you a fine we work uh in which he that issue oh well will be C i E oh a function of yeah mean oh what we action a a yeah for had a a function oh would you that of a function i three oh the future it actual P in a total of not it's a a a a single the issue and uh it's all those a you know because uh one thing to have a different difference oh it's was five so you know have and total um it's not yeah um can be a change just you three five regiment oh of of of a should a shot yeah i i but is only um a response and uh sum some they uh some spatial position and the whole procedure is oh we see time as you me so you want to have a but and uh can you model to recreate then in we a charge yeah oh but a higher order to C yeah i'm going to uh uh and for the use the three D five you a a continuous hrtf model uh here's the a a a a reference with with the house uh that's we can see that um in the model model of is the frequency components to from spatial component and because call it so that the you know oh function and it a a very easy to reconstruct a shot yeah at a at a a a three that they shouldn't and in the and a and G O frequency point a we have to question is for this model oh well as to how should it this model and the seconds i also and that's if you are are also if representation is that we to here oh oh one of this question oh first the we you can have a you know that he man to match to they should be and then oh we use the true a he met to evaluate the function able there are very oh we have you a random or it can be expressed as a linear combination oh on it and then no determined that deterministic all normal functions is weighted a random variables oh the um that C functions are orthonormal with read that to and in a product in fact is we use a rate be free small approximate this is using a an it's number of of the old normal function then and O the expected value of the squared norm of error of the phoenix representation can be given by these uh by prominent a two where a is the random process and has a a it representation of the random four uh the core work if they don't be also also no expansion the or so that he man a now we focus on a team for at least for illustration but we have a a random you find on them and that interval with zero mean and and in in the G you can handle um all normal compression be in a four inches rule that um the random draw that can be right yeah um and the you combination or you know uh uh another uh or in finance uh the complete a basis and way by a very well is a random variable is given by the end of all that so at the end the complete basis and the truncation um for for five or shows the arrow for uh oh of in a representation and the fact that the right along oh oh error a we a good a part of um that thing and so we can see that that was that so will change and and it you can do oh in that that is all of the a a representation so to the meeting my the that have that oh oh we need to make my uh the second time now oh you got a a a a a second term you take that second so that second so um a a you know by a by a far as as useful we a random variable is uh a given by a you know but that so at the end i T so from the calculation uh they they fire a can be right yeah a a problem that uh where yeah see the autocorrelation function of the random process and the uh a a a at the one change so we can say that a a a a a a a mean it's on the choice of the complete a base okay but to uh uh any a complete or normal because can be used so we have a question which is a that now a a a a a just five C uh uh i i think of of the for in will in creation with for no the also correlation function of the random drug that's and then we use each um i think function uh to we spend the random for that at the formal or the and and the oh random for a random variable a a is given by you inner product of that and the and the these oh i can function now oh compute a a screen play five from the calculation we can see that oh okay "'cause" i was to uh that some model a a a a and i i is the eigenvalue and we know that a a a that was to i can function account i well as i my of error a uh variability of the random process at was able so we we say that we a a "'cause" i have three you or greater than that you buy out the a a complete basis and then all with a a a a that can be a a a a similar if then a long uh i can function but quite well and the distribution of property in the random i thought i a i don't know all too complicated to be described as think they all in close to form so at to read about it extremely you can go to find a oh okay L expression for the random problem i uh given a a a a a set of real i they shouldn't of of the random process oh and it's and i three are all normal be we can calculate uh the random error oh variable able for each realisation and then we apply that there random variable and use a a of various to the them that so the that the energy of the random or and then the ah a a a a a a hell of a a a is a random variable so are part uh screen a five in we know that it's of ones that are then a a sign which is given by a oh of to more expansion so we for a T max oh which is that um well and i think the sample variance are are among random variable oh which is involved in the model now still we use the i um i don't five three made to evaluate the function model i oh the kl expansion is unavailable oh there are two seconds to is are and a consideration oh the uh the representation is not offer more redundant you must at this to the in the mall then how do we measure the redundancy or equivalence is the H E i we know that is small so in the oh model uh imply that error of the representation is a there is a trade-off efficient the end and ri uh you can uh uh uh and six fashion oh we can calculate a very is for and coefficient then we find that only only uh or i coefficients are a very small which used the corresponding sounds to be removed them from the model that's in a large than the error and i so only uh and i a uh so that the model and uh a so uh we can you to me the efficiency of the model in terms of that so which are given by a and the it then uh that i is one is oh there are many a point is all orthonormal basis so will which one is a bass oh and uh oh we know that a human uh well i think that all of normal basis we can calculate a oh but and all coefficients and a i screen a a i friends so we compare them at all three play then the lack of that bad has so um the well known be up by thing a like to create a a a a is the best choice okay oh we use the uh proposed a map to be evaluate to each you yeah no for the efficiency in a a spatial component is there's in a a a there is an um each each they show the spatial components it a a a a a a a very low the harmonic and uh a a i i the coefficients still we hold spherical harmonic uh coefficients which is a given by a of the you know what are so it not yeah a and a very money and uh we might not be way and have to a a and is given by a uh uh right um and it is a need to me by a a a a wave number of K okay and not a oh oh of for that model we have oh have they have a capital and coefficient then oh we can do the are there the whole all these there will have money oh oh coefficient oh we find that and right oh okay efficient a a a a a nine one nine then of the total energy so uh for me looking and uh we define the H I T N as the initial efficient the a a and the whole key oh i shows um um the uh very is all all their a harmonic coefficients for the frequency and for a you know that and with C that the was the C coefficients of hand oh most of the energy and then uh think of be shows that the speaking a at okay so and and the capital and wrong calculate and in these oh to try to go and O a a and one the red a down and a problem if we should both he we can uh as you can be a the of they show of component expansion is a wrong seventeen then and then a a a a think good shows a migration a model the man a H I yeah the blue one and then a a a a a a a one in a a a a we constructed each each yeah using and and for a capital and to themselves spherical a a harmonic and that really one still uh the reconstructed hrtf oh using and trying in terms of spherical harmonic that we want to different this speaking writing one and right one is oh or wrong to one percent i oh let's say which are normal with select uh a base it is that a frequency components there is a a a a a a in it is a three D uh hrtf model we use uh spherical be L to expend the of frequency component and uh i i is that there will be a more efficient of which is given by be formula i still we have a other classes that's a a complex exponentials oh and agenda probably and T V share on a because uh are they are all you can have but it's in expanding of frequency components use or on the in term and uh collocation can be given by oh these three you cliche respectively then a here it would treat the and the a property of H T of components oh models using these four sets of orthonormal basis and but that and so on i shows the screen play and we can see that a a a a new value for for a a a a a uh according to compress C spun that actually is quite close to that there will be a function but still we model the note that uh i think he said all a a will be out in a sample and i with and still of the total energy of we're oh while uh i think in a comp simple and now shows only a have for three presents no the oh and G so with i here are spread will be found at most and is the passage voice C it's yeah frequency expansion okay uh motion uh and i right know we a a a a set the question how to we if they really the efficiency of a and oh a function of hrtf model and oh we use a we use the some of the where of random variable in in the model to uh evaluate the efficiency and the read that still efficiency of the model oh a spatial component expansion is around seventy percent and the but what is still uh a frequency component pension is the spherical bessel don't function thanks for attention you i i i okay i and all i i the that do that but um i think it it can be uh for the D C U and was to for all the prosody oh a a representation mm so i think it's can four hmmm i yeah hmmm hmmm hmmm yeah i i