Single-trial multiwavelet coherence in application to neurophysiological time series

A method of single-trial coherence analysis is presented, through the application of continuous muldwavelets. Multiwavelets allow the construction of spectra and bivariate statistics such as coherence within single trials. Spectral estimates are made consistent through optimal time-frequency localization and smoothing. The use of multiwavelets is considered along with an alternative single-trial method prevalent in the literature, with the focus being on statistical, interpretive and computational aspects. The multiwavelet approach is shown to possess many desirable properties, including optimal conditioning, statistical descriptions and computational efficiency. The methods. are then applied to bivariate surrogate and neurophysiological data for calibration and comparative study. Neurophysiological data were recorded intracellularly from two spinal motoneurones innervating the posterior,biceps muscle during fictive locomotion in the decerebrated cat

Design and Improvement of HiperLAN/2 Physical Layer Model Based Multiwavelet Signals

Currently, Wireless Local Area Networks (WLANs) supporting broadband multimedia communications are being advanced, and standardized. HIPERLAN/2 standard is defined by ETSI BRAN. In this paper, we improve HIPERLAN/2 based Orthogonal Frequency-Division Multiplexing OFDM, Discrete Multiwavelet Transform (DMWT) performance via a MATLAB/ Simulink simulation .These systems provide channel adaptive data rates up to 54 Mb/s (in a 20 MHz channel spacing) in the 5 GHz radio band. For different channels. MATLAB/ Simulink modeling demonstrated that the performance of multiwavelet OFDM has a remarkable degradation in the packet (PDU or PSDU) error rate (PER) compared to based OFDM Fast Fourier transform (FFT) due to the considerable channel models. With DMWT-OFDM, Carrier-to-Noise Ratio (C/N) improvement compared to FFT-OFDM is achieved. Keywords: HiperLAN/2, OFDM, DMWT, IDMWT

MC-DS-CDMA System based on DWT and STBC in ITU Multipath Fading Channels Model

 في هذه الورقة، تم تحسين أداء النفوذ المتعدد بالتقسيم لرمز السلسلة المباشر متعدد الموجات (MC-DS-CDMA) في تطبيقات MC-DS-CDMA الثابتة والتطبيقات MC-DS-CDMA  المتنقلة باستعمال تعويضات التشفير الزمنية الفضائية وتحويل فورير السريعة المنفصلة (FFT) أو تحويل المويجات المنفصلة DWT. وقد تمت محاكاة أنظمة MC-DS-CDMA  باستخدام ماتلاب 2015a. من خلال محاكاة النظام المقترح، يمكن تغيير المعالم المختلفة واختبارها. ويتم الحصول على معدل خطأ البيانات (BER) لهذه الأنظمة على مدى واسع من نسبة الإشارة إلى الضوضاء. وقد قورنت جميع نتائج المحاكاة مع بعضها البعض باستخدام حجم الموجة الحاملة الفرعية المختلفة FFT أو DWT مع ل STBC 1،2،3 و 4 هوائيات في المرسل وفي مختلف قنوات الخبو في متعددة الممرات ITU ومختلف ترددات دوبلر (fd).In this paper, the performance of multicarrier direct sequence code division multiple access (MC-DS-CDMA) in fixed MC-DS-CDMA and Mobile MC-DS-CDMA applications have been improved by using the compensations of space time block coding and Discrete Fast Fourier transforms (FFT) or Discrete Wavelets transform DWT. These MC-DS-CDMA systems had been simulated using MATLAB 2015a. Through simulation of the proposed system, various parameters can be changed and tested. The Bit Error Rate (BERs) of these systems are obtained over wide range of signal to noise ratio. All simulation results had been compared with each other using different subcarrier size of FFT or DWT with STBC for 1,2,3 and 4 antennas in transmitter and under different ITU multipath fading channels and different Doppler frequencies (fd). The proposed structures of STBC-MC-DS-CDMA system based on (DWT) batter than based on (FFT) in varies Doppler frequencies and subcarrier size. Also, proposed system with STBC based on 4 transmitters better than other systems based on 1 or 2 or 3 transmitters in all Doppler frequencies and subcarrier size in all simulation results

Field programmable gate array implementation of multiwavelet transform based orthogonal frequency division multiplexing system

This article offers an efficient design and implementation of a discrete multiwavelet critical-sampling transform based orthogonal frequency division multiplexing (DMWCST-OFDM) transceiver using field programmable gate array (FPGA) platform. The design uses 16-point discrete multiwavelet critical-sampling transform (DMWCST) and its inverse as main processing modules. All modules were designed using a part of Vivado® Design Suite version (2015.2), which is Xilinx system generator (XSG), and is compatible with MATLAB Simulink version R2013b. The FPGA implementation is carried out on a Zynq (XC7Z020-1CLG484) evaluation board with joint test action group (JTAG) hardware co-simulation. According to the results obtained from the implementation tools, the implemented system is efficient in terms of resource utilization and could support the real-time operations

Comparative study and performance evaluation of MC-CDMA and OFDM over AWGN and fading channels environment

Η απαίτηση για εφαρμογές υψηλής ταχύτητας μετάδοσης δεδομένων έχει αυξηθεί σημαντικά τα τελευταία χρόνια. Η πίεση των χρηστών σήμερα για ταχύτερες επικοινωνίες, ανεξαρτήτως κινητής ή σταθερής, χωρίς επιπλέον κόστος είναι μια πραγματικότητα. Για να πραγματοποιηθούν αυτές οι απαιτήσεις, προτάθηκε ένα νέο σχήμα που συνδυάζει ψηφιακή διαμόρφωση και πολλαπλές προσβάσεις, για την ακρίβεια η Πολλαπλή Πρόσβαση με διαίρεση Κώδικα Πολλαπλού Φέροντος (Multi-Carrier Code Division Multiple Access MC-CDMA). Η εφαρμογή του Γρήγορου Μετασχηματισμού Φουριέ (Fast Fourier Transform,FFT) που βασίζεται στο (Orthogonal Frequency Division Multiplexing, OFDM) χρησιμοποιεί τις περίπλοκες λειτουργίες βάσεως και αντικαθίσταται από κυματομορφές για να μειώσει το επίπεδο της παρεμβολής. Έχει βρεθεί ότι οι μετασχηματισμένες κυματομορφές (Wavelet Transform,W.T.) που βασίζονται στον Haar είναι ικανές να μειώσουν το ISI και το ICI, που προκαλούνται από απώλειες στην ορθογωνιότητα μεταξύ των φερόντων, κάτι που τις καθιστά απλούστερες για την εφαρμογή από του FFT. Επιπλέον κέρδος στην απόδοση μπορεί να επιτευχθεί αναζητώντας μια εναλλακτική λειτουργία ορθογωνικής βάσης και βρίσκοντας ένα καλύτερο μετασχηματισμό από του Φουριέ (Fourier) και τον μετασχηματισμό κυματομορφής (Wavelet Transform). Στην παρούσα εργασία, υπάρχουν τρία προτεινόμενα μοντέλα. Το 1ο, ( A proposed Model ‘1’ of OFDM based In-Place Wavelet Transform), το 2ο, A proposed Model ‘2’ based In-Place Wavelet Transform Algorithm and Phase Matrix (P.M) και το 3ο, A proposed Model ‘3’ of MC-CDMA Based on Multiwavelet Transform. Οι αποδόσεις τους συγκρίθηκαν με τα παραδοσιακά μοντέλα μονού χρήστη κάτω από διαφορετικά κανάλια (Κανάλι AWGN, επίπεδη διάλειψη και επιλεκτική διάλειψη).The demand for high data rate wireless multi-media applications has increased significantly in the past few years. The wireless user’s pressure towards faster communications, no matter whether mobile, nomadic, or fixed positioned, without extra cost is nowadays a reality. To fulfill these demands, a new scheme which combines wireless digital modulation and multiple accesses was proposed in the recent years, namely, Multicarrier-Code Division Multiple Access (MC-CDMA). The Fourier based OFDM uses the complex exponential bases functions and it is replaced by wavelets in order to reduce the level of interference. It is found that the Haar-based wavelets are capable of reducing the ISI and ICI, which are caused by the loss in orthogonality between the carriers. Further performance gains can be made by looking at alternative orthogonal basis functions and finding a better transform rather than Fourier and wavelet transform. In this thesis, there are three proposed models [Model ‘1’ (OFDM based on In-Place Wavelet Transform, Model ‘2’ (MC-CDMA based on IP-WT and Phase Matrix) and Model ‘3’ (MC-CDMA based on Multiwavelet Transform)] were created and then comparison their performances with the traditional models for single user system were compared under different channel characteristics (AWGN channel, flat fading and selective fading). The conclusion of my study as follows, the models (1) was achieved much lower bit error rates than traditional models based FFT. Therefore these models can be considered as an alternative to the conventional MC-CDMA based FFT. The main advantage of using In-Place wavelet transform in the proposed models that it does not require an additional array at each sweep such as in ordered Fast Haar wavelet transform, which makes it simpler for implementation than FFT. The model (2) gave a new algorithm based on In-Place wavelet transform with first level processing multiple by PM was proposed. The model (3) gave much lower bit error than other two models in additional to traditional models

Crack detection in a pipe by adaptive subspace iteration algorithm and least square support vector regression

A new combination method of beam-type finite element multiwavelet-based algorithm and least square support vector regression (LSSVR) algorithm is proposed for detecting the location and size of a crack in a pipe. According to operators of engineering problems, Rayleigh-Euler and Rayleigh-Timoshenko beam-type multiwavelets are constructed using the stable completion in the multiresolution finite element space. A rotational spring model is used for cracked pipe modeling and the local flexibility due to the crack is calculated by discrete approximation method. An adaptive subspace iteration algorithm (ASIA) is applied to efficiently approximate the exact solution of pipe model by adding new beam-type multiwavelets in each scale. To avoid the difficulty of constructing well-defined mathematical models, the normalized crack location and depth is detected by using LSSVR algorithm. The numerical and experimental results verify that the presented method can accurately identify the location and depth of crack in a pipe

An Investigation of Orthogonal Wavelet Division Multiplexing Techniques as an Alternative to Orthogonal Frequency Division Multiplex Transmissions and Comparison of Wavelet Families and Their Children

Recently, issues surrounding wireless communications have risen to prominence because of the increase in the popularity of wireless applications. Bandwidth problems, and the difficulty of modulating signals across carriers, represent significant challenges. Every modulation scheme used to date has had limitations, and the use of the Discrete Fourier Transform in OFDM (Orthogonal Frequency Division Multiplex) is no exception. The restriction on further development of OFDM lies primarily within the type of transform it uses in the heart of its system, Fourier transform. OFDM suffers from sensitivity to Peak to Average Power Ratio, carrier frequency offset and wasting some bandwidth to guard successive OFDM symbols. The discovery of the wavelet transform has opened up a number of potential applications from image compression to watermarking and encryption. Very recently, work has been done to investigate the potential of using wavelet transforms within the communication space. This research will further investigate a recently proposed, innovative, modulation technique, Orthogonal Wavelet Division Multiplex, which utilises the wavelet transform opening a new avenue for an alternative modulation scheme with some interesting potential characteristics. Wavelet transform has many families and each of those families has children which each differ in filter length. This research consider comprehensively investigates the new modulation scheme, and proposes multi-level dynamic sub-banding as a tool to adapt variable signal bandwidths. Furthermore, all compactly supported wavelet families and their associated children of those families are investigated and evaluated against each other and compared with OFDM. The linear computational complexity of wavelet transform is less than the logarithmic complexity of Fourier in OFDM. The more important complexity is the operational complexity which is cost effectiveness, such as the time response of the system, the memory consumption and the number of iterative operations required for data processing. Those complexities are investigated for all available compactly supported wavelet families and their children and compared with OFDM. The evaluation reveals which wavelet families perform more effectively than OFDM, and for each wavelet family identifies which family children perform the best. Based on these results, it is concluded that the wavelet modulation scheme has some interesting advantages over OFDM, such as lower complexity and bandwidth conservation of up to 25%, due to the elimination of guard intervals and dynamic bandwidth allocation, which result in better cost effectiveness

Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space

We present a novel method for stochastic interpolation of sparsely sampled time signals based on a superstatistical random process generated from a multivariate Gaussian scale mixture. In comparison to other stochastic interpolation methods such as Gaussian process regression, our method possesses strong multifractal properties and is thus applicable to a broad range of real-world time series, e.g. from solar wind or atmospheric turbulence. Furthermore, we provide a sampling algorithm in terms of a mixing procedure that consists of generating a 1 + 1-dimensional field u(t, {\xi}), where each Gaussian component u{\xi}(t) is synthesized with identical underlying noise but different covariance function C{\xi}(t,s) parameterized by a log-normally distributed parameter {\xi}. Due to the Gaussianity of each component u{\xi}(t), we can exploit standard sampling alogrithms such as Fourier or wavelet methods and, most importantly, methods to constrain the process on the sparse measurement points. The scale mixture u(t) is then initialized by assigning each point in time t a {\xi}(t) and therefore a specific value from u(t, {\xi}), where the time-dependent parameter {\xi}(t) follows a log-normal process with a large correlation time scale compared to the correlation time of u(t, {\xi}). We juxtapose Fourier and wavelet methods and show that a multiwavelet-based hierarchical approximation of the interpolating paths, which produce a sparse covariance structure, provide an adequate method to locally interpolate large and sparse datasets.Comment: 25 pages, 14 figure