Frequency Tracking and Parameter Estimation for Robust Quantum State-Estimation

In this paper we consider the problem of tracking the state of a quantum system via a continuous measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state-estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequencyComment: 6 figures, 13 page

Burg algorithm for enhancing measurement performance in wavelength scanning interferometry

Wavelength scanning interferometry (WSI) is a technique for measuring surface topography that is capable of resolving step discontinuities and does not require any mechanical movement of the apparatus or measurand, allowing measurement times to be reduced substantially in comparison to related techniques. The axial (height) resolution and measurement range in WSI depends in part on the algorithm used to evaluate the spectral interferograms. Previously reported Fourier transform based methods have a number of limitations which is in part due to the short data lengths obtained. This paper compares the performance auto-regressive model based techniques for frequency estimation in WSI. Specifically, the Burg method is compared with established Fourier transform based approaches using both simulation and experimental data taken from a WSI measurement of a step-height sample

SARAS 2: A Spectral Radiometer for probing Cosmic Dawn and the Epoch of Reionization through detection of the global 21 cm signal

The global 21 cm signal from Cosmic Dawn (CD) and the Epoch of Reionization (EoR), at redshifts $z \sim 6-30$, probes the nature of first sources of radiation as well as physics of the Inter-Galactic Medium (IGM). Given that the signal is predicted to be extremely weak, of wide fractional bandwidth, and lies in a frequency range that is dominated by Galactic and Extragalactic foregrounds as well as Radio Frequency Interference, detection of the signal is a daunting task. Critical to the experiment is the manner in which the sky signal is represented through the instrument. It is of utmost importance to design a system whose spectral bandpass and additive spurious can be well calibrated and any calibration residual does not mimic the signal. SARAS is an ongoing experiment that aims to detect the global 21 cm signal. Here we present the design philosophy of the SARAS 2 system and discuss its performance and limitations based on laboratory and field measurements. Laboratory tests with the antenna replaced with a variety of terminations, including a network model for the antenna impedance, show that the gain calibration and modeling of internal additives leave no residuals with Fourier amplitudes exceeding 2~mK, or residual Gaussians of 25 MHz width with amplitudes exceeding 2~mK. Thus, even accounting for reflection and radiation efficiency losses in the antenna, the SARAS~2 system is capable of detection of complex 21-cm profiles at the level predicted by currently favoured models for thermal baryon evolution.Comment: 44 pages, 17 figures; comments and suggestions are welcom

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

Time-frequency Signature Sparse Reconstruction using Chirp Dictionary

This paper considers local sparse reconstruction of time-frequency signatures of windowed non-stationary radar returns. These signals can be considered instantaneously narrow-band, thus the local time-frequency behaviour can be recovered accurately with incomplete observations. The typically employed sinusoidal dictionary induces competing requirements on window length. It confronts converse requests on the number of measurements for exact recovery, and sparsity. In this paper, we use chirp dictionary for each window position to determine the signal instantaneous frequency laws. This approach can considerably mitigate the problems of sinusoidal dictionary, and enable the utilization of longer windows for accurate time-frequency representations. It also reduces the picket fence by introducing a new factor, the chirp rate . Simulation examples are provided, demonstrating the superior performance of local chirp dictionary over its sinusoidal counterpart

Two-dimensional spectrum estimation using the radon transform

An alternative approach to two-dimensional power spectrum estimation incorporating the Radon transform in conjunction with each of the one-dimensional periodogram, Blackman-Tukey, and Autoregressive parameter estimation algorithms is examined. The Radon transform is used to express a two-dimensional data set in terms of its projections onto a set of one-dimensional radial lines, effectively reducing the two-dimensional estimation problem to a series of one-dimensional problems. The resulting two-dimensional power spectrum estimates are compared to the known power spectra for a variety of data types. The Radon transform approach combined with autoregressive parameter estimation can provide a high-resolution power spectrum estimate, effectively surpassing the resolution limitations of the Fourier methods without the cumbersome implementations of the more direct high resolution estimation methods in two dimensions

Sound Source Separation

This is the author's accepted pre-print of the article, first published as G. Evangelista, S. Marchand, M. D. Plumbley and E. Vincent. Sound source separation. In U. Zölzer (ed.), DAFX: Digital Audio Effects, 2nd edition, Chapter 14, pp. 551-588. John Wiley & Sons, March 2011. ISBN 9781119991298. DOI: 10.1002/9781119991298.ch14file: Proof:e\EvangelistaMarchandPlumbleyV11-sound.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:e\EvangelistaMarchandPlumbleyV11-sound.pdf:PDF owner: markp timestamp: 2011.04.2