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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact

Science: general issues --- Psychology --- approximate number system --- Number Sense --- non-symbolic number acuity --- Numerical cognition --- Mathematics

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Living at the beginning of the 21st century requires being numerate, because numerical abilities not only essential for life prospects of individuals but also for economic interests of post-industrial knowledge societies. Thus, numerical development is at the core of both individual as well as societal interests. There is the notion that we are already born with a very basic ability to deal with small numerosities. Yet, this often called “number sense” seems to be very restricted, approximate, and driven by perceptual constraints. During our numerical development in formal (e.g., school) but also informal contexts (e.g., family, street) we acquire culturally developed abstract symbol systems to represent exact numerosities – in particular number words and Arabic digits – refining our numerical capabilities. In recent years, numerical development has gained increasing research interest documented in a growing number of behavioural, neuro-scientific, educational, cross-cultural, and neuropsychological studies addressing this issue. Additionally, our understanding of how numerical competencies develop has also benefitted considerably from the advent of different neuro-imaging techniques allowing for an evaluation of developmental changes in the human brain. In sum, we are now starting to put together a more and more coherent picture of how numerical competencies develop and how this development is associated with neural changes as well. In the end, this knowledge might also lead to a better understanding of the reasons for atypical numerical development which often has grieve consequences for those who suffer from developmental dyscalculia. Therefore, this Research Topic deals with all aspects of numerical development: findings from behavioural performance to underlying neural substrates, from cross-sectional to longitudinal evaluations, from healthy to clinical populations. To this end, we encourage empirical contributions using different experimental methodologies but also welcome theoretical contributions, review articles, or opinion papers. We hope that in this Research Topic the expertise of researchers from different backgrounds will be brought together to advance a topic with both scientific and every-day relevance.

Calculus --- Mathematics --- Physical Sciences & Mathematics --- developmental dyscalculia --- mathematics learning disability --- approximate number system --- language development --- spatial-numerical association --- numerical development

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Modern computer technology has opened up new opportunities for the development of digital signal processing methods. The applications of digital signal processing have expanded significantly and today include audio and speech processing, sonar, radar, and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others. This Special Issue is aimed at wide coverage of the problems of digital signal processing, from mathematical modeling to the implementation of problem-oriented systems. The basis of digital signal processing is digital filtering. Wavelet analysis implements multiscale signal processing and is used to solve applied problems of de-noising and compression. Processing of visual information, including image and video processing and pattern recognition, is actively used in robotic systems and industrial processes control today. Improving digital signal processing circuits and developing new signal processing systems can improve the technical characteristics of many digital devices. The development of new methods of artificial intelligence, including artificial neural networks and brain-computer interfaces, opens up new prospects for the creation of smart technology. This Special Issue contains the latest technological developments in mathematics and digital signal processing. The stated results are of interest to researchers in the field of applied mathematics and developers of modern digital signal processing systems.

Information technology industries --- digital filter --- finite field algebra --- conversion device --- module --- memory device --- residue --- feedback regulation --- digital signal analysis --- control efficacy --- residue number system --- redundant residue number system --- modular division --- fraction --- algorithm --- mathematical models of digital signal processing --- digital filtering --- maximum correntropy --- impulsive noise --- sparse channel estimation --- discrete wavelet transform --- medical imaging --- 3D image processing --- quantization noise --- harmonic wavelets --- classification --- kNN-algorithm --- deep neural networks --- machine learning --- Fourier transform --- short-time Fourier transform --- wavelet transform --- spectrogram --- confusion matrix --- ROC curve --- 3D model --- prosthetic design --- orientation --- positioning --- reconstruction --- speech enhancement --- adaptive filter --- microphone array --- sub-band processing --- filter bank --- posture classification --- skeleton detection --- motion capture --- exercise classification --- virtual rehabilitation --- wood defect --- CNN --- ELM --- genetic algorithm --- detection --- digital filter --- finite field algebra --- conversion device --- module --- memory device --- residue --- feedback regulation --- digital signal analysis --- control efficacy --- residue number system --- redundant residue number system --- modular division --- fraction --- algorithm --- mathematical models of digital signal processing --- digital filtering --- maximum correntropy --- impulsive noise --- sparse channel estimation --- discrete wavelet transform --- medical imaging --- 3D image processing --- quantization noise --- harmonic wavelets --- classification --- kNN-algorithm --- deep neural networks --- machine learning --- Fourier transform --- short-time Fourier transform --- wavelet transform --- spectrogram --- confusion matrix --- ROC curve --- 3D model --- prosthetic design --- orientation --- positioning --- reconstruction --- speech enhancement --- adaptive filter --- microphone array --- sub-band processing --- filter bank --- posture classification --- skeleton detection --- motion capture --- exercise classification --- virtual rehabilitation --- wood defect --- CNN --- ELM --- genetic algorithm --- detection

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Modern computer technology has opened up new opportunities for the development of digital signal processing methods. The applications of digital signal processing have expanded significantly and today include audio and speech processing, sonar, radar, and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others. This Special Issue is aimed at wide coverage of the problems of digital signal processing, from mathematical modeling to the implementation of problem-oriented systems. The basis of digital signal processing is digital filtering. Wavelet analysis implements multiscale signal processing and is used to solve applied problems of de-noising and compression. Processing of visual information, including image and video processing and pattern recognition, is actively used in robotic systems and industrial processes control today. Improving digital signal processing circuits and developing new signal processing systems can improve the technical characteristics of many digital devices. The development of new methods of artificial intelligence, including artificial neural networks and brain-computer interfaces, opens up new prospects for the creation of smart technology. This Special Issue contains the latest technological developments in mathematics and digital signal processing. The stated results are of interest to researchers in the field of applied mathematics and developers of modern digital signal processing systems.

Information technology industries --- digital filter --- finite field algebra --- conversion device --- module --- memory device --- residue --- feedback regulation --- digital signal analysis --- control efficacy --- residue number system --- redundant residue number system --- modular division --- fraction --- algorithm --- mathematical models of digital signal processing --- digital filtering --- maximum correntropy --- impulsive noise --- sparse channel estimation --- discrete wavelet transform --- medical imaging --- 3D image processing --- quantization noise --- harmonic wavelets --- classification --- kNN-algorithm --- deep neural networks --- machine learning --- Fourier transform --- short-time Fourier transform --- wavelet transform --- spectrogram --- confusion matrix --- ROC curve --- 3D model --- prosthetic design --- orientation --- positioning --- reconstruction --- speech enhancement --- adaptive filter --- microphone array --- sub-band processing --- filter bank --- posture classification --- skeleton detection --- motion capture --- exercise classification --- virtual rehabilitation --- wood defect --- CNN --- ELM --- genetic algorithm --- detection