scholarly journals Splitting of Framelets and Framelet Packets

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 697
Author(s):  
Zhihua Zhang

Due to resilience to background noise, stability of sparse reconstruction, and ability to capture local time-frequency information, the frame theory is becoming a dynamic forefront topic in data science. In this study, we overcome the disadvantages in the construction of traditional framelet packets derived by frame multiresolution analysis and square iterative matrices. We propose two novel approaches: One is to directly split known framelets again and again; the other approach is based on a generalized scaling function whose shifts are not a frame of some space. In these two approaches, the iterative matrices used are not square and the number of rows in the iterative matrix can be any integer number.

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1050
Author(s):  
Zhihua Zhang

Framelets have been widely used in narrowband signal processing, data analysis, and sampling theory, due to their resilience to background noise, stability of sparse reconstruction, and ability to capture local time-frequency information. The well-known approach to construct framelets with useful properties is through frame multiresolution analysis (FMRA). In this article, we characterize the frequency domain of bandlimited FMRAs: there exists a bandlimited FMRA with the support of frequency domain G if and only if G satisfies G⊂2G, ⋃m2mG≅Rd, and G\G2⋂G2+2πν≅∅(ν∈Zd).


2017 ◽  
Author(s):  
Amelia McNamara ◽  
Nicholas J Horton

Data wrangling is a critical foundation of data science, and wrangling of categorical data is an important component of this process. However, categorical data can introduce unique issues in data wrangling, particularly in real-world settings with collaborators and periodically-updated dynamic data. This paper discusses common problems arising from categorical variable transformations in R, demonstrates the use of factors, and suggests approaches to address data wrangling challenges. For each problem, we present at least two strategies for management, one in base R and the other from the ‘tidyverse.’ We consider several motivating examples, suggest defensive coding strategies, and outline principles for data wrangling to help ensure data quality and sound analysis.


2014 ◽  
Vol 945-949 ◽  
pp. 1112-1115
Author(s):  
Yuan Zhou ◽  
Bin Chen ◽  
Bao Cheng Gao ◽  
Si Jie Zhang

For the variable speed estimation of wheel-bearings in strong background noise, a novel method with the short-time Fourier transform and BP neural network (STFT-BPNN) is proposed. In the method, it calculates the time-frequency spectrum with STFT technique. Then the instantaneous frequency is estimated by peak detection. Taking the instantaneous frequencies as the input vectors, the BP neural network is trained to fit the discrete instantaneous frequencies. The effectiveness of proposed method is demonstrated by simulation. Experimental results show that proposed method provides better performance on variable speed estimation for wheel-bearings.


Author(s):  
C. Philip Beaman

The modern world is noisy. Streets are cacophonies of traffic noise; homes and workplaces are replete with bleeping timers, announcements, and alarms. Everywhere there is the sound of human speech—from the casual chatter of strangers and the unwanted intrusion from electronic devices through to the conversations with friends and loved ones one may actually wish to hear. Unlike vision, it is not possible simply to “close our ears” and shut out the auditory world and nor, in many cases, is it desirable. On the one hand, soft background music or environmental sounds, such as birdsong or the noise of waves against the beach, is often comfortingly pleasurable or reassuring. On the other, alarms are usually auditory for a reason. Nevertheless, people somehow have to identify, from among the babble that surrounds them, the sounds and speech of interest and importance and to follow the thread of a chosen speaker in a crowded auditory environment. Additionally, irrelevant or unwanted chatter or other background noise should not hinder concentration on matters of greater interest or importance—students should ideally be able to study effectively despite noisy classrooms or university halls while still being open to the possibility of important interruptions from elsewhere. The scientific study of auditory attention has been driven by such practical problems: how people somehow manage to select the most interesting or most relevant speaker from the competing auditory demands made by the speech of others or isolate the music of the band from the chatter of the nightclub. In parallel, the causes of auditory distraction—and how to try to avoid it where necessary—have also been subject to scrutiny. A complete theory of auditory attention must account for the mechanisms by which selective attention is achieved, the causes of auditory distraction, and the reasons why individuals might differ in their ability in both cases.


2020 ◽  
Author(s):  
Saeed Nosratabadi ◽  
Amir Mosavi ◽  
Puhong Duan ◽  
Pedram Ghamisi ◽  
Filip Ferdinand ◽  
...  

Abstract This paper provides the state of the art of data science in economics. Through a novel taxonomy of applications and methods advances in data science are investigated. The data science advances are investigated in three individual classes of deep learning models, ensemble models, and hybrid models. Application domains include stock market, marketing, E-commerce, corporate banking, and cryptocurrency. Prisma method, a systematic literature review methodology is used to ensure the quality of the survey. The findings revealed that the trends are on advancement of hybrid models as more than 51% of the reviewed articles applied hybrid model. On the other hand, it is found that based on the RMSE accuracy metric, hybrid models had higher prediction accuracy than other algorithms. While it is expected the trends go toward the advancements of deep learning models.


Author(s):  
Judith Justin ◽  
Vanithamani R.

In this chapter, a speech enhancement technique is implemented using a neuro-fuzzy classifier. Noisy speech sentences from NOIZEUS and AURORA databases are taken for the study. Feature extraction is implemented through modifications in amplitude magnitude spectrograms. A four class neuro-fuzzy classifier splits the noisy speech samples into noise-only part, signal only part, more noise-less signal part, and more signal-less noise part of the time-frequency units. Appropriate weights are applied in the enhancement phase. The enhanced speech sentence is evaluated using objective measures. An analysis of the performance of the Neuro-Fuzzy 4 (NF 4) classifier is done. A comparison of the performance of the classifier with other conventional techniques is done for various noises at different noise levels. It is observed that the numerical values of the measures obtained are better when compared to the others. An overall comparison of the performance of the NF 4 classifier is done and it is inferred that NF4 outperforms the other techniques in speech enhancement.


1999 ◽  
Vol 169 ◽  
pp. 312-319
Author(s):  
Dietrich Baade

If observing time and number of photons are not the limit, it will probably be very difficult to find any Be star or BA supergiant that is not variable. Moreover, there is hardly any major set of observations that is not tempting to explain at least partly in terms of nonradial (g-mode) pulsations. Since a few years ago, such conjectures are also theoretically permissible because improved opacity calculations have established the classical к-mechanism as a viable source of pulsation driving (cf. Pamyatnykh, these proceedings).Contrary to Be stars, it can for any given BA supergiant nevertheless be arbitrarily difficult to diagnose nonradial pulsations (NRP’s) with certainty because they need to be detected against considerable background ‘noise’ of other physical processes, most of which are related to mass loss and/or rotation. To make things worse, there is some evidence that NRP’s can have some effect on the dynamics of the mass loss. On the other hand, variable and non-spherical winds is the subject of this Colloquium, and this paper is accordingly biased towards the interplay between pulsation and mass loss.


1999 ◽  
Vol 121 (4) ◽  
pp. 488-494 ◽  
Author(s):  
S. K. Lee ◽  
P. R. White

Impulsive sound and vibration signals in gears are often associated with faults which result from impacting and as such these impulsive signals can be used as indicators of faults. However it is often difficult to make objective measurements of impulsive signals because of background noise signals. In order to ease the measurement of impulsive sounds embedded in background noise, it is proposed that the impulsive signals are enhanced, via a two stage ALE (Adaptive Line Enhancer), and that these enhanced signals are then analyzed in the time and frequency domains using a Wigner higher order time-frequency representation. The effectiveness of this technique is demonstrated by application to gear fault data.


2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Haniyeh Salehi ◽  
Vijay Parsa ◽  
Paula Folkeard

Wireless remote microphones (RMs) transmit the desired acoustic signal to the hearing aid (HA) and facilitate enhanced listening in challenging environments. Fitting and verification of RMs, and benchmarking the relative performance of different RM devices in varied acoustic environments are of significant interest to Audiologists and RM developers. This paper investigates the application of instrumental speech intelligibility and quality metrics for characterizing the RM performance in two acoustic environments with varying amounts of background noise and reverberation. In both environments, two head and torso simulators (HATS) were placed 2 m apart, where one HATS served as the talker and the other served as the listener. Four RM systems were interfaced separately with a HA programmed to match the prescriptive targets for the N4 standard audiogram and placed on the listener HATS. The HA output in varied acoustic conditions was recorded and analyzed offline through computational models predicting speech intelligibility and quality. Results showed performance differences among the four RMs in the presence of noise and/or reverberation, with one RM exhibiting significantly better performance. Clinical implications and applications of these results are discussed.


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