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In order to measure the quality of the logs, one can with help of Fast Fourier Transform technique get the signals resonance peaks. With help of these peaks you can see whether the quality of a tree is good or bad. This report contains the work of a where a program has been developed to be able to process a vibration created by an automatic hammer hitting on a log of wood. From the processed signal the program should be able to show both the raw wavesignal and the processed measured data from the resonance peaks. Beyond the raw wavesignal and resonance peaks the program should also be able to control the automatic hammer. The goal with the project is to have a program that get the same measure results as an already functioning measuring equipment. The result was a success when with the help of the program you were both able to control the hammer, measure the results and save the data with an accurate results.

This thesis is concerned with various aspects of stationary and nonstationary time series analysis. In the nonstationary case, we study estimation of the Wold-Cram'er evolutionary spectrum, which is a time-dependent analogue of the spectrum of a stationary process. Existing estimators of the Wold-Cram'er evolutionary spectrum suffer from several problems, including bias in boundary regions of the time-frequency plane, poor frequency resolution, and an inability to handle the presence of purely harmonic frequencies. We propose techniques to handle all three of these problems. We propose a new estimator of the Wold-Cram'er evolutionary spectrum (the BCMTFSE) which mitigates the first problem. Our estimator is based on an extrapolation of the Wold-Cram'er evolutionary spectrum in time, using an estimate of its time derivative. We apply our estimator to a set of simulated nonstationary processes with known Wold-Cram'er evolutionary spectra to demonstrate its performance. We also propose an estimator of the Wold-Cram'er evolutionary spectrum, valid for uniformly modulated processes (UMPs). This estimator mitigates the second problem, by exploiting the structure of UMPs to improve the frequency resolution of the BCMTFSE. We apply this estimator to a simulated UMP with known Wold-Cram'er evolutionary spectrum. To deal with the third problem, one can detect and remove purely harmonic frequencies before applying the BCMTFSE. Doing so requires a consideration of the aliasing problem. We propose a frequency-domain technique to detect and unalias aliased frequencies in bivariate time series, based on the observation that aliasing manifests as nonlinearity in the phase of the complex coherency between a stationary process and a time-delayed version of itself. To illustrate this ``unaliasing'' technique, we apply it to simulated data and a real-world example of solar noon flux data. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-02-05 10:18:13.476

Thesis (M.S.)--Brigham Young University. Dept. of Audiology and Speech-Language Pathology, 2005. / Includes bibliographical references (p. 40-45).

The ability to probe molecular electronic and vibrational structures gives rise to optical absorption spectroscopy, which is a credible tool used in molecular quantification and classification with high sensitivity, low limit of detection (LoD), and immunity to electromagnetic noises. Spectra are sensitive to slight analyte variations, so they are often used to identify a sample’s components. This thesis proposes several methods for quick classification and quantification of analysts based on their absorbance spectra. functional Principal Component Analysis (fPCA) is employed for feature extraction and dimension reduction. For 1,000-pixel spectra data, fPCA can capture the majority variance with as few output scores as the number of expected analytes. This reduces the amount of calculation required for the following machine learning algorithms. Further, the output scores are fed into XGBoost and logistic regression for classification, and fed into XGBoost and linear regression for quantification. Our models were tested on both synthesized datasets and experimentally acquired dataset. Our models demonstrated similar performance compared to deep learning but with much faster processing speeds. For the synthesized 30 dB dataset, our model XGBoost with fPCA could reach a micro-averaged f1 score of 0.9551 ± 0.0008, while FNN-OT [1] could obtain 0.940±0.001. fPCA helped the algorithms extract the feature of each analyte; furthermore, the output scores nearly had a linear relationship with their concentrations. It was much easier for the algorithm to find the mapping function between the inputs and the outputs with fPCA, which shortened the training and testing time. / Graduate

Spectral density function (SDF) plays a critical role in spatio-temporal data analysis, where the data are analyzed in the frequency domain. Although many methods have been proposed for SDF estimation, real-world applications in many research fields, such as neuroscience and environmental science, call for better methodologies. In this thesis, we focus on the spectral density functions for time series and spatial data, develop new estimation algorithms, and use the estimators as features for clustering and classification purposes. The first topic is motivated by clustering electroencephalogram (EEG) data in the spectral domain. To identify synchronized brain regions that share similar oscillations and waveforms, we develop two robust clustering methods based on the functional data ranking of the estimated SDFs. The two proposed clustering methods use different dissimilarity measures and their performance is examined by simulation studies in which two types of contaminations are included to show the robustness. We apply the methods to two sets of resting-state EEG data collected from a male college student. Then, we propose an efficient collective estimation algorithm for a group of SDFs. We use two sets of basis functions to represent the SDFs for dimension reduction, and then, the scores (the coefficients of the basis) estimated by maximizing the penalized Whittle likelihood are used for clustering the SDFs in a much lower dimension. For spatial data, an additional penalty is applied to the likelihood to encourage the spatial homogeneity of the clusters. The proposed methods are applied to cluster the EEG data and the soil moisture data. Finally, we propose a parametric estimation method for the quantile spectrum. We approximate the quantile spectrum by the ordinary spectral density of an AR process at each quantile level. The AR coefficients are estimated by solving Yule- Walker equations using the Levinson algorithm. Numerical results from simulation studies show that the proposed method outperforms other conventional smoothing techniques. We build a convolutional neural network (CNN) to classify the estimated quantile spectra of the earthquake data in Oklahoma and achieve a 99.25% accuracy on testing sets, which is 1.25% higher than using ordinary periodograms.

<p> Walsh functions are defined both by recursive and non-r~cursive equations. A synopsis is given of the properties of Walsh functions relevant to this thesis. Two algorithms for simple evaluation of an arbitrary point on a Walsh function that use only the binary codes for the parameters of the Walsh function result from the non-r~cursive definitions. Direct hardware implementation of the evaluation algorithms yields programmable digital Halsh function generators. One of the generators, which produces functions that are free of hazards or ambigious states, is modified to produce a parallel array of Walsh functions. This generator is used in a Walsh Spectral Analyzer that evaluates simultaneously several Walsh series coefficients of an input signal. </p> <p> Walsh series analysis and the concepts of the design of a digital Walsh Spectral Analyzer are discussed. The equation that is used to determine a Walsh series coefficient is modified so that each portion of the equation can be manipulated conveniently by a digital instrument. Although the instrument was designed primarily to analyze periodic waves, extensions to the design can be made to accommodate aperiodic signals. Signals with frequencies from the audio range downwards can be analyzed by the Walsh Spectral Analyzer. </p> <p> Walsh series to Fourier series conversion is dealt with. It has been found that the Fourier coefficients of signals that are limited either in frequency or in sequency can be evaluated precisely using a finite number of Walsh coefficients of the same signal. A dual relationship holds for Fourier to Walsh series conversion. The Fourier series coefficients of Walsh functions comprise part of the conversion relationships. The Fourier transforms of Walsh functions, from which the above coefficients can be obtained, are derived in non-recursive form. </p> / Thesis / Doctor of Philosophy (PhD)

Yes / We develop a novel approach to estimate the n unknown constituent frequencies of a noiseless signal that comprises of unknown number, n, of sinusoids of unknown phases and unknown amplitudes. The new two way approach uses two constraints to accurately estimate the unknown frequencies of the sinusoidal components in a signal. The new approach serves as a verification test for the estimated unknown frequencies through the estimated count of the unknown number of frequencies. The Hankel matrix, of the time domain samples of the signal, is used as a basis for further analysis in the Pisarenko harmonic decomposition. The new constraints, the Existence Factor (EF) and the Component Factor (CF), have been introduced in the methodology based on the relationships between the components of the sinusoidal signal and the eigenspace of the Hankel matrix. The performance of the developed approach has been tested to correctly estimate any number of frequencies within a signal with or without a fixed unknown bias. The method has also been tested to accurately estimate the very closely spaced low frequencies. / Innovate UK

There has been in the past and still is controversy over the genesis of the third heart sound (S3). Recent studies, strongly suggest that S3 is a manifestation of a sudden intrinsic limitation in the expansion of the left ventricle. The thesis has aimed to explore that hypothesis further using combined echocardiographic and spectral analysis techniques. Spectral analysis was carried out via conventional fast fourier transform methods and the maximum entropy method. The efficacy of these techniques, in relation to clinical and scientific application, was explored further. Briefly discussed was the application of autoregressive-moving average (ARMA) modelling for spectral analysis of S3, in relation to further work. Following is a brief synopsis of the thesis: CHAPTER 1 This gives an historical and general introduction to heart sound analysis. Discussed briefly is the physiology of the heart and heart sounds and the diagnostic implications of S3 analysis. CHAPTER 2 Here is discussed the instrumentation system used and phonocardiographic and echocardiographic data aquisition. Data preprocessing and storage is also covered. CHAPTER 3 In this chapter the application of a FFT method and correlation of resultant spectral parameters with echocardiographic parameters is reported. CHAPTER 4 The theoretical development of the maximum entropy technique (based on published papers and expanded) is discussed here. Numerical experiments with the method and associated problems are also discussed. CHAPTER 5 The MEM is applied to the spectral analysis of S3 and compared with the FFT method. Correlation analysis of MEM derived spectral parameters with echocardiograhic data is performed. CHAPTER 6 Here ARMA modelling and application to further work is discussed. An ARMA model from the maxixum entropy coefficients is derived. The application of this model to the deconvolution of the chest wall transfer function is discussed as an approach for further work. / Thesis (M.Sc.)--School of Mathematical Sciences, 1989.

There has been in the past and still is controversy over the genesis of the third heart sound (S3). Recent studies, strongly suggest that S3 is a manifestation of a sudden intrinsic limitation in the expansion of the left ventricle. The thesis has aimed to explore that hypothesis further using combined echocardiographic and spectral analysis techniques. Spectral analysis was carried out via conventional fast fourier transform methods and the maximum entropy method. The efficacy of these techniques, in relation to clinical and scientific application, was explored further. Briefly discussed was the application of autoregressive-moving average (ARMA) modelling for spectral analysis of S3, in relation to further work. Following is a brief synopsis of the thesis: CHAPTER 1 This gives an historical and general introduction to heart sound analysis. Discussed briefly is the physiology of the heart and heart sounds and the diagnostic implications of S3 analysis. CHAPTER 2 Here is discussed the instrumentation system used and phonocardiographic and echocardiographic data aquisition. Data preprocessing and storage is also covered. CHAPTER 3 In this chapter the application of a FFT method and correlation of resultant spectral parameters with echocardiographic parameters is reported. CHAPTER 4 The theoretical development of the maximum entropy technique (based on published papers and expanded) is discussed here. Numerical experiments with the method and associated problems are also discussed. CHAPTER 5 The MEM is applied to the spectral analysis of S3 and compared with the FFT method. Correlation analysis of MEM derived spectral parameters with echocardiograhic data is performed. CHAPTER 6 Here ARMA modelling and application to further work is discussed. An ARMA model from the maxixum entropy coefficients is derived. The application of this model to the deconvolution of the chest wall transfer function is discussed as an approach for further work. / Thesis (M.Sc.)--School of Mathematical Sciences, 1989.