Analysis of Wavelet Based Alternatives for OFDM

The objective of this thesis is to analyze wavelet based alternatives for orthogonal frequency division multiplexing (OFDM) and find whether a better system performance is achieved when compared to the discrete Fourier transform (DFT)-based OFDM. We analyze DFT, discrete wavelet transform (DWT), and dual tree complex wavelet transform (DT-CWT) based systems in an additive white Gaussian noise (AWGN) channel. The analysis is verified by Monte Carlo simulation. The results in the thesis indicate that the bit error probability (BEP) performance is the same for all types of systems. This confirms some results presented in the literature but differs from others. Some report better BEP performance for the DWT based system than for the DFT based system, and some report worse. In addition, the literature reports better BEP performance for DT-CWT-based system than both DFT-based and DWT-based systems. We compare the peak to average power ratio (PAPR) for the alternatives. The results show improvement in PAPR for the wavelet based system. That is, the DT-CWT performs the best, then the DWT, and the worst is for the DFT based system

Novel Fourier Quadrature Transforms and Analytic Signal Representations for Nonlinear and Non-stationary Time Series Analysis

The Hilbert transform (HT) and associated Gabor analytic signal (GAS) representation are well-known and widely used mathematical formulations for modeling and analysis of signals in various applications. In this study, like the HT, to obtain quadrature component of a signal, we propose the novel discrete Fourier cosine quadrature transforms (FCQTs) and discrete Fourier sine quadrature transforms (FSQTs), designated as Fourier quadrature transforms (FQTs). Using these FQTs, we propose sixteen Fourier-Singh analytic signal (FSAS) representations with following properties: (1) real part of eight FSAS representations is the original signal and imaginary part is the FCQT of the real part, (2) imaginary part of eight FSAS representations is the original signal and real part is the FSQT of the real part, (3) like the GAS, Fourier spectrum of the all FSAS representations has only positive frequencies, however unlike the GAS, the real and imaginary parts of the proposed FSAS representations are not orthogonal to each other. The Fourier decomposition method (FDM) is an adaptive data analysis approach to decompose a signal into a set of small number of Fourier intrinsic band functions which are AM-FM components. This study also proposes a new formulation of the FDM using the discrete cosine transform (DCT) with the GAS and FSAS representations, and demonstrate its efficacy for improved time-frequency-energy representation and analysis of nonlinear and non-stationary time series.Comment: 22 pages, 13 figure

Analyzing Frequency Event Detection Algorithm Performance Using Different Denoising Methods

Maintaining grid frequency at its nominal value is crucial for power system stability and supply-demand balance. Swift and accurate detection of frequency events is vital for providing primary frequency response support. Frequency event detection algorithms often rely on Phasor Measurement Unit data, which may contain noise. Implementing a denoising preprocessing step enhances detection precision and accuracy. In previous works, a frequency event detection algorithm based on wavelet transform was developed, which uses discrete wavelet transform (DWT) for denoising purposes. In this paper, several denoising techniques are considered as potential replacements for the current DWT method. This research investigates and compares three denoising techniques: Fast Fourier Transform, Butterworth, and Simple Moving Average, as alternatives to DWT. Unlike other studies using metrics like Signal-to-Noise Ratio, Root Mean Square Error, and Percentage Root Mean Square Error, this research analyzes the impact of each denoising method on event detection performance and visually assesses pre- and post-denoised frequency data. The results highlight the effectiveness of the new denoising methods, suggesting them as optimal replacements for the DWT technique in terms of detection performance evaluation

A survey of uncertainty principles and some signal processing applications

The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and motivated by signal processing problems, from which significant advances have been made recently. Relations with sparse approximation and coding problems are emphasized

Optimal Representation of Anuran Call Spectrum in Environmental Monitoring Systems Using Wireless Sensor Networks

The analysis and classification of the sounds produced by certain animal species, notably anurans, have revealed these amphibians to be a potentially strong indicator of temperature fluctuations and therefore of the existence of climate change. Environmental monitoring systems using Wireless Sensor Networks are therefore of interest to obtain indicators of global warming. For the automatic classification of the sounds recorded on such systems, the proper representation of the sound spectrum is essential since it contains the information required for cataloguing anuran calls. The present paper focuses on this process of feature extraction by exploring three alternatives: the standardized MPEG-7, the Filter Bank Energy (FBE), and the Mel Frequency Cepstral Coefficients (MFCC). Moreover, various values for every option in the extraction of spectrum features have been considered. Throughout the paper, it is shown that representing the frame spectrum with pure FBE offers slightly worse results than using the MPEG-7 features. This performance can easily be increased, however, by rescaling the FBE in a double dimension: vertically, by taking the logarithm of the energies; and, horizontally, by applying mel scaling in the filter banks. On the other hand, representing the spectrum in the cepstral domain, as in MFCC, has shown additional marginal improvements in classification performance.University of Seville: Telefónica Chair "Intelligence Networks

Design of Acoustic Bifocal Lenses Using a Fourier-Based Algorithm

[EN] In this work, we develop a new design method based on fast Fourier transform (FFT) for implementing zone plates (ZPs) with bifocal focusing profiles. We show that the FFT of the governing binary sequence provides a discrete sequence of the same length, which indicates the location of the main foci at the ZP focusing profile. Then, using reverse engineering and establishing a target focusing profile, we are capable of generating a binary sequence that provides a ZP with the desired focusing profile. We show that this design method, based on the inverse fast Fourier transform (IFFT), is very flexible and powerful and allows to tailor the design of bifocal ZPs to achieve focusing profiles with the desired foci locations and resolutions. The key advantage of our design algorithm, compared to other alternatives presented in previous works, is that our method provides bifocal focusing profiles with an absolute control of the foci locations. Moreover, although we analyze the performance of this novel design algorithm for underwater ultrasonics, it can also be successfully extended to different fields of physics, such as optics or microwaves, where ZPs are widely employed.This work has been supported by the Spanish MICINN RTI2018-100792-B-I00 project and Generalitat Valenciana AICO/2020/139 project.Fuster Escuder, JM.; Pérez-López, S.; Candelas Valiente, P. (2021). Design of Acoustic Bifocal Lenses Using a Fourier-Based Algorithm. Sensors. 21(24):1-17. https://doi.org/10.3390/s21248285S117212

An Algorithm for the Continuous Morlet Wavelet Transform

This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet. The energy values of the Wavelet transform are compared with the power spectrum of the Fourier transform. Useful definitions for power spectra are given. The focus of the work is on simple measures to evaluate the transform with the Morlet wavelet in an efficient way. The use of the transform and the defined values is shown in some examples.Comment: 15 pages, 4 figures, revised for MSS