Parallel Iteration Method for Frequency Estimation Using Trigonometric Decomposition

The parallel iteration method for frequency estimation based on trigonometric decomposition is presented. First, the multi-frequency signal can be expressed in a matrix form based on the trigonometric decomposition, which implies a possibility to solve the nonlinear mapping functions of frequency estimation by a parallel iteration procedure. Then, frequency estimation with the minimized square errors is achieved by using the gradient-descent method in the parallel iteration procedure, which can effectively restrain the interferences from harmonics and noise. Finally, the workflow is shown, and the efficiency of the proposed method was demonstrated through computer simulations and experiments

Stepwise Iterative Fourier Transform: The SIFT

A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study

Demodulation of Spatial Carrier Images: Performance Analysis of Several Algorithms Using a Single Image

http://link.springer.com/article/10.1007%2Fs11340-013-9741-6#Optical full-field techniques have a great importance in modern experimental mechanics. Even if they are reasonably spread among the university laboratories, their diffusion in industrial companies remains very narrow for several reasons, especially a lack of metrological performance assessment. A full-field measurement can be characterized by its resolution, bias, measuring range, and by a specific quantity, the spatial resolution. The present paper proposes an original procedure to estimate in one single step the resolution, bias and spatial resolution for a given operator (decoding algorithms such as image correlation, low-pass filters, derivation tools ...). This procedure is based on the construction of a particular multi-frequential field, and a Bode diagram representation of the results. This analysis is applied to various phase demodulating algorithms suited to estimate in-plane displacements.GDR CNRS 2519 “Mesures de Champs et Identification en Mécanique des Solide

Investigation of Non-coherent Discrete Target Range Estimation Techniques for High-precision Location

Ranging is an essential and crucial task for radar systems. How to solve the range-detection problem effectively and precisely is massively important. Meanwhile, unambiguity and high resolution are the points of interest as well. Coherent and non-coherent techniques can be applied to achieve range estimation, and both of them have advantages and disadvantages. Coherent estimates offer higher precision but are more vulnerable to noise and clutter and phase wrap errors, particularly in a complex or harsh environment, while the non-coherent approaches are simpler but provide lower precision. With the purpose of mitigating inaccuracy and perturbation in range estimation, miscellaneous techniques are employed to achieve optimally precise detection. Numerous elegant processing solutions stemming from non-coherent estimate are now introduced into the coherent realm, and vice versa. This thesis describes two non-coherent ranging estimate techniques with novel algorithms to mitigate the instinct deficit of non-coherent ranging approaches. One technique is based on peak detection and realised by Kth-order Polynomial Interpolation, while another is based on Z-transform and realised by Most-likelihood Chirp Z-transform. A two-stage approach for the fine ranging estimate is applied to the Discrete Fourier transform domain of both algorithms. An N-point Discrete Fourier transform is implemented to attain a coarse estimation; an accurate process around the point of interest determined in the first stage is conducted. For KPI technique, it interpolates around the peak of Discrete Fourier transform profiles of the chirp signal to achieve accurate interpolation and optimum precision. For Most-likelihood Chirp Z-transform technique, the Chirp Z-transform accurately implements the periodogram where only a narrow band spectrum is processed. Furthermore, the concept of most-likelihood estimator is introduced to combine with Chirp Z-transform to acquire better ranging performance. Cramer-Rao lower bound is presented to evaluate the performance of these two techniques from the perspective of statistical signal processing. Mathematical derivation, simulation modelling, theoretical analysis and experimental validation are conducted to assess technique performance. Further research will be pushed forward to algorithm optimisation and system development of a location system using non-coherent techniques and make a comparison to a coherent approach

Least-Squares Wavelet Analysis and Its Applications in Geodesy and Geophysics

The Least-Squares Spectral Analysis (LSSA) is a robust method of analyzing unequally spaced and non-stationary data/time series. Although this method takes into account the correlation among the sinusoidal basis functions of irregularly spaced series, its spectrum still shows spectral leakage: power/energy leaks from one spectral peak into another. An iterative method called AntiLeakage Least-Squares Spectral Analysis (ALLSSA) is developed to attenuate the spectral leakages in the spectrum and consequently is used to regularize data series. In this study, the ALLSSA is applied to regularize and attenuate random noise in seismic data down to a certain desired level. The ALLSSA is subsequently extended to multichannel, heterogeneous and coarsely sampled seismic and related gradient measurements intended for geophysical exploration applications that require regularized (equally spaced) data free from aliasing effects. A new and robust method of analyzing unequally spaced and non-stationary time/data series is rigorously developed. This method, namely, the Least-Squares Wavelet Analysis (LSWA), is a natural extension of the LSSA that decomposes a time series into the time-frequency domain and obtains its spectrogram. It is shown through many synthetic and experimental time/data series that the LSWA supersedes all state-of-the-art spectral analyses methods currently available, without making any assumptions about or preprocessing (editing) the time series, or even applying any empirical methods that aim to adapt a time series to the analysis method. The LSWA can analyze any non-stationary and unequally spaced time series with components of low or high amplitude and frequency variability over time, including datum shifts (offsets), trends, and constituents of known forms, and by taking into account the covariance matrix associated with the time series. The stochastic confidence level surface for the spectrogram is rigorously derived that identifies statistically significant peaks in the spectrogram at a certain confidence level; this supersedes the empirical cone of influence used in the most popular continuous wavelet transform. All current state-of-the-art cross-wavelet transforms and wavelet coherence analyses methods impose many stringent constraints on the properties of the time series under investigation, requiring, more often than not, preprocessing of the raw measurements that may distort their content. These methods cannot generally be used to analyze unequally spaced and non-stationary time series or even two equally spaced time series of different sampling rates, with trends and/or datum shifts, and with associated covariance matrices. To overcome the stringent requirements of these methods, a new method is developed, namely, the Least-Squares Cross-Wavelet Analysis (LSCWA), along with its statistical distribution that requires no assumptions on the series under investigation. Numerous synthetic and geoscience examples establish the LSCWA as the method of methods for rigorous coherence analysis of any experimental series