"'kay" thank you all for coming um my talks about applications of short space time for analysis in digital acoustics john to work uh with mark actually so what is digital still acoustics so what we call the field of a dimensional a a signal processing that involve a a sampling and reconstructing the weight uh a typical using uh a of microphones and well course so these are race they act as a a a a D computers and the egg cover respect of so it means that uh i after sampling between we have a matrix of a samples of course a temporal and spatial samples that we can process using two S P and my michael oh cool um so for example if there's a source um in the acoustic scene that we want to get rid of we could apply to the mission filter and uh we could get rid of this source and have only the one that manners oh we could for example and these are to to applications gonna talk about um a in coal the information that is sampled with your array of microphones and all star it in an i pod for example so then later we can reconstruct it with a a for example way feel to um but sort order this kind of um processing to the mission signal processing we need to mission signal processing tools and the first to i want to talk about is the spatial temporal free a transform and this involves taking the if transform across you're right X so why would you want to do this well essentially actually uh the wave equation tells us that um if the way feel this harmonic in time then necessarily certainly it's harmonic in space so there's a the here and the fourier transform a a the array access use went to exploit this how it in space for example if if you contrast a bit uh looking at each microphone individually i this case you have three sources i it's not very clear uh where the information from each source is going to appear so um all this doesn't give you a clear visual impression of what is it "'cause" sixteen what is if you take the free transform across and not all these three sources are nice place in this uh a two dimensional frequency domain in one acts you have the regular frequency um to improve frequency and any the other acts you have the spatial frequency or the wave number and you see that um the displacement of source uh with respect to to the every X is going to place um this lines where all the energies constant uh so for example we can even complicated bit more if there's a source like can schools or to your rate you also see a nice pat an where where these lines open up as a triangle so we're gonna see more detail what is mean um and so for example in this situation oh where have two sources that matter and you have this this two in the far field and you have this near field in the for we wanna uh i get rid of uh it is very clear what we have to do here uh we the play field they're that to get rid of these components so in the end we'll have a the two components that my so for for doing this kind of uh applications we need to understand um one simple scenario which is the the point source in there so what happens the spectral representation when you have a point source this you oh a this point sources i is a driven can by uh a signal S of T and the angle with respect to X is this off X i has a minimum angle and i some angle depends on the length of the right and if you look at to to the mission spectrum you actually see that um the special pattern is uh this trying to region with a few ripples on the outside um so this trying to region is the limited by the by the cosine sign of the two angles "'cause" of these two angles a a a completely define what is the aperture of this trying to reach and the ripples on the outside which come from the effect from doing so the thing function fact they're oriented toward the continuous average uh of the angle of course the the entire so not one the the whole mathematical michael expression because the be dense uh but i'm gonna tell you that's um this is actually means um that you have is the free transform of the source signal but multiplied by a combination of max operation of the sinc function E fact caused by window and this trying the region that depends on the distance of the source you're right and this represents presents are information and this one presents a spatial information so there set and so using this result how how could we uh for example filter to source in the way feel so we all have to go where the energy we have to define a filter that takes um at this trying to that preserved this trying to the region a where all the energies contain and um this all the rest so this would be like as a simple two dimensional filter design problem okay so you define what are defined where of the transition region um you could be fine if it's linear phase are you can find the the bandpass ripples and the um the best top people's and then you could use a to design technique uh i two dimensions uh to obtain the realizable filter oh these are a few examples for example using the win me method or the part some um but that is very easy one you have only one source so what happens when you have more than one or don't have as as the following it's each source uh each point source has uh what a called this chat the reason behind it uh that if if it's going to overlap with the shot a region of another source that here for sure you gonna have spectral overlapping okay so this these two trying to regions um which chris want which source i want to overlap in just something and so with menu filtering you cannot for you uh week cover um uh each source the one thing you can do to to read this problem is we split up there are the array into um equal parts and then we're gonna see that for example and the left block the shall a reason is he's reduce for the two sources i don't what we're gonna have much less overlapping in this in the spectral domain and the same thing gonna happen for the block on the right and so you can do this um you can keep uh dividing you're a into smaller parts and you gonna see that's the these trying to reason is gonna get smaller and smaller row the other hand you wanna have uh other if effect are harmful which for example if you reduced to mean the size you're gonna have a much more sing function effects so there's a balance um there's like a limit uh a limited number of times that you can divide you can split up to three i and smaller parts so you might have you might have already noticed that this is analogous to a short time fourier transform except you're doing it in a to do this um in in this space and time uh it's essentially you can do it essentially with a a a a dimensional uh filter bank oh which implements a a a a a lapped transform so it's the in this example for you have us a source and a new field a be closer to the right near rate and you see that you have a a lot more curvature in the space time representation you have a lot more curvature in a region that is close to the source um so of course is the filter bank is but reconstruction than the input is gonna be the same as the output and in the middle you see the the actual composition you have a in one direction you have the the special blocks and in the vertical axis you have the temporal blocks if you look close or to the spatial uh the dimension you see that a for each of these blocks this trying to reason is much more narrow and it to fall O uh the location of the source okay as the as a block was close or two to word the source um here's one example this is one issue in the paper um it's a it's a it's a nice worst case scenario oh where and you for source is cool line with a with a far source of the far for source actually with respect to the rate is behind the near field source and you can see the spectra representation that the far field source completely immersive um in the spectrum of of the new so if we do this decomposition uh let's see one iteration you have you you start seeing that the the new two source yeah the sure of the trying to gets reduced so they start getting separate and you can do a with a larger when the size um and then in the end if you want to filter to one of those um you apply it to each of the blocks able apply filter that's isolates source so this is a a a result the one we we got um the best results in the mean sense was for uh a window size of thirty two K and you can see that in the space time representation there's a there's a source in the new field mixed up with one in the far field and here to get this if you string to get clues a the second application wanna to talk about this coding so how do we code the wave field in this domain uh the structure we use is is very similar to what's um state of art you call there's to let's say in P three or a C so you actually take it to my mission filter bank um that is the the fourier transform across cross time and space and then in this domain you're going to quantise code um all this uh coefficients so this is the bit allocation problem and that for comparing the results uh we do the inverse uh feel the the inverse quantization and then comparing the mean scores um and so if you look at our of worst case scenario uh we see that so this is this is the plots uh the rate distortion plot uh i the mean square sense you have in this is the the rate we use we used for encoding the spectrum and the distortion we get yeah a so a first thing you see here is that the worst the worst result to can possibly have is actually if you code each each channel independently okay so this would be this a a line a on the uh the outer line would be for a window size of one so that is equivalent to coding each microphone signal in the pen um but the interesting thing here is that if you look at if you take the fourier transform across the entire array you don't actually get the best results you get an need to results so this would be like be quite D correlating this or a signals wouldn't give you the the best result you see that the actual best results comes again for a a a window size uh of thirty two okay like like seen before so just by um just by changing the window size um you can get a much clear improvement uh compared to either called in each one individually or D correlating your a i and this point here you C is the um these the operating point of M P three um if we take into account the the um the average bit-rate uh we're not using psychoacoustics your and so from here to here you have a a about uh uh seven a factor of seven of compression so in conclusion i and still acoustics of the wave fields are discrete eyes and process as to the mission signal a short space time free analysis that like presented um improves the performance of sound field processing operations such a spatial filtering coding and these experiments with the with a case scenario they suggest that um have you a window that uh a complete complete in close as the entire rate it's not the best result nor is to have uh only one microphone is actually about the fourth of the length of your that's we have time for a few questions oh i i oh but before maybe form or um what that was a study um from by i swear that yeah you know i how how this a representation the domain um how it changes with sources a there's are five uh and here a trying you're oh condition you can uh uh say that well if the source yeah they i and you can i oh my for example the spectrum of a great a right and you you can um you a much right than uniform i can design so it it has an i yeah yeah i i okay that i i so nine the space so that would be if you if you if it trace the vertical profile L you one mike the signal you in one that's i alright right oh you mean i i i yeah so if you are a representation here a four dimensional i which which we can that here but of course there you mean need to consider it as and the non-separable space i right one know i you a right or not and efficient that oh right source so that makes sense to to use not separable the yeah yeah i'm not not aware of but we work with uh where i is from which uh_huh no we actually a um we we don't have of the the rate the actual reconstruction of the wave uh we just a which is go got to how to process it you know no we assume that is possible to reconstruct you know it's just not or not i just one in the samples of the old and and the interpolation space that's for the which also and or a no where actually the the purpose here is not to do beamforming is just a present uh no know tool that is visually appealing and it can be used for uh uh a design i feel there's uh very effective a what actually trying to compare it we beamforming algorithms or uh a source separation of you know we doesn't yeah there's a lot of analogy when the problem domain main at we it in the spatial domain or a time space to domain i just have shot question in the conclusion about the uh uh a optimal side of the we of is it's in and dependent particular i is you P now fact that in use scenario you yep new field source and a lot so she just for i could be funny uh where are and the right because that's where i a problem when one spectrum like i uh and you the question okay so on that that's that's that is gone