An improved fast Fourier transform algorithm using mixed frequency and time decimations

金沢大学金沢大学大学院自然科学研究科情報システム金沢大学工学部An improved FFT (fast Fourier transform) algorithm combining both decimations in frequency and in time is presented. Stress is placed on a derivation of general formulas for submatrices and multiplicands. Computational efficiency is briefly discussed

Structured FFT and TFT: symmetric and lattice polynomials

International audienceIn this paper, we consider the problem of efficient computations with structured polynomials. We provide complexity results for computing Fourier Transform and Truncated Fourier Transform of symmetric polynomials, and for multiplying polynomials supported on a lattice

Suitability of chaotic iterations schemes using XORshift for security applications

International audienceThe design and engineering of original cryptographic solutions is a major concern to provide secure information systems. In a previous study, we have described a generator based on chaotic iterations, which uses the well-known XORshift generator. By doing so, we have improved the statistical performances of XORshift and make it behave chaotically, as defined by Devaney. The speed and security of this former generator have been improved in a second study, to make its usage more relevant in the Internet security context. In this paper, these contributions are summarized and a new version of the generator is introduced. It is based on a new Lookup Table implying a large improvement of speed. A comparison and a security analysis between the XORshift and these three versions of our generator are proposed, and various new statistical results are given. Finally, an application in the information hiding framework is presented, to give an illustrative example of the use of such a generator in the Internet security field

Single Pulse Detection Algorithms for Real-time Fast Radio Burst Searches using GPUs

The detection of non-repeating or irregular events in time-domain radio astronomy has gained importance over the last decade due to the discovery of fast radio bursts. Existing or upcoming radio telescopes are gathering more and more data and consequently the software, which is an important part of these telescopes, must process large data volumes at high data rates. Data has to be searched through to detect new and interesting events, often in real-time. These requirements necessitate new and fast algorithms which must process data quickly and accurately. In this work we present new algorithms for single pulse detection using boxcar filters. We have quantified the signal loss introduced by single pulse detection algorithms which use boxcar filters and based on these results, we have designed two distinct "lossy" algorithms. Our lossy algorithms use an incomplete set of boxcar filters to accelerate detection at the expense of a small reduction in detected signal power. We present formulae for signal loss, descriptions of our algorithms and their parallel implementation on NVIDIA GPUs using CUDA. We also present tests of correctness, tests on artificial data and the performance achieved. Our implementation can process SKA-MID-like data 266$\times$ faster than real-time on a NVIDIA P100 GPU and 500x faster than real-time on a NVIDIA Titan V GPU with a mean signal power loss of 7%. We conclude with prospects for single pulse detection for beyond SKA era, nanosecond time resolution radio astronomy.Comment: Published in The Astrophysical Journal Supplement Serie

The Bioinformatics Tools for Discovery of Genetic Diversity by Means of Elastic Net and Hurst Exponent

The genome era allowed us to evaluate different aspects on genetic variation, with a precise manner followed by a valuable tip to guide the improvement of knowledge and direct to upgrade to human life. In order to scrutinize these treasured resources, some bioinformatics tools permit us a deep exploration of these data. Among them, we show the importance of the discrete non-decimated wavelet transform (NDWT). The wavelets have a better ability to capture hidden components of biological data and an efficient link between biological systems and the mathematical objects used to describe them. The decomposition of signals/sequences at different levels of resolution allows obtaining distinct characteristics in each level. The analysis using technique of wavelets has been growing increasingly in the study of genomes. One of the great advantages associated to this method corresponds to the computational gain, that is, the analyses are processed almost in real time. The applicability is in several areas of science, such as physics, mathematics, engineering, and genetics, among others. In this context, we believe that using R software and applied NDWT coupled with elastic net domains and Hurst exponent will be of valuable guideline to researchers of genetics in the investigation of the genetic variability

Identification of Transient Speech Using Wavelet Transforms

It is generally believed that abrupt stimulus changes, which in speech may be time-varying frequency edges associated with consonants, transitions between consonants and vowels and transitions within vowels are critical to the perception of speech by humans and for speech recognition by machines. Noise affects speech transitions more than it affects quasi-steady-state speech. I believe that identifying and selectively amplifying speech transitions may enhance the intelligibility of speech in noisy conditions. The purpose of this study is to evaluate the use of wavelet transforms to identify speech transitions. Using wavelet transforms may be computationally efficient and allow for real-time applications. The discrete wavelet transform (DWT), stationary wavelet transform (SWT) and wavelet packets (WP) are evaluated. Wavelet analysis is combined with variable frame rate processing to improve the identification process. Variable frame rate can identify time segments when speech feature vectors are changing rapidly and when they are relatively stationary. Energy profiles for words, which show the energy in each node of a speech signal decomposed using wavelets, are used to identify nodes that include predominately transient information and nodes that include predominately quasi-steady-state information, and these are used to synthesize transient and quasi-steady-state speech components. These speech components are estimates of the tonal and nontonal speech components, which Yoo et al identified using time-varying band-pass filters. Comparison of spectra, a listening test and mean-squared-errors between the transient components synthesized using wavelets and Yoo's nontonal components indicated that wavelet packets identified the best estimates of Yoo's components. An algorithm that incorporates variable frame rate analysis into wavelet packet analysis is proposed. The development of this algorithm involves the processes of choosing a wavelet function and a decomposition level to be used. The algorithm itself has 4 steps: wavelet packet decomposition; classification of terminal nodes; incorporation of variable frame rate processing; synthesis of speech components. Combining wavelet analysis with variable frame rate analysis provides the best estimates of Yoo's speech components

Exploiting signal processing approaches for broadband echosounders

© International Council for the Exploration of the Sea, 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in ICES Journal of Marine Science 74 (2017): 2262–2275, doi:10.1093/icesjms/fsx155.Broadband echosounders, which transmit frequency-modulated pulses, increase the spectral characterization of targets relative to narrowband echosounders, which typically transmit single-frequency pulses, and also increase the range resolution through broadband matched-filter signal processing approaches. However, the increased range resolution does not necessarily lead to improved detection and characterization of targets close to boundaries due to the presence of undesirable signal processing side lobes. The standard approach to mitigating the impact of processing side lobes is to transmit tapered signals, which has the consequence of also reducing spectral information. To address this, different broadband signal processing approaches are explored using data collected in a large tank with both a Kongsberg–Simrad EK80 scientific echosounder with a combination of single- and split-beam transducers with nominal centre frequencies of 18, 38, 70, 120, 200, and 333 kHz, and with a single-beam custom-built echosounder spanning the frequency band from 130 to 195 kHz. It is shown that improved detection and characterization of targets close to boundaries can be achieved by using modified replica signals in the matched filter processing. An additional benefit to using broadband echosounders involves exploiting the frequency dependence of the beam pattern to calibrate single-beam broadband echosounders using an off-axis calibration sphere.This research was supported by the NOAA Office of Science and Technology, Advanced Sampling Technology Working Group. G.L.L. was partially supported by NOAA Cooperative Agreements NA09OAR4320129 and NA14OAR4320158 through the NOAA Fisheries Quantitative Ecology and Socieconomics Training (QUEST) program. A.C.L. was partially supported through the Office of Naval Research Ocean Acoustics Program

Investigation of techniques for automatic polyphonic music transcription using wavelets.

Thesis (M.Sc) - University of KwaZulu-Natal, Pietermaritzburg, 2009.It has been said (although sadly I have no source) that music is one of the most useful yet useless phenomena known to mankind. Useless in that it has, apparently, no tangible or immediately practical function in our lives, but extremely useful in that it is a truly universal language between human beings, which transcends boundaries and allows us to express ourselves and experience emotions in rather profound ways. For the majority of us, music exists to be listened to, appreciated, admired (sometimes reviled) but generally as some sort of stimulus for our auditory senses. Some of us feel the need to produce music, perhaps simply for our own creative enjoyment, or maybe because we crave the power it lends us to be able to inspire feelings in others. For those of us who love to know “the reason why” or “how things work” and wish to discover the secrets of music, arguably the greatest of all the arts, there can surely be no doubt that a fascinating world of mathematics, harmony and beauty awaits us. Perhaps the reason why music is able to convey such strong emotions in us is because we are (for whatever strange evolutionary reason or purpose) designed to be innately pattern pursuing, sequence searching and harmony hungry creatures. Music, as we shall discover in this research, is chock-a-block full of the most incredible patterns, which are just waiting to be deciphered