search for: b_k

...sum = 0; for( int k = 0; k < 2*N; k++ ) { sum += in[k]*cos(M_PI*(2*j+1+N)*(2*k+1)/8/N); } out[j] = sum; } } > It just a normal shifted mdct, like the one used in mpeg layer 3. > it's equations are: > (time domain: a_j, freq domain: b_k; w_j is the window) > forward: > b_k = sum(j=0..4N-1) a_j * w_j * cos( (2k+1)(2j+1+-N) / 8N ) // forward > a_j = w_j * sum(k=0..2N-1) a_j * cos( (2k+1)(2j+1+-N) / 8N ) // backward (missing PI in the cos, and a_j should be b_k in summation) > where +- means: I'm not sure whether it...

Hello, I was wondering if someone knows the formula used by the function lm to compute the t-values. I am trying to implement a linear regression myself. Assuming that I have K variables, and N observations, the formula I am using is: For the k-th variable, t-value= b_k/sigma_k With b_k is the coefficient for the k-th variable, and sigma_k =(t(x) x )^(-1) _kk is its standard deviation. I find sigma_k = sigma * n/(n*Sum x_{k,i}^2 -(sum x_{k,i}^2)) With sigma: the estimated standard deviation of the residuals, Sigma = sqrt(1/(N-K-1)*Sum epsilon_i^2) Wit...

...I'm to lazy to do it (and besides, I don't have access to TeX, X, or anything else from a text terminal with gcc and vi right now). Hope you like it, Segher -- Suppose we want to calculate a MDCT (encode side): (x_ is input (time) samples, w_ is window, b_ is output (freq) samples): b_k = \sum_{j=0}^{4N-1} x_j w_j \cos{(2k+1)(2j+1-2N) \over 8N} \pi After setting a_j := w_{-j-1+N} x{-j-1+N} + w_{j+N} x{j+N}, j < N a_j := w_{j-1-N} x{j-1-N} - w_{j+3N} x{j+3N}, otherwise (or something similar; the cos'es should agree) we get b_k = \sum_{j=0}^{2N-1} a_j \cos{(2k+1)(2j+...

...olf at math.unb.ca rather than via this list. My question is essentially about Fourier coefficients: Suppose pi / 2*pi*a_k = | f(omega)*exp(-i*k*omega) d omega / -pi and pi / 2*pi*b_k = | G(omega)*f(omega)*exp(-i*k*omega) d omega / -pi (The ``*''-s just mean multiplication here, not convolution; i is of course sqrt(-1).) The function f() is positive and symmetric about 0 (it's actually a spectral density function) and G() is the...

...lity, leading to lost log data. Now, as I see it, rsync would be a useful tool for this job, except that it would mean that we end up scanning a large file on both servers every 10 minutes. I've played around on paper and come up with a reversed version of the rolling checksum (i.e. given a_k, b_k calculate a_k-1 and b_k-1). The idea is that I calculate the checksum of the final block of the log on the loghost and pass that to the remote host. A program there starts reading backwards through the logfile, until it finds a checksum match. It then feeds back everything in the file after that po...

Is there a weighted median function out there similar to weighted.mean() but for medians? If not, I'll try implement or port it myself. The need for a weighted median came from the following optimization problem: x* = arg_x min (a|x| + sum_{k=1}^n |x - b_k|) where a : is a *positive* real scalar x : is a real scalar n : is an integer b_k: are negative and positive scalars which is a "median with a shift towards zero". This can be rewritten as x* = arg_x min (sum_{k=0}^n w_k|x - b_k|) where w = (a, 1, 1, ..., 1) and b_0 =...

...tially a sum over the volume at each p. When the individual models are computed, coefficients should be chosen so that this is satisfied. How to do this in R? Without the coupling the least-squares formulation would seek coefficients a_p and b_p to minimize: sum_p(sum_p((s_id,p - a_p t_id,p + b_k)^2)). Minimization at each p is independent. With coupling, there would be an additional term: sum_id((sum_p(vp)-h_id)^2) where vp is a function of a_p t_id,p + b_k and of t_id. The functions for vp are nonlinear, but if necessary with some work it should be possible to get a linear function t...

Dear readers, Is it possible to specify a model y=X %*% beta + Z %*% b ; b=(b_1,..,b_k) and b_i~N(0,v^2) for i=1,..,k that is, a model where the random slopes for different covariates are i.i.d., in lmer() and how? In lme() one needs a constant grouping factor (e.g.: all=rep(1,n)) and would then specify: lme(fixed= y~X, random= list(all=pdIdent(~Z-1)) ) , that?s how it's done i...

Hi I Have a very large dataset that I would like to conduct ANOVA tests on. Im not a very strong programmer so any help would be appreciated. the format is Identifier             A1       A2        B1      B2       C1   C2      Norm1         Norm2 1234                  1        1            NA     NA      4       3        NA               NA 4567                  2        2              4     

...ally (below, i = 1 to N) does rsync --backup-dir=a_<i> work -> archive and rsync --compare-dest=archive work -> b_<i> Then suppose one wants to recover the work directory as it was at time k. Using the b_<i> directories, one would merely merge b_k with the archive directory. But using the a_<i> directories one would have to merge a_<j> with archive starting with j=N and going down sequentially to j=k. Is my understanding correct? More importantly, I would like to know under what conditions and for what goals people u...

Hi, Can someone tell me which MDCT and invMDCT equation uses? I implemented the invMDCT one given in eusipco.corrected.ps file (handed out by Monty way back) and it produces different time domain samples. I tried both the FFT method and the slow way directly from the equation and couldn't reproduce the results from the original code. This leads me to believe that the forward MDCT used in

...cite transformation of the dependent. Below some details. I'm not very familiar with the concept. As far as I have understood it's all about transformation of the dependent variable if one have frequency data (grouped data, instead of raw binaries): ln(^p(i)/(1-^p(i)) = c + b_1(X_1) +...+ b_k(X_k) + e(i). where ^p(i) is (estimated) frequency of incident (happened/all = n(i)/N), i is index of observation, c and b_. are coefficients (objects of the estimation), X_. are the explanatory variables and e is residual. So a linear regression. And some testing: > y <- runif(100) >...

...the input file: -------------------------------------------- With \eqn{J} possible outcomes and \eqn{p_j}{p(j)} the probability of the \eqn{j}'th outcome, the formula is \deqn{\newcommand{\B}{{\bf \beta}}\newcommand{\X}{{\bf X}} p_j = \frac{e^{\X\B_j}}{\displaystyle\sum_{k=0}^J e^{\X\B_k}}.}{ p(j) = exp[X*b(j)]/sum{exp[X*b(k)], k=0 to J}.} \eqn{{\bf\beta}_j}{b(j)} is the vector of coefficients for outcome \eqn{j} and \eqn{{\bf X}}{X} are the covariates. -------------------------------------------- By the way, the \newcommand is not global, so I can't use \B (for examp...

...lation of the standard errors or provide code that explains the inner workings of this function. Thanks! Example of the model I am running: model1<- gls(Y~ X1I + X2 + X3 + X4, data=Dat1, correlation = corAR1(), method = "ML") My understanding of model errors: Y = b_0 + X1 b_1+ ...Xk b_k + Z Z_t =phi Z_{t-1) + e_t The residuals reported by GLS are the Z's, while the white noise terms are the e's. I cannot replicate the reported residuals using this approach. I also do not know how Z_0 should be calculated, i.e. what does the first step of this recursive procedure look like...

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