
0:10:39probably propagation direction or whatever
0:10:41propagation gaze direction by changing but all speakers to use
0:10:44in this example of it is also
0:10:50so uh you to but to use uh in terms of spatial that is the and in the following of
0:10:55results which are related to focus source
0:10:58this has to be used on the one hand at is and is not particular about
0:11:02and on the other hand
0:11:03this is this this and if you H T F to so interesting
0:11:07because uh
0:11:08H H G T S a change from dramatically for sources which are close to that this
0:11:12so for two or three meters the a story
0:11:15a we by what
0:11:17to go for example half a meter or you you trying to see as the changes that what brought so
0:11:21that's quite interesting
0:11:23since if you
0:11:27yeah a some results uh the how to the it that that a straightforward uh uh use the time domain
0:11:32implementation of but it's and this is so just some waiting and a with the so that really straightforward
0:11:38a little more tricks a a and that things about both
0:11:41oh have a this this
0:11:42create realisation of the bit i'm going to
0:11:45a more detail no
0:11:46what if a if you want to and thing you have that that
0:11:49yeah is that you're spatial exactly
0:11:52and also
0:11:52the distance
0:11:53but also
0:11:54front of you to some button
0:11:57and and S um
0:11:58a systematic and to if it is to come back in a minute
0:12:01and uh for evaluation and used a love we uh a data set of H
0:12:05um range uh
0:12:08you can also
0:12:11and it shows some results from you
0:12:14so this is you one this is that in is not uh from
0:12:17and source
0:12:22yeah or note
0:12:23to uh uh uh uh this uh
0:12:26to use "'em"
0:12:28if you consider that case is that you have a a S and homes on the plane
0:12:32uh this is a a a a so for the how the man
0:12:36oh the you the issues would assume
0:12:38that uh
0:12:39the also because would you look at a of you in if we dimensional space that's not the case for
0:12:44or something plane and you know i'm about
0:12:46so that lot that around you
0:12:48and the also some
0:12:49physically error
0:12:52physically motivated has nothing to do with that
0:12:55so um
0:12:57and you have some systematic and deviation
0:13:00or shown but no yeah for example if you have the you have a plane wave travelling
0:13:04from the from uh from up to down
0:13:07you can see a course a and B the polls years three you this well like
0:13:12to have it
0:13:13oh we have a if the and example
0:13:16this site here
0:13:17he that is some and
0:13:18to to uh
0:13:20"'kay" should not assume of the head
0:13:23so uh
0:13:24yeah compensate for
0:13:26that's score
0:13:27if you would not do so
0:13:28and level difference i i feel a uh wrong and i D is are very well for you uh for
0:13:35perception of you
0:13:38co four
0:13:40so some results
0:13:42that's is the one of the age of them
0:13:45related impulse responses that uh
0:13:47for for a four
0:13:48each other
0:13:50using uh and a data
0:13:53a one
0:13:55and C
0:13:56quite nice
0:13:57a a a a a a a major data set of how how meter
0:14:01and see some
0:14:04or here
0:14:05there are a mind a and if you listen to the data set
0:14:08yeah most
0:14:09so the question
0:14:14well for and a direct used the control level difference
0:14:18results it is well known that the i'll likely be used for you by also so for example
0:14:25the line and
0:14:26yeah you do line
0:14:28shows to measure data sets for for a good you and for how you can see that i i E
0:14:34increases what we want and uh using a whole
0:14:37except at at and also see
0:14:39that uh uh i i be also increases
0:14:42almost a low
0:14:43to we measured one of a me to just did he is missus
0:14:47might you to the fact that the or measurements
0:14:49that all speaker
0:14:50for half the measurements
0:14:51some you the fact center
0:14:57so it's also known that for nearby source is the low frequency response of the system
0:15:03from increase in low frequencies from source is
0:15:06that's shown here so that again
0:15:07the dashed line
0:15:09the the measurement a red fine
0:15:11X one point at three the how i mean
0:15:14you one
0:15:15a made of one mean you can see
0:15:17we can model
0:15:18yeah use low frequency increases the
0:15:21and also the overall all frequency one uh
0:15:24a the little
0:15:25of course there's some issue
0:15:32so some in
0:15:34i see that the application of
0:15:35so so but will wave field synthesis
0:15:37a matrix relation
0:15:39but especially especially are correct results
0:15:41the the form you know you're
0:15:44and and uh
0:15:45for for for of the for all the distances is that the false also works
0:15:49get some spatial aliasing artifacts a question as for a C there are
0:15:53and that's not
0:15:55in number and the number they and the small realisation no involvement must in in the
0:16:01but we might in that case it that's very low
0:16:03big city
0:16:04and you can also use
0:16:06although the what was models and point sources
0:16:09so i this is if you sources
0:16:12and if you like to hear how it sounds than a mode some this in a lot more
0:16:17form inside i'm sources
0:16:19yeah are very minor differences between them and
0:16:24um i'm that some way to increase the uh
0:16:27speech at is we can see
0:16:29it can use multiple make it this is a present that this is the last week and the S
0:16:35a four
0:16:35and of course uh would be very interest
0:16:38taking a uh
0:16:39if you to fixed using to models
0:16:42i some this
0:16:46oh actually a
0:16:58and that
0:17:25oh well
0:17:32yeah and is not not to ring
0:17:34for calculating you ones so if you have a data
0:17:37a measure one and we meeting
0:17:40you can have for example assume that the data set for however
0:17:43quite a different
0:17:44you can really here
0:17:45do this
0:17:48a a and then the think examples can really here that there's a big difference with
0:17:51we we don't have a
0:17:52really here
0:17:53a coming close
0:17:56and otherwise it would have to matter all this this this which is uh
0:18:03that's the main make sure i play a
0:18:29yeah yeah and yeah
0:18:31hmmm so
0:18:43yeah that that's also the reason why we
0:18:46because of you know that very must yeah that's small was the way to do it
0:18:50or or or or also here are already that a spherical harmonics and uh and that's
0:18:55and the you it's a more
0:19:00yeah okay