0:00:13"'kay" thank you all for coming
0:00:14um my talks about applications of short space time for analysis
0:00:18in digital acoustics
0:00:20john to work uh with mark actually
0:00:24so what is digital still acoustics
0:00:26so what we call the field of a dimensional a a signal processing
0:00:31that involve
0:00:32a a sampling and reconstructing the weight
0:00:35uh a typical using
0:00:37uh a of microphones and well course
0:00:41so these are race they act
0:00:43as a a a a D computers
0:00:44and the egg cover
0:00:46respect of
0:00:47so it means that
0:00:49uh i after sampling between we have
0:00:51a matrix
0:00:52of a samples
0:00:54of course
0:00:55a temporal and spatial samples
0:00:57that we can process using
0:00:58two S P
0:01:00and my michael
0:01:04oh
0:01:05cool
0:01:09um so for example
0:01:11if there's a source
0:01:12um
0:01:13in the acoustic scene
0:01:15that we want to get rid of we could apply to the mission filter
0:01:18and uh we could get rid of this source and have only the one that manners
0:01:23oh we could for example
0:01:25and these are to to applications gonna talk about
0:01:27um
0:01:29a in coal
0:01:30the information that is sampled with your array of microphones
0:01:33and all star it in an i pod for example
0:01:35so then later we can reconstruct it with
0:01:38a a for example way feel to
0:01:41um but sort order this kind of um processing to the mission signal processing we need
0:01:47to mission signal processing tools
0:01:50and the first to i want to talk about is the spatial temporal free a transform
0:01:55and this involves taking the if transform across
0:01:58you're right X
0:02:00so
0:02:01why would you want to do this
0:02:03well essentially actually
0:02:05uh the wave equation tells us that
0:02:07um
0:02:08if the way feel this harmonic in time
0:02:10then necessarily certainly it's harmonic in space
0:02:12so there's a the here and the fourier transform a
0:02:15a the array access use went to exploit this
0:02:17how it in space
0:02:20for example if
0:02:21if you contrast a bit uh looking at each microphone individually
0:02:25i this case you have three sources
0:02:27i it's not very clear
0:02:29uh where the information from each source is going to appear so
0:02:33um all this doesn't give you a clear visual impression of what is it "'cause" sixteen
0:02:38what is if you take the free transform across and
0:02:41not all these three sources
0:02:43are nice place
0:02:44in this uh
0:02:45a two dimensional frequency domain in one acts you have the regular frequency
0:02:50um to improve frequency
0:02:52and any the other acts you have the spatial frequency
0:02:54or the wave number
0:02:57and you see that um
0:03:00the displacement of source uh with respect to to the every X is going to place
0:03:06um
0:03:07this lines where all the energies constant
0:03:11uh so for example we can even complicated bit more if there's a source like can schools or to your
0:03:16rate
0:03:17you also see a nice pat an where where these lines open up as a triangle so we're gonna see
0:03:21more detail
0:03:22what is mean
0:03:24um and so for example in this situation
0:03:27oh where have two sources that matter and you have this
0:03:30this two in the far field
0:03:32and you have this near field in the for we wanna
0:03:34uh i get rid of
0:03:36uh
0:03:37it is very clear what we have to do here
0:03:39uh we the play field they're that to get rid of these components
0:03:43so in the end
0:03:43we'll have a the two components that my
0:03:48so for for doing this kind of uh applications we need to understand
0:03:53um
0:03:54one simple scenario which is the the point source in there
0:03:58so what happens the spectral representation when you have a point source this you
0:04:03oh a this point sources
0:04:04i is a driven can by uh a signal S of T
0:04:07and the angle with respect to X is this off X
0:04:10i has a minimum angle and i some angle depends on the length of the right
0:04:14and if you look at to to the mission spectrum
0:04:17you actually see that
0:04:18um
0:04:19the special pattern is uh this trying to region
0:04:22with a few ripples on the outside
0:04:25um
0:04:26so this trying to region
0:04:28is the limited by the by the cosine sign of the two angles
0:04:32"'cause" of these two angles
0:04:34a a a completely define what is the aperture of this trying to reach
0:04:38and the ripples on the outside
0:04:40which come from the effect from doing
0:04:42so the thing function fact
0:04:44they're oriented toward
0:04:45the continuous average
0:04:47uh of the angle of course
0:04:49the the entire
0:04:51so not one the the whole mathematical michael expression because the be dense
0:04:56uh but i'm gonna tell you that's
0:04:58um this is actually means
0:05:00um
0:05:01that you have
0:05:03is the free transform of the source signal
0:05:06but multiplied
0:05:07by a combination of max operation
0:05:10of the sinc function E fact caused by window
0:05:13and this trying the region
0:05:15that depends on the distance
0:05:16of the source
0:05:18you're right
0:05:19and this represents presents are information and this one presents a spatial information so there set
0:05:26and so using this result how how could we uh for example filter to source
0:05:30in the way feel
0:05:32so
0:05:32we all have to go where the energy
0:05:34we have to define a filter
0:05:37that takes
0:05:38um at this trying to that preserved this trying to the region
0:05:42a where all the energies contain
0:05:44and um this all the rest
0:05:47so this would be like as a simple two dimensional filter design problem
0:05:50okay so you define what are
0:05:53defined where of the transition region
0:05:56um you could be fine if it's linear phase are you can find the
0:06:00the bandpass ripples and the
0:06:02um
0:06:03the best top people's
0:06:06and then you could use a to design technique
0:06:08uh i two dimensions
0:06:09uh to obtain the realizable filter
0:06:12oh these are a few examples
0:06:14for example using the win me method or the
0:06:16part some
0:06:18um
0:06:20but that is very easy one you have only one source
0:06:23so what happens when you have more than one or
0:06:27don't have as as the following it's
0:06:28each source
0:06:30uh each point source
0:06:31has uh what a called this chat the reason behind it
0:06:35uh that if if it's going to overlap
0:06:37with
0:06:37the shot a region of another source
0:06:40that here
0:06:41for sure you gonna have spectral overlapping
0:06:43okay so this these two trying to regions
0:06:45um which chris want which source
0:06:48i want to overlap in just something
0:06:49and so with menu filtering you cannot for you uh week cover
0:06:53um
0:06:54uh each source
0:06:56the one thing you can do to to read this problem
0:06:59is we split up there are the array into
0:07:01um
0:07:02equal parts
0:07:04and then we're gonna see that
0:07:05for example and the left block
0:07:07the shall a reason is
0:07:08he's reduce for the two sources
0:07:10i don't what we're gonna have
0:07:11much less overlapping
0:07:13in this in the spectral domain
0:07:14and the same thing gonna happen for
0:07:17the block on the right
0:07:20and so you can do this um you can keep uh dividing
0:07:24you're a into smaller parts
0:07:26and you gonna see that's the these trying to reason is gonna get smaller and smaller
0:07:30row the other hand you wanna have
0:07:32uh other if effect
0:07:34are harmful which for example if you reduced to mean the size
0:07:38you're gonna have a much more sing function effects so there's a balance
0:07:41um there's like a limit
0:07:43uh
0:07:44a limited number of times
0:07:46that you can divide you can split up to three
0:07:48i and smaller parts
0:07:50so you might have
0:07:50you might have already noticed that
0:07:52this is
0:07:53analogous to a short time fourier transform
0:07:55except you're doing it in
0:07:58a to do this
0:07:59um in in this space and time
0:08:02uh it's essentially you can do it essentially with a a a a dimensional
0:08:05uh filter bank
0:08:06oh which implements a a a a a lapped transform
0:08:11so it's the in this example for you have us
0:08:13a source and a new field
0:08:15a be closer to the right near rate
0:08:17and you see that you have
0:08:18a a lot more curvature
0:08:20in the space time representation
0:08:22you have a lot more curvature in a region that is close to the source
0:08:27um so of course is the filter bank is but reconstruction than the input is gonna be the same as
0:08:32the output
0:08:32and in the middle you see the the actual composition
0:08:36you have a in one direction you have the the special blocks
0:08:40and in the vertical axis you have the temporal blocks
0:08:42if you look close or
0:08:44to the spatial uh the dimension
0:08:46you see that
0:08:47a for each of these blocks
0:08:49this trying to reason is much more narrow
0:08:52and it to fall O uh the location of the source
0:08:56okay
0:08:56as the as a block was close or two
0:08:59to word the source
0:09:03um here's one example this is one issue in the paper
0:09:06um
0:09:07it's a it's a it's a nice worst case scenario
0:09:11oh where and you for source
0:09:13is cool line with a with a far source of the far for source actually
0:09:17with respect to the rate is behind the near field source
0:09:20and you can see the spectra representation that
0:09:23the far field source completely immersive
0:09:25um in the spectrum of of the new
0:09:29so if we do this decomposition
0:09:31uh let's see one iteration you have
0:09:34you you start seeing that the the new two source
0:09:37yeah the sure of the trying to gets reduced
0:09:40so they start getting separate
0:09:42and you can do a with a larger when the size
0:09:45um and then in the end if you want to filter to one of those
0:09:49um
0:09:51you apply it to each of the blocks able apply filter
0:09:55that's isolates
0:09:56source
0:09:58so this is a a a result the one we we got um
0:10:02the best results in the mean sense
0:10:04was for uh
0:10:05a window size of thirty two
0:10:07K and you can see that
0:10:09in the space time representation
0:10:10there's a there's a source in the new field
0:10:12mixed up with one in the far field
0:10:14and here to get this if you string to get clues
0:10:19a the second application wanna to talk about this
0:10:22coding
0:10:23so how do we code
0:10:24the wave field in this domain
0:10:26uh the structure we use
0:10:28is is very similar to what's
0:10:30um state of art you call there's to let's say in P three or a C
0:10:35so you actually take it to my mission filter bank
0:10:37um
0:10:39that is the the fourier transform across cross
0:10:41time and space
0:10:44and then in this domain
0:10:45you're going to
0:10:46quantise code
0:10:48um
0:10:49all this uh coefficients
0:10:51so this is the bit allocation problem
0:10:54and that for comparing the results
0:10:55uh we do the inverse uh
0:10:57feel the the inverse quantization and then
0:11:00comparing the mean scores
0:11:03um
0:11:05and so if you look at our of worst case scenario
0:11:09uh we see that
0:11:10so this is this is the plots
0:11:12uh the rate distortion plot
0:11:14uh i the mean square sense
0:11:16you have in this is the the rate we use we used for
0:11:19encoding the spectrum and the distortion
0:11:21we get
0:11:22yeah
0:11:25a so a first thing you see here
0:11:27is that
0:11:28the worst
0:11:28the worst result to can possibly have
0:11:31is actually if you code each each channel independently
0:11:35okay so this would be
0:11:36this
0:11:37a a line a on the uh the outer line would be
0:11:40for a window size of one
0:11:41so that is equivalent to coding each microphone signal in the pen
0:11:46um but
0:11:48the interesting thing here is that
0:11:51if you look at
0:11:52if you take the fourier transform across the entire array
0:11:55you don't actually get the best results
0:11:57you get an need to results so this would be like
0:12:00be quite D correlating this
0:12:01or a signals
0:12:03wouldn't give you the the best result
0:12:05you see that the actual best results
0:12:07comes again for a a a window size
0:12:10uh of thirty two
0:12:11okay like like seen before
0:12:14so just by um
0:12:16just by changing the window size
0:12:18um you can get a much clear improvement
0:12:21uh compared to either called in each one individually or D correlating your a
0:12:26i
0:12:26and this point here you C is the um these the operating point of M P three
0:12:31um if we take into account the the um
0:12:34the average bit-rate
0:12:36uh we're not using psychoacoustics your
0:12:38and so from here to here
0:12:40you have a a about uh uh seven
0:12:43a factor of seven of compression
0:12:48so in conclusion i and still acoustics of the wave fields are discrete eyes and process
0:12:53as to the mission signal
0:12:55a short space time free analysis that like presented
0:12:58um
0:12:59improves the performance of sound field processing operations
0:13:02such a spatial filtering coding
0:13:05and these experiments with the with a case scenario they suggest that
0:13:09um
0:13:10have you a window that
0:13:12uh a complete complete in close as the entire rate
0:13:15it's not the best result nor is to have uh
0:13:18only one microphone
0:13:20is actually about the fourth
0:13:21of the length of your
0:13:23that's
0:13:30we have time for a few questions
0:13:39oh
0:13:41i
0:13:45i
0:13:47oh
0:14:04but before
0:14:05maybe form or
0:14:17um
0:14:18what that was a study um
0:14:21from by i swear
0:14:23that
0:14:23yeah you know i how how this a representation
0:14:27the domain
0:14:28um
0:14:29how it changes with sources
0:14:31a there's are five
0:14:34uh
0:14:36and
0:14:36here
0:14:37a
0:14:38trying
0:14:40you're
0:14:41oh condition
0:14:42you can uh
0:14:45uh
0:14:46say that
0:14:47well if the source
0:14:48yeah
0:14:49they
0:14:51i
0:14:52and you can
0:14:53i
0:14:54oh my for example the spectrum
0:14:56of
0:14:57a
0:15:01great
0:15:03a
0:15:04right
0:15:05and
0:15:06you
0:15:09you can
0:15:10um you a much right than
0:15:11uniform
0:15:13i
0:15:14can design
0:15:16so
0:15:17it it has an
0:15:23i
0:15:24yeah
0:15:26yeah
0:15:40i
0:15:41i
0:15:43okay that i
0:15:46i
0:15:50so nine
0:15:51the space so that would be if you if you if it trace the vertical profile L you one mike
0:15:56the signal you in one
0:15:59that's
0:16:01i
0:16:07alright right oh you mean i
0:16:10i
0:16:11i
0:16:12yeah
0:16:13so if you are a representation here
0:16:16a four dimensional
0:16:18i
0:16:20which which we can that here but
0:16:21of course there
0:16:28you mean need to consider it as and the non-separable space
0:16:31i
0:16:33right
0:16:34one know i
0:16:36you
0:16:38a
0:16:38right
0:16:39or not
0:16:40and efficient that
0:16:43oh
0:16:43right
0:16:44source
0:16:45so that makes sense to to use not separable
0:16:51the
0:16:58yeah yeah
0:17:00i'm not not aware of but we work with uh
0:17:03where i is from which
0:17:12uh_huh
0:17:19no we actually a um
0:17:22we we don't have of the the rate the actual reconstruction
0:17:25of the wave
0:17:26uh we just a which is go got to how to process it you know
0:17:34no we assume that is possible to reconstruct
0:17:37you know it's just
0:17:39not or not
0:17:39i just one in the samples of the old
0:17:41and and the interpolation space
0:17:43that's for the which also
0:17:45and
0:17:45or a
0:18:08no where
0:18:08actually the the purpose here is not to do beamforming is just a present
0:18:12uh
0:18:13no know tool that is
0:18:15visually appealing and it can be used for uh
0:18:18uh a design
0:18:20i feel there's
0:18:21uh
0:18:21very effective
0:18:22a what actually trying to compare it we
0:18:24beamforming algorithms or
0:18:27uh a source separation of
0:18:29you know we doesn't yeah there's a lot of analogy
0:18:33when
0:18:34the problem
0:18:35domain main at we it in the spatial domain or
0:18:38a time space to domain
0:18:44i just have shot question
0:18:46in the conclusion about the uh uh a optimal side
0:18:50of the we of is it's in and dependent
0:18:52particular i is you P now fact that
0:18:55in use scenario you yep
0:18:57new field source and a lot so she just for
0:19:00i could be funny uh where
0:19:02are
0:19:03and the
0:19:05right
0:19:06because that's where
0:19:07i
0:19:08a problem when
0:19:09one spectrum
0:19:12like
0:19:13i
0:19:13uh
0:19:17and you the question
0:19:20okay so on that
0:19:21that's that's that is gone