There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Real and Complex Analysis

Ultra Wideband Signals and Systems in Communication Engineering

This is a book review of 'The Micro-Doppler Effect in Radar' by V. C. Chen. Artech House, 16 Sussex Street, London, SW1V 4RW, UK. 2011. 290pp + diskette. Illustrated. £90. ISBN 978-1-60807-057-2.

'The Micro-Doppler Effect in Radar' by V.C. Chen

The authors introduce an iterative algorithm, called matching demodulation transform (MDT), to generate a time-frequency (TF) representation with satisfactory energy concentration. As opposed to conventional TF analysis methods, this algorithm does not have to devise ad-hoc parametric TF dictionary. Assuming the FM law of a signal can be well characterized by a determined mathematical model with reasonable accuracy, the MDT algorithm can adopt a partial demodulation and stepwise refinement strategy for investigating TF properties of the signal. The practical implementation of the MDT involves an iterative procedure that gradually matches the true instantaneous frequency (IF) of the signal. Theoretical analysis of the MDT's performance is provided, including quantitative analysis of the IF estimation error and the convergence condition. Moreover, the MDT-based synchrosqueezing algorithm is described to further enhance the concentration and reduce the diffusion of the curved IF profile in the TF representation of original synchrosqueezing transform. The validity and practical utility of the proposed method are demonstrated by simulated as well as real signal.

Matching Demodulation Transform and SynchroSqueezing in Time-Frequency Analysis

A compressive sensing (CS) approach for nonstationary signal separation is proposed. This approach is motivated by challenges in radar signal processing, including separations of micro-Doppler and main body signatures. We consider the case where the signal of interest assumes sparse representation over a given basis. Other signals present in the data overlap with the desired signal in the time and frequency domains, disallowing conventional windowing or filtering operations to be used for desired signal recovery. The proposed approach uses linear time-frequency representations to reveal the data local behavior. Using the L-statistics, only the time-frequency (TF) points that belong to the desired signal are retained, whereas the common points and others pertaining only to the undesired signals are deemed inappropriate and cast as missing samples. These samples amount to reduced frequency observations in the TF domain. The linear relationship between the measurement and sparse domains permits the application of CS techniques to recover the desired signal without significant distortion. We focus on sinusoidal desired signals with sparse frequency-domain representation but show that the analysis can be straightforwardly generalized to nonsinusoidal signals with known structures. Several examples are provided to demonstrate the effectiveness of the proposed approach.

Compressive Sensing Based Separation of Nonstationary and Stationary Signals Overlapping in Time-Frequency

Fast communication: An automated signal reconstruction method based on analysis of compressive sensed signals in noisy environment

A new approach for classification of human gait based on time-frequency feature representations

Multimedia signals include different data types (text, sound, graphics, picture, animations, video, etc.), which can be time-dependent (sound, video and animation) or spatially-dependent (images, text and graphics). Hence, the multimedia systems represent an interdisciplinary cross-section of the following areas: digital signal processing, computer architecture, computer networks and telecommunications. Multimedia Signals and Systems is an introductory text, designed for students or professionals and researchers in other fields, with a need to learn the basics of signals and systems. A considerable emphasis is placed on the analysis and processing of multimedia signals (audio, images, video). Additionally, the book connects these principles to other important elements of multimedia systems such as the analysis of optical media, computer networks, QoS, and digital watermarking.

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Multimedia Signals and Systems

The L-estimate transforms and time-frequency representations are presented within the framework of compressive sensing. The goal is to recover signal or local auto-correlation function samples corrupted by impulse noise. The signal is assumed to be sparse in a transform domain or in a joint-variable representation. Unlike the standard L-statistics approach, which suffers from degraded spectral characteristics due to the omission of samples, the compressive sensing in combination with the L-estimate permits signal reconstruction that closely approximates the noise free signal representation.

Irena Orovic

Papers

Compressive Sensing Based Separation of Nonstationary and Stationary Signals Overlapping in Time-Frequency

Fast communication: An automated signal reconstruction method based on analysis of compressive sensed signals in noisy environment

A new approach for classification of human gait based on time-frequency feature representations

Multimedia Signals and Systems

Robust Time-Frequency Analysis Based on the L-Estimation and Compressive Sensing