D: I guess Yep . I guess that 's it .
D: And , uh , th th that 's where I am right now .
D: So .
F: Oh . How about you , Carmen ?
E: Mmm . I 'm working with VTS .
E: Um , I do several experiment with the Spanish database first ,
E: only with VTS and nothing more .
E: Not VAD ,
E: no LDA ,
E: nothing more .
F: What what is VTS again ?
D: New E: Eh , Vectorial Taylor Series .
F: Oh , yes .
F: Right , right .
E: To remove the noise too .
F: I think I ask you that every single meeting ,
F: don't I ?
E: What ?
F: I ask you that question every meeting .
E: Yeah .
E: If Well B: So , that 'd be good from for analysis .
B: It 's good to have some , uh , cases of the same utterance at different different times .
F: Yeah .
F: " What is VTS ? "
B: Yeah .
E: VTS .
E: I 'm sor
E: Well , um , the question is that E: Well .
E: Remove some noise but not too much .
E: And when we put the m m the , em , VAD , the result is better .
E: And we put everything , the result is better ,
E: but it 's not better than the result that we have without VTS .
E: No , no .
B: I see .
B: So that @ @ <comment> given that you 're using the VAD also , the effect of the VTS is not so far E: Is not .
B: Do you How much of that do you think is due to just the particular implementation and how much you 're adjusting it ?
B: Or how much do you think is intrinsic to ?
E: Pfft . I don't know
E: because E: Hhh ,
C: Are you still using only the ten first frame for noise estimation
C: or ?
E: Uh , I do the experiment using only the f onl eh , to use on only one fair estimation of the noise .
C: Or i ?
C: Yeah .
C: Hmm .
E: And also I did some experiment , uh , doing , um , a lying estimation of the noise .
E: And , well , it 's a little bit better but not E: n
C: Maybe you have to standardize this thing also ,
C: noise estimation ,
C: because all the thing that you are testing use a different E: Mmm .
D: Mmm .
C: They all need some some noise noise spectra
E: No , I do that two t did two time .
C: but they use every all use a different one .
B: I have an idea .
B: If if , uh , uh ,
B: y you 're right .
B: I mean , each of these require this .
B: Um , given that we 're going to have for this test at least of uh , boundaries , what if initially we start off by using known sections of nonspeech for the estimation ?
E: Mm - hmm .
C: Mm - hmm .
B: Right ?
C: Yeah .
B: S so , e um ,
C: Mm - hmm .
B: first place , I mean even if ultimately we wouldn't be given the boundaries , uh , this would be a good initial experiment to separate out the effects of things .
B: I mean , how much is the poor  you know , relatively , uh , unhelpful result that you 're getting in this or this or this
B: is due to some inherent limitation to the method for these tasks
B: and how much of it is just due to the fact that you 're not accurately finding enough regions that that are really n noise ?
D: Mmm .
E: Mm - hmm .
C: Mm - hmm .
B: Um .
B: So maybe if you tested it using that , you 'd have more reliable stretches of nonspeech to do the estimation from
B: and see if that helps .
E: Yeah .
E: Another thing is the , em the codebook ,
E: the initial codebook .
E: That maybe ,
E: well , it 's too clean
E: and B: Mm - hmm .
E: Cuz it 's a E: I don't know .
E: The methods E: If you want , you c I can say something about the method .
B: Mm - hmm .
E: Yeah . In the E: Because it 's a little bit different of the other method .
E: Well , we have E: If this if this is the noise signal , <nonvocalsound> uh , in the log domain , we have something like this .
E: Now , we have something like this .
E: And the idea of these methods is to  n given a , um E: How do you say ?
E: I will read because it 's better for my English .
E: I i given
E: is the estimate of the PDF of the noise signal
E: when we have a , um , a statistic of the clean speech and an statistic of the noisy speech .
E: And the clean speech the statistic of the clean speech is from a codebook .
E: Mmm ? This is the idea .
E: Well , like , this relation is not linear .
E: The methods propose to develop this in a vectorial Taylor series approximation .
B: I I 'm actually just confused about the equations you have up there .
B: So , uh ,
B: the top equation is is is E: No , this in the it 's this is the log domain .
E: I I must to say that .
B: Which is which is the log domain ?
E: Is the T is egual <comment> is equal to , uh , log of B: And B: but Y is what ?
B: Y of the spectrum
E: Uh , this this is this
B: or ?
E: and this is this .
B: No , no .
B: The top Y is what ?
E: Mm - hmm .
B: Is that power spectrum ?
E: Uh , this is the noisy speech .
C: p s this B: No , is that power spectrum ?
B: Is it ?
C: Yeah . I guess it 's the power spectrum of noisy speech .
E: Yeah . It 's the power spectrum .
B: Oh , OK .
C: Yeah . And B: So that 's uh E: This is the noisy E: Yeah , it 's E: of the value B: OK .
B: Yeah ,
B: OK .
B: So this it 's the magnitude squared or something .
E: Yeah .
B: OK , so you have power spectrum added there
B: and down here you have  you you put the B: depends on T ,
E: w o
B: but b all of this is just you just mean E: Yeah . It 's the same .
B: you just mean the log of the of the one up above .
E: Yeah .
C: Mm - hmm .
B: And , uh , so that is X times ,
B: uh ,
E: Yeah , maybe D: One one plus N by X .
E: But , n
B: o
E: Well , y we can expre we can put this expression B: X times one plus , uh , N uh , N N N minus X ?
E: The E: Yeah .
B: And then ,
E: And the noise signal .
B: uh So that 's log of X plus log of one plus , uh B: Well .
B: Is that right ?
B: Log of D: One plus N by X .
E: Well , mmm B: I actually don't see how you get that .
E: Well , if we apply the log , we have E is n
B: Uh .
C: Mmm .
E: uh , log <nonvocalsound> E is equal , oh , to log of X plus N .
D: Uh , and B: Yeah .
E: And , well ,
D: And , log of E: uh , we can say that E <nonvocalsound> is equal to log of , <nonvocalsound> <nonvocalsound> um , exponential of X plus exponential of N .
B: Uh D: Mm - hmm .
B: No .
D: No .
B: That doesn't follow .
D: Well , if E restricts D: It is y
E: Well , this is this is in the ti the time domain .
E: Well , we have that ,
E: um E: We have first that , for example , X is equal ,
E: uh E: Well .
E: This is the frequency domain
E: and we can put u that n the log domain B: Yeah .
E: log of X omega ,
E: but , well , in the time domain we have an exponential .
E: No ?
E: No ?
E: Oh , maybe it 's I am E: I 'm problem .
B: Yeah .
B: I mean , just never mind what they are .
B: Uh , it 's just if X and N are variables B: Right ?
D: What is , uh ?
B: The the the log of X plus N is not the same as the log of E to the X plus E to the N .
E: Yeah .
E: But this i
E: Well , I don't E: Well , uh ,
B: Maybe we can take it off - line ,
E: maybe B: but I I don't know .
E: I I can do this incorrectly .
E: Well , the expression that appear in the in the paper , <nonvocalsound> is , uh D: The log D: the Taylor series expansion for log one plus N by X is E: is X C: Is it the first - order expansion ?
B: OK .
B: I i
D: Yeah , the first one .
C: Yeah , I guess .
D: Yeah .
D: Yeah .
B: OK .
C: Yeah .
B: Yeah . Cuz it doesn't just follow what 's there .
C: Uh - huh .
D: Y yeah . If if you take log X into log one plus N by X , and then expand the log one plus N by X into Taylor series B: It has to be some , uh , Taylor series C: Yeah .
E: Now , this is the E: and then C: Yeah , but the the second expression that you put is the first - order expansion of the nonlinear relation between E: Not exactly .
B: No .
E: No , no , no .
E: It 's not the first space .
E: Well , we have pfft , uh , em E: Well , we can put that X is equal I is equal to log of , uh ,
E: mmm B: That doesn't follow .
E: Well , we can put , uh , this ?
D: Mmm .
D: No .
B: That I mean , that the f top one does not imply the second one .
E: The top ?
B: Because cuz the log of a sum is not the same as th
E: Yeah , yeah , yeah , yeah , yeah .
B: I mean , as B: Yeah .
E: But we can E: uh , we we know that , for example , the log of E plus B is equal to log of E plus log to B .
B: Right .
E: And we can say here , it i
B: Right . So you could s
C: What is that ?
E: And we can , uh , put this inside .
B: Yeah .
E: And then we can ,
E: uh ,
E: you know B: N no ,
B: but E: Yeah .
D: Uh .
B: I don't see how you get the second expression from the top one .
B: The I mean , just more generally here , if you say " log of , um , A plus B " ,
B: the log of log of A plus B is not B: or A plus B is not the , um , log of E to the A plus E to the B .
E: No , no , no , no , no , no , no .
E: This not .
E: No .
B: Right ?
B: And that 's what you seem to be saying .
E: No .
E: It 's not . But this is the same E: oh .
B: Right ?
B: Cuz you cuz you up here you have the A plus B E: No .
E: I say if I apply log , I have , uh , log of E is equal to log of , uh in this side , is equal to log of X
B: Plus N .
E: plus N .
B: Right .
E: No ?
E: Right .
B: Right .
B: And then how do you go from there to the ?
E: This is right .
E: And then if I apply exponential , to have here E B: Look .
B: OK ,
B: so let 's B: I mean , C equals A plus B ,
C: It 's log o of capital Y .
C: Yeah , right .
B: and then E: Yeah .
C: Capital Y .
D: X . X .
D: This is X , inside .
C: Mm - hmm .
E: We have this ,
B: Right .
E: no ?
B: Yeah .
B: That one 's right .
E: Mm - hmm .
D: One and E: S uh , i th we can put here the set transformation .
B: Oh .
B: I see .
E: No ?
B: I see .
B: OK , I understand now .
B: Alright , thanks .
E: Yeah .
E: In this case , well , we can put here a <nonvocalsound> Y .
B: OK .
B: So , yeah .
B: It 's just by definition that the individual  that the , uh B: So , capital X is by definition the same as E to the little X
B: because she 's saying that the little X is is the , uh is the log .
B: Alright .
E: Now we can put this .
B: Yeah .
E: No ?
E: And here we can multiply by X .
B: Alright .
B: I think these things are a lot clearer when you can use fonts different fonts there
E: Oh , yes .
B: so you know which is which .
E: Yeah , yeah .
B: But I I under I understand what you mean now .
E: That 's true .
E: That 's true .
B: OK .
E: But this this is correct ?
B: Sure .
E: And now I can do it ,
E: uh E: pfff !
E: I can put log <nonvocalsound> of EX plus log B: Oh .
B: Yes . I understand now .
E: And this is B: And that 's where it comes from .
B: Yeah .
C: Yeah . Right .
B: Right .
E: Now it 's correct .
B: Right .
B: OK .
B: Thanks .
E: Well . The idea E: Well ,
E: we have fixed this equa
B: OK . So now once you get that that one , then you then you do a first or second - order , or something , Taylor series expansion of this .
E: Yeah .
E: This is another linear relation that this to develop this in vector s Taylor series .
C: Yeah , sure .
B: Right .
E: Mm - hmm .
E: And for that , well , the goal is to obtain , um   est estimate a PDF for the noisy speech
E: when we have a  a statistic for clean speech and for the noisy speech .
E: Mmm ?
E: And when w
E: the way to obtain the PDF for the noisy speech is E: well , we know this statistic
E: and we know the noisy st
E: well , we can apply first order of the vector st Taylor series of the of the of well , the order that we want , increase the complexity of the problem .
B: Mm - hmm .
E: And then when we have a expression , uh , for the mean and variance of the noisy speech , we apply a technique of minimum mean - square estimation
B: Mm - hmm .
E: to obtain the expected value of the clean speech given the this statistic for the noisy speech B: Mm - hmm .
E: the statistic for clean speech and the statistic of the noisy speech .
E: This only that .
E: But the idea is that C: And the the model of clean speech is a codebook . Right ?
E: u
E: Yeah .
E: We have our codebook with different density Gaussian .
B: Mm - hmm .
E: We can expre we can put that the PDF <comment> for the clean test , probability of the clean speech is equal to B: Yeah .
C: Mm - hmm .
B: So , um ,
B: how h
B: how much in in the work they reported , how much noisy speech did you need to get , uh , good enough statistics
B: for the to get this mapping ?
E: I don't know exactly .
B: Yeah .
E: I I need to s
B: Yeah .
E: I don't know exactly .
B: Cuz I think what 's certainly characteristic of a lot of the data in this test is that , um , you don't have  the B: the training set may not be a a great estimator for the noise in the test set .
B: Sometimes it is
B: and sometimes it 's not .
E: Yeah .
E: I the clean speech the codebook for clean speech , I am using TIMIT .
E: And I have now , uh , sixty - four <nonvocalsound> Gaus - Gaussian .
B: Uh - huh .
B: And what are you using for the noisy ?
B: Y y doing that strictly E: Of the noise E: I estimate the noises wi
E: Well , for the noises I only use one Gaussian .
B: Mm - hmm .
B: And and you and you train it up entirely from , uh , nonspeech sections in the test ?
C: Hmm .
E: Uh , yes .
E: The first experiment that I do it is solely to calculate the , mmm well , this value B: Yeah .
E: uh , the compensation of the dictionary o one time
E: using the the noise at the f beginning of the sentence .
E: This is the first experiment .
B: Mm - hmm .
B: Yeah .
E: And I fix this for all the all the sentences .
E: Uh , because E: well , the VTS methods E: In fact the first thing that I do is to to obtain , uh , an expression for E E: probability e expression of of E .
E: That mean that the VTS mmm , with the VTS we obtain ,
E: uh E: well , we we obtain the means for each Gaussian <comment> and the variance .
B: Mm - hmm .
E: This is one .
E: Eh , this is the composition of the dictionary .
B: Mm - hmm .
E: This one thing .
E: And the other thing that this with these methods is to , uh , obtain to calculate this value .
B: Mm - hmm .
E: Because we can write E: uh , we can write that the estimation of the clean speech is equal at an expected value of the clean speech conditional to , uh , the noise signal  the probability f of the the statistic of the clean speech and the statistic of the noise .
B: Mm - hmm .
B: Mm - hmm .
E: This is the methods that say that we 're going obtain this .
B: Mm - hmm .
E: And we can put that this is equal to the estimated value of E minus a function that conditional to E to the T to the noise signal .
E: Well , this is this function is the the term after develop this , the term that we we take .
E: Give PX and , uh , P the noise .
D: X K C noise .
B: Mmm .
E: And I can put that this is equal to the noise signal minus E: Well , I put before this name ,
E: uh E: And I can calculate this .
B: What is the first variable in that probability ?
E: Uh , this is the Gaussian .
B: No , no . I 'm sorry .
B: In in the one you pointed at .
E: v
B: What 's that variable ?
E: Uh , this is the D: Weak .
D: So probably it it would do that .
E: like this ,
C: It 's one mixture of the model . Right ?
E: but conditional .
E: No , it 's condition
E: it 's not exactly this .
E: It 's modify .
E: Uh , if we have clean speech we have the dictionary for the clean speech , we have a probability f of our our weight for each Gaussian .
E: No .
E: And now , this weight is different now
B: OK .
B: Yes .
E: because it 's conditional .
E: And this I need to to calcu
E: I know this
B: Uh - huh .
E: and I know this
E: because this is from the dictionary that you have .
B: Uh - huh .
E: I need to calculate this .
E: And for calculate this , I have an I I can develop an expression that is
B: Yes .
D: It 's overlapping .
E: that .
E: I can calculate I can I calculated this value , uh , with the statistic of the noisy speech that I calculated before with the VTS approximation .
B: Mm - hmm .
E: And well , normalizing .
E: And I know everything .
E: Uh , with the ,
E: nnn E: when I develop this in s Taylor Taylor series , I can't , um , calculate the mean and the variance of the for each of the Gaussian of the dictionary for the noisy speech .
E: Now .
E: And this is fixed .
B: Mm - hmm .
E: If I never do an estimat a newer estimation of the noise , this mean as mean and the variance are fixed .
B: Mm - hmm .
E: And for each s uh , frame of the speech the only thing that I need to do is to calculate this