Interpolated-DFT-Based Fast and Accurate Amplitude and Phase Estimation for the Control of Power

The quality of energy produced in renewable energy systems has to be at the high level specified by respective standards and directives. The estimation accuracy of grid signal parameters is one of the most important factors affecting this quality. This paper presents a method for a very fast and accurate amplitude and phase grid signal estimation using the Fast Fourier Transform procedure and maximum decay sidelobes windows. The most important features of the method are the elimination of the impact associated with the conjugate's component on the results and the straightforward implementation. Moreover, the measurement time is very short - even far less than one period of the grid signal. The influence of harmonics on the results is reduced by using a bandpass prefilter. Even using a 40 dB FIR prefilter for the grid signal with THD = 38%, SNR = 53 dB and a 20-30% slow decay exponential drift the maximum error of the amplitude estimation is approximately 1% and approximately 0.085 rad of the phase estimation in a real-time DSP system for 512 samples. The errors are smaller by several orders of magnitude for more accurate prefilters.Comment: in Metrology and Measurement Systems, 201

A hybrid phase-based single frequency estimator

The topic of low computational complexity frequency estimation of a single complex sinusoid corrupted by additive white Gaussian noise has received significant attention over the last decades due to the wide applicability of such estimators in a variety of fields. In this letter, we propose a computationally fast and statistically improved hybrid phase-based estimator that outperforms other recently proposed approaches, lowering the signal-to-noise ratio at which the Cramér–Rao lower bound is closely followed

Characterizing Signal Loss in the 21 cm Reionization Power Spectrum: A Revised Study of PAPER-64

The Epoch of Reionization (EoR) is an uncharted era in our Universe's history during which the birth of the first stars and galaxies led to the ionization of neutral hydrogen in the intergalactic medium. There are many experiments investigating the EoR by tracing the 21cm line of neutral hydrogen. Because this signal is very faint and difficult to isolate, it is crucial to develop analysis techniques that maximize sensitivity and suppress contaminants in data. It is also imperative to understand the trade-offs between different analysis methods and their effects on power spectrum estimates. Specifically, with a statistical power spectrum detection in HERA's foreseeable future, it has become increasingly important to understand how certain analysis choices can lead to the loss of the EoR signal. In this paper, we focus on signal loss associated with power spectrum estimation. We describe the origin of this loss using both toy models and data taken by the 64-element configuration of the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER). In particular, we highlight how detailed investigations of signal loss have led to a revised, higher 21cm power spectrum upper limit from PAPER-64. Additionally, we summarize errors associated with power spectrum error estimation that were previously unaccounted for. We focus on a subset of PAPER-64 data in this paper; revised power spectrum limits from the PAPER experiment are presented in a forthcoming paper by Kolopanis et al. (in prep.) and supersede results from previously published PAPER analyses.Comment: 25 pages, 18 figures, Accepted by Ap

Modified fast frequency acquisition via adaptive least squares algorithm

A method and the associated apparatus for estimating the amplitude, frequency, and phase of a signal of interest are presented. The method comprises the following steps: (1) inputting the signal of interest; (2) generating a reference signal with adjustable amplitude, frequency and phase at an output thereof; (3) mixing the signal of interest with the reference signal and a signal 90 deg out of phase with the reference signal to provide a pair of quadrature sample signals comprising respectively a difference between the signal of interest and the reference signal and a difference between the signal of interest and the signal 90 deg out of phase with the reference signal; (4) using the pair of quadrature sample signals to compute estimates of the amplitude, frequency, and phase of an error signal comprising the difference between the signal of interest and the reference signal employing a least squares estimation; (5) adjusting the amplitude, frequency, and phase of the reference signal from the numerically controlled oscillator in a manner which drives the error signal towards zero; and (6) outputting the estimates of the amplitude, frequency, and phase of the error signal in combination with the reference signal to produce a best estimate of the amplitude, frequency, and phase of the signal of interest. The preferred method includes the step of providing the error signal as a real time confidence measure as to the accuracy of the estimates wherein the closer the error signal is to zero, the higher the probability that the estimates are accurate. A matrix in the estimation algorithm provides an estimate of the variance of the estimation error

Enhancing the Instantaneous Dynamic Range of Electronic Warfare Receivers Using Statistical Signal Processing

Accurately processing multiple, time-coincident signals presents a challenge to Electronic Warfare (EW) receivers, especially if the signals are close in frequency and/or mismatched in amplitude. The metric that quantifies an EW receiver\u27s ability to measure time-coincident signals is the Instantaneous Dynamic Range (IDR), defined for a given frequency estimation accuracy, a given frequency separation and a given SNR as the maximum signal amplitude ratio that can be accommodated. Using a two sinusoid time-series model, this thesis analyzes IDR for ideal intercept and parametric digital EW receivers. In general, the number of signals contained in the EW receiver measurement interval is unknown. Thus, the non-parametric Discrete Fourier Transform (DFT) is employed in an EW intercept receiver with the associated amplitude dependent spectral leakage which limits IDR. A novel method to improve the DFT-based intercept receiver IDR by compensating for the high amplitude signal\u27s spectral leakage using computationally efficient 3 bin interpolation algorithms is proposed and analyzed. For a desired frequency estimation accuracy of 1.5 bins, the method achieves an IDR of 57 dB with little frequency separation dependence when the signals are separated by more than 2 bins with a low amplitude signal SNR of 10 dB. For situations where the number of signals contained in the measurement interval is known, the IDR of an Iterative Generalized Least Squares (IGLS) algorithm-based parametric receiver is analyzed. A real and complex signal IDR Cramer-Rao Bound (IDR-CRB) is derived for parametric receivers by extending results contained in Rife. For tight frequency estimate requirements (these requirements depend on the number of measurement samples), the IDR-CRB yields achievable bounds. For less stringent frequency estimate requirements, the IDR-CRB is unrealisti

SDPLL-Based Frequency Estimation of a Sinusoid in Colored Noise

The problem of frequency estimation of a single sinusoid observed in colored noise is addressed. Our estimator is based on the operation of the sinusoidal digital phase-locked loop (SDPLL) which carries the frequency information in its phase error after the noisy sinusoid has been acquired by the SDPLL. We show by computer simulations that this frequency estimator beats the Cramer-Rao bound (CRB) on the frequency error variance for moderate and high SNRs when the colored noise has a general low-pass filtered (LPF) characteristic, thereby outperforming, in terms of frequency error variance, several existing techniques some of which are, in addition, computationally demanding. Moreover, the present approach generalizes on existing work that addresses different methods of sinusoid frequency estimation involving specific colored noise models such as the moving average (MA) noise model. An insightful theoretical analysis is presented to support the practical findings