1,255 research outputs found
Design of FIR digital filters for pulse shaping and channel equalization using time-domain optimization
Three algorithms are developed for designing finite impulse response digital filters to be used for pulse shaping and channel equalization. The first is the Minimax algorithm which uses linear programming to design a frequency-sampling filter with a pulse shape that approximates the specification in a minimax sense. Design examples are included which accurately approximate a specified impulse response with a maximum error of 0.03 using only six resonators. The second algorithm is an extension of the Minimax algorithm to design preset equalizers for channels with known impulse responses. Both transversal and frequency-sampling equalizer structures are designed to produce a minimax approximation of a specified channel output waveform. Examples of these designs are compared as to the accuracy of the approximation, the resultant intersymbol interference (ISI), and the required transmitted energy. While the transversal designs are slightly more accurate, the frequency-sampling designs using six resonators have smaller ISI and energy values
A new view of nonlinear water waves: the Hilbert spectrum
We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes
Data-Driven Time-Frequency Analysis
In this paper, we introduce a new adaptive data analysis method to study
trend and instantaneous frequency of nonlinear and non-stationary data. This
method is inspired by the Empirical Mode Decomposition method (EMD) and the
recently developed compressed (compressive) sensing theory. The main idea is to
look for the sparsest representation of multiscale data within the largest
possible dictionary consisting of intrinsic mode functions of the form , where , consists of the
functions smoother than and . This problem can
be formulated as a nonlinear optimization problem. In order to solve this
optimization problem, we propose a nonlinear matching pursuit method by
generalizing the classical matching pursuit for the optimization problem.
One important advantage of this nonlinear matching pursuit method is it can be
implemented very efficiently and is very stable to noise. Further, we provide a
convergence analysis of our nonlinear matching pursuit method under certain
scale separation assumptions. Extensive numerical examples will be given to
demonstrate the robustness of our method and comparison will be made with the
EMD/EEMD method. We also apply our method to study data without scale
separation, data with intra-wave frequency modulation, and data with incomplete
or under-sampled data
Phase Harmonic Correlations and Convolutional Neural Networks
A major issue in harmonic analysis is to capture the phase dependence of
frequency representations, which carries important signal properties. It seems
that convolutional neural networks have found a way. Over time-series and
images, convolutional networks often learn a first layer of filters which are
well localized in the frequency domain, with different phases. We show that a
rectifier then acts as a filter on the phase of the resulting coefficients. It
computes signal descriptors which are local in space, frequency and phase. The
non-linear phase filter becomes a multiplicative operator over phase harmonics
computed with a Fourier transform along the phase. We prove that it defines a
bi-Lipschitz and invertible representation. The correlations of phase harmonics
coefficients characterise coherent structures from their phase dependence
across frequencies. For wavelet filters, we show numerically that signals
having sparse wavelet coefficients can be recovered from few phase harmonic
correlations, which provide a compressive representationComment: 26 pages, 8 figure
Reconstruction of Binary Functions and Shapes from Incomplete Frequency Information
The characterization of a binary function by partial frequency information is
considered. We show that it is possible to reconstruct binary signals from
incomplete frequency measurements via the solution of a simple linear
optimization problem. We further prove that if a binary function is spatially
structured (e.g. a general black-white image or an indicator function of a
shape), then it can be recovered from very few low frequency measurements in
general. These results would lead to efficient methods of sensing,
characterizing and recovering a binary signal or a shape as well as other
applications like deconvolution of binary functions blurred by a low-pass
filter. Numerical results are provided to demonstrate the theoretical
arguments.Comment: IEEE Transactions on Information Theory, 201
Frequency and Phase Synchronization in Stochastic Systems
The phenomenon of frequency and phase synchronization in stochastic systems
requires a revision of concepts originally phrased in the context of purely
deterministic systems. Various definitions of an instantaneous phase are
presented and compared with each other with special attention payed to their
robustness with respect to noise. We review the results of an analytic approach
describing noise-induced phase synchronization in a thermal two-state system.
In this context exact expressions for the mean frequency and the phase
diffusivity are obtained that together determine the average length of locking
episodes. A recently proposed method to quantify frequency synchronization in
noisy potential systems is presented and exemplified by applying it to the
periodically driven noisy harmonic oscillator. Since this method is based on a
threshold crossing rate pioneered by S.O. Rice the related phase velocity is
termed Rice frequency. Finally, we discuss the relation between the phenomenon
of stochastic resonance and noise-enhanced phase coherence by applying the
developed concepts to the periodically driven bistable Kramers oscillator.Comment: to appear in the Chaos focus issue on "Control, communication, and
synchronization in chaotic dynamical systems
A Novel Techniques for Classification of Musical Instruments
Musical instrument classification provides a framework for developing and evaluating features for any type of content-based analysis of musical signals. Signal is subjected to wavelet decomposition. A suitable wavelet is selected for decomposition. In our work for decomposition we used Wavelet Packet transform. After the wavelet decomposition, some sub band signals can be analyzed, particular band can be representing the particular characteristics of musical signal. Finally these wavelet features set were formed and then musical instrument will be classified by using suitable machine learning algorithm (classifier). In this paper, the problem of classifying of musical instruments is addressed. We propose a new musical instrument classification method based on wavelet represents both local and global information by computing wavelet coefficients at different frequency sub bands with different resolutions. Using wavelet packet transform (WPT) along with advanced machine learning techniques, accuracy of music instrument classification has been significantly improved. Keywords: Musical instrument classification, WPT, Feature Extraction Techniques, Machine learning techniques
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