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This Letter deals with a practical signal processing problem where the filter is zero‐phase and is specified by the frequency response. The authors show that if the signal is symmetrically extended, then the fast Fourier transform (FFT)‐based algorithm can be efficiently implemented by using the discrete cosine transform without signal extension. They extend the proposed algorithm to 2D filters and show that computationally it is at least four times more efficient than the FFT‐based algorithm. A practical application of the new algorithm is a fast Wiener inverse filter, which is used to estimate images taken under the condition of air turbulence. [ABSTRACT FROM AUTHOR]

We describe four novel algorithms, , and , which compute the Boltzmann partition function for global structural constraints-respectively for the number of hairpins, the number of multiloops, maximum order (or depth) of multiloops, and the simultaneous number of hairpins and multiloops. Given an RNA sequence of length n and a user-specified integer 0 ≤ K ≤ n, (resp. and ) computes the partition functions Z( k) for each 0 ≤ k ≤ K in time O( K2 n3) and space O( Kn2), while computes the partition functions Z( m, h) for 0 ≤ mm ≤ M multiloops and 0 ≤ h ≤ H hairpins, with run time O( M2 H2 n3) and space O( MHn2). In addition, programs such as (resp. ) sample from the low-energy ensemble of structures having h hairpins (resp. m multiloops and h hairpins), for given h, m. Moreover, by using the fast Fourier transform (FFT), and have been improved to run in time O( n4) and space O( n2), although this improvement is not possible for . We present two applications of the novel algorithms. First, we show that for many Rfam families of RNA, structures sampled from are more accurate than the minimum free-energy structure; for instance, sensitivity improves by almost 24% for transfer RNA, while for certain ribozyme families, there is an improvement of around 5%. Second, we show that the probabilities p( k)= Z( k) /Z of forming k hairpins (resp. multiloops) provide discriminating novel features for a support vector machine or relevance vector machine binary classifier for Rfam families of RNA. Our data suggests that multiloop order does not provide any significant discriminatory power over that of hairpin and multiloop number, and since these probabilities can be efficiently computed using the FFT, hairpin and multiloop formation probabilities could be added to other features in existent noncoding RNA gene finders. Our programs, written in C/C++, are publicly available online at: . [ABSTRACT FROM AUTHOR]

Data mining algorithms and statistical methods are applied to analyze the jerk data obtained from monitoring the gearbox of a wind turbine. Two types of analyses are performed—failure component identification and monitoring vibration excitement. In failure component identification, the failed stages of the gearbox are identified in time-domain analysis and frequency-domain analysis. In the time domain, correlation coefficient and clustering analysis are applied. The fast Fourier transformation with time windows is utilized to analyze the frequency data. To monitor the vibration excitement of the gearbox in its high-speed stage, data mining algorithms and statistical quality control theory are combined to develop a monitoring model. The capability of the monitoring model to detect changes in the gearbox vibration excitement is validated by the collected data. [ABSTRACT FROM PUBLISHER]

The relationship between the electro-encephalographic (EEG) alpha and beta oscillations in the resting condition was investigated in the study. EEGs were recorded in 33 subjects, and alpha (7.5-12.5 Hz) and beta (15-25 Hz) oscillations were extracted with the use of a modified wavelet transform. Power, peak frequency and phase synchronisation were evaluated for both types of oscillation. The average beta-alpha peak frequency ratio was about 1.9-2.0 for all electrode derivations. The peak frequency of beta activity was within 70-90 % of the 95 % confidence interval of twice the alpha frequency. A significant (p < 0.05) linear regression was found between beta and alpha power in all derivations in 32 subjects, with the slope of the regression line being approximately 0.3. There was no significant difference in the slope of the line in different electrode locations, although the power correlation was strongest in the occipital locations where alpha and beta oscillations had the largest power. A significant 1:2 phase synchronisation was present between the alpha and beta oscillations, with a phase lag of about pi/2 in all electrode derivations. The strong frequency relationship between the resting beta and alpha oscillations suggests that they are generated by a common mechanism. Power and phase relationships were weaker, suggesting that these properties can be modulated by additional mechanisms as well as be influenced by noise. A careful distinction between alpha-dependent and alpha-independent beta activity should be considered when making statements about the possible significance of genuine beta activity in different neurophysiological mechanisms. [ABSTRACT FROM AUTHOR]

We develop a new algorithm for the fast computation of matrix–vector products with special matrices. More precisely we develop a method for the fast computation of sums f(yj):= ∑k=1NαkK(yj-xk) at non-equispaced nodes xk and yj (j=1,...,M) which requires only &Oscr;(N log N + (M + N)) arithmetic operations. Our algorithm is based on a novel approach to fast discrete trigonometric transforms at non-equispaced nodes. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]