The behavior of quantization spectra as a function of signal-to-noise ratio

An expression for the spectrum of quantization error in a discrete-time system whose input is a sinusoid plus white Gaussian noise is derived. This quantization spectrum consists of two components: a white-noise floor and spurious harmonics. The dithering effect of the input Gaussian noise in both components of the spectrum is considered. Quantitative results in a discrete Fourier transform (DFT) example show the behavior of spurious harmonics as a function of the signal-to-noise ratio (SNR). These results have strong implications for digital reception and signal analysis systems. At low SNRs, spurious harmonics decay exponentially on a log-log scale, and the resulting spectrum is white. As the SNR increases, the spurious harmonics figure prominently in the output spectrum. A useful expression is given that roughly bounds the magnitude of a spurious harmonic as a function of the SNR

Lacunarity of Fractal Superlattices: a Remote Estimation using Wavelets

The lacunarity provides a useful parameter for describing the distribution of gap sizes in discrete self-similar (fractal) superlattices and is used in addition to the similarity dimension to describe fractals. We show here that lacunarity, as well as the similarity dimension, can be remotely estimated from the wavelet analysis of superlattices impulse response. As a matter of fact, the skeleton—the set of wavelet-transform modulus-maxima—of the reflected signal overlaps two hierarchical structures in the time-scale domain: such that one allows the direct remote extraction of the similarity dimension, while the other may provide an accurate estimation of the lacunarity of the interrogated superlattice. Criteria for the choice of the mother wavelet are established for impulse response corrupted by additive Gaussian white noise

Speaker Identification Using Wavelet Packet Transform and Feed Forward Neural Network

It has been known for a long time that speakers can be identified from their voices. In this work we introduce a speaker identification system using wavelet packet transform. This is one of a wavelet transform analysis for feature extraction and a neural network for classification. This system is applied on ten speakers Instead of applying framing on the signal, the wavelet packet transform is applied on the whole range of the signal. This reduces the calculation time. The speech signal is decomposed into 24 sub bands, according to Mel-scale frequency. Then, for each of these bands, the log energy is taken. Finally, the discrete cosine transform is applied on these bands. These are taken as features for identifying the speaker among many speakers. For the classification task, Feed Forward multi layer perceptron, trained by backpropagation, is proposed for use as training and classification feature vectors of the speaker. We propose to construct a single neural network for each speaker of interest. Training and testing of isolated words in three cases, Vis one-, two-, and three-syllable words, were obtained by recording these words from the LAB colleagues using a low-cost microphone

Stock market returns and economic activity: evidence from wavelet analysis

In this paper we investigate the relationship between stock market returns and economic activity by using signal decomposition techniques based on wavelet analysis. In particular, we apply the maximum overlap discrete wavelet transform (MODWT) to the DJIA stock price index and the industrial production index for US over the period 1961:1- 2005:3 and using the definitions of wavelet variance, wavelet correlation and cross-correlations analyze the association as well as the lead/lag relationship between stock prices and industrial production at the different time scales. Our results show that stock market returns tends to lead the level of economic activity but only at the highest scales (lowest frequencies), corresponding to periods of 16 months and longer, and that the periods by which stock returns lead output increase as the wavelet time scale increases.stock market, industrial production, wavelet analysis

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Matched wavelet construction and its application to target detection

This dissertation develops a new wavelet design technique that produces a wavelet that matches a desired signal in the least squares sense. The Wavelet Transform has become very popular in signal and image processing over the last 6 years because it is a linear transform with an infinite number of possible basis functions that provides localization in both time (space) and frequency (spatial frequency). The Wavelet Transform is very similar to the matched filter problem, where the wavelet acts as a zero mean matched filter. In pattern recognition applications where the output of the Wavelet Transform is to be maximized, it is necessary to use wavelets that are specifically matched to the signal of interest. Most current wavelet design techniques, however, do not design the wavelet directly, but rather, build a composite wavelet from a library of previously designed wavelets, modify the bases in an existing multiresolution analysis or design a multiresolution analysis that is generated by a scaling function which has a specific corresponding wavelet. In this dissertation, an algorithm for finding both symmetric and asymmetric matched wavelets is developed. It will be shown that under certain conditions, the matched wavelets generate an orthonormal basis of the Hilbert space containing all finite energy signals. The matched orthonormal wavelets give rise to a pair of Quadrature Mirror Filters (QMF) that can be used in the fast Discrete Wavelet Transform. It will also be shown that as the conditions are relaxed, the algorithm produces dyadic wavelets which when used in the Wavelet Transform provides significant redundancy in the transform domain. Finally, this dissertation develops a shift, scale and rotation invariant technique for detecting an object in an image using the Wavelet Radon Transform (WRT) and matched wavelets. The detection algorithm consists of two levels. The first level detects the location, rotation and scale of the object, while the second level detects the fine details in the object. Each step of the wavelet matching algorithm and the object detection algorithm is demonstrated with specific examples

Discrete-Time continuous-dilation construction of linear scale-invariant systems and multi-dimensional self-similar signals

This dissertation presents novel models for purely discrete-time self-similar processes and scale- invariant systems. The results developed are based on the definition of a discrete-time scaling (dilation) operation through a mapping between discrete and continuous frequencies. It is shown that it is possible to have continuous scaling factors through this operation even though the signal itself is discrete-time. Both deterministic and stochastic discrete-time self-similar signals are studied. Conditions of existence for self-similar signals are provided. Construction of discrete-time linear scale-invariant (LSI) systems and white noise driven models of self-similar stochastic processes are discussed. It is shown that unlike continuous-time self-similar signals, a wide class of non-trivial discrete-time self-similar signals can be constructed through these models. The results obtained in the one-dimensional case are extended to multi-dimensional case. Constructions of discrete-space self-similar ran dom fields are shown to be potentially useful for the generation, modeling and analysis of multi-dimensional self-similar signals such as textures. Constructions of discrete-time and discrete-space self-similar signals presented in the dissertation provide potential tools for applications such as image segmentation and classification, pattern recognition, image compression, digital halftoning, computer vision, and computer graphics. The other aspect of the dissertation deals with the construction of discrete-time continuous-dilation wavelet transform and its existence condition, based on the defined discrete-time continuous-dilation scaling operator

A Detail Study of Wavelet Families for EMG Pattern Recognition

Wavelet transform (WT) has recently drawn the attention of the researchers due to its potential in electromyography (EMG) recognition system. However, the optimal mother wavelet selection remains a challenge to the application of WT in EMG signal processing. This paper presents a detail study for different mother wavelet function in discrete wavelet transform (DWT) and continuous wavelet transform (CWT). Additionally, the performance of different mother wavelet in DWT and CWT at different decomposition level and scale are also investigated. The mean absolute value (MAV) and wavelength (WL) features are extracted from each CWT and reconstructed DWT wavelet coefficient. A popular machine learning method, support vector machine (SVM) is employed to classify the different types of hand movements. The results showed that the most suitable mother wavelet in CWT are Mexican hat and Symlet 6 at scale 16 and 32, respectively. On the other hand, Symlet 4 and Daubechies 4 at the second decomposition level are found to be the optimal wavelet in DWT. From the analysis, we deduced that Symlet 4 at the second decomposition level in DWT is the most suitable mother wavelet for accurate classification of EMG signals of different hand movements.

Shannon Wavelet Entropy and Acoustic Emission Applied to Assess Damage in Concrete in Dynamical Tests

Shannon wavelet entropy (SWE), a powerful mathematical tool for transient signal analysis, is applied to acoustic emission signals originated in crack like damages. In previous work, the complex Morlet Continuous Wavelet Transform (CWT) was applied to acoustic emission (AE) signals from dynamic tests conducted on a reinforced concrete slab with a shaking table. Comparison of the evolution of the scale position of maximum values of CWT coefficients and the histories of response acceleration obtained in different seismic simulations allowed us to identify the frequency band corresponding to the fracture of concrete, which is the main failure mechanism. In the present work, the same frequency band, assigned to fracture, was considered. The discrete dyadic wavelet transform (DDWT), a faster transform algorithm, is first used as a filter to obtain the coefficients in the desired frequency band, and then SWE is calculated. SWE is extracted from each AE hit, which allows us to obtain the SWE evolution overthe test duration and connect sharp transitions of entropy values with the occurrence of dangerous macrocracks.Publicado en: Mecánica Computacional vol. XXXV no.44Facultad de Ingenierí