Andjela Draganic

Time-Frequency Analysis and Singular Value Decomposition Applied to the Highly Multicomponent Musical Signals

An algorithm for decomposition of highly multicomponent signals, with variable components energy, has been proposed. The algorithm combines the singular value decomposition with the suitable time-frequency analysis approach. The auto-correlation matrix is obtained by applying the inverse form of the cross-terms free time-frequency distribution. The decomposition of the time-frequency based auto-correlation matrix produces vectors that correspond to the individual signal components. The efficiency of the proposed algorithm has been tested on different signals.

Compressive Sensing as a watermarking attack

The performance of watermark detection under Compressive Sensing (CS) attack is analyzed in the paper. Watermark is created as a pseudorandom sequence and it is embedded into the DCT image coefficients. CS, as method that provides reconstruction of the signals with small number of samples, is used as watermarking attack. Reconstruction procedure assumes certain number of low frequency DCT coefficients, as well as certain number of randomly chosen middle and high frequency DCT coefficients. It is shown that CS can provide good quality image reconstruction with reduced number of samples and, at the same time, to remove the watermark. The theory is supported by experimental results.

Blind signals separation in wireless communications based on Compressive Sensing

The algorithm for separation of signals from two different wireless standards (Bluetooth and IEEE 802.11b standard), operating within the same frequency band is proposed in this paper. The components separation is performed using the time-frequency representation and the concept of Compressive Sensing. Knowing the signals nature, it is possible to select just a small set of time-frequency points that entirely belongs to the IEEE 802.11b signal. These points are extracted from the original time-frequency representation and are used to recover the full signal by using Compressive Sensing method. Once when the components of IEEE 802.11b signal are known, it is possible to reconstruct the remaining components in the band, belonging to the Bluetooth signal. Unlike the conventional separation methods, such as windowing or filtering, this approach works well even in the case of overlapping signals as well. The theory is proved with experimental results.

FHSS signal characterization based on the crossterms free time-frequency distributions

The application of the Cohen class time-frequency distributions has been considered for the analysis of signals in wireless communications. Several distributions are considered: spectrogram, Wigner-Ville, S-method, Born-Jordan, Choi-Williams, rectangular and Gaussian kernel based distribution. The possibility of using time-frequency distributions in decomposition of multicomponent wireless signals is examined. The signal separation procedure is based on eigenvalues and eigenvectors decomposition. Time duration and frequency range are estimated after the separation for each signal component. The theory is supported by the experimental results.

An approach to classification and under-sampling of the interfering wireless signals

Abstract Classification of interfering signals that belong to different wireless standards is important topic in wireless communications. In this paper, we propose a procedure for separation and classification of wireless signals belonging to the Bluetooth and to the IEEE 802.11b standards. These signals operate in the same frequency band and may interfere with each other. The procedure is made of a few steps. In the first step, the separation of signal components is done using the eigenvalue decomposition approach. The second stage is based on the compressive sensing approach, used to reduce the number of transmitted samples. A suitable transform domain is chosen for each separated component using l 1 -norm as a measure of sparsity. Since the Bluetooth signals are less sparse compared to the IEEE 802.11b signals, after choosing sparse domain, additional sparsification needs to performed to further enhance the sparsity. In the last step of the procedure, the classification is performed by observing the time-frequency characteristics of the reconstructed separated components. The theory is proved by the experimental results.

Reconstruction and classification of wireless signals based on compressive sensing approach

The procedure for the classification and reconstruction of randomly under-sampled signals transmitted through the communication channel, is proposed in this paper. The focus of this work is on the wireless communication signals that operate in the same frequency band and may interfere with each other. In the first stage, the separation of signal components is done by applying the concept of eigenvalue decomposition. Next, the compressive sensing approach is used to reduce the number of transmitted samples and to provide accurate signal reconstruction upon transmission. In the last step, the classification is done by observing the time-frequency characteristics of reconstructed separated components. The theory is proved by the experimental results.

An analysis of CS algorithms efficiency for sparse communication signals reconstruction

As need for increasing the speed and accuracy of the real applications is constantly growing, the new algorithms and methods for signal processing are intensively developing. Traditional sampling approach based on Sampling theorem is, in many applications, inefficient because of production a large number of signal samples. Generally, small number of significant information is presented within the signal compared to its length. Therefore, the Compressive Sensing method is developed as an alternative sampling strategy. This method provides efficient signal processing and reconstruction, without need for collecting all of the signal samples. Signal is sampled in a random way, with number of acquired samples significantly smaller than the signal length. In this paper, the comparison of the several algorithms for Compressive Sensing reconstruction is presented. The one dimensional band-limited signals that appear in wireless communications are observed and the performance of the algorithms in non-noisy and noisy environments is tested. Reconstruction errors and execution times are compared between different algorithms, as well.

A Virtual Instrument for Compressive Sensing of multimedia signals

Compressive Sensing (CS) is currently a very popular signal acquisition approach. It provides an alternative way of signal sampling which is based on a small random set of measurements. The entire signal can be reconstructed from the measurements with high accuracy by using very complex mathematical algorithms if the certain conditions are met. Various algorithms for CS reconstruction have been proposed for different types of signals and different application requirements. In this paper, several commonly used algorithms for one-dimensional (1D) and two-dimensional (2D) signals reconstruction are implemented within the Virtual Instrument for CS signals reconstruction. The Virtual Instrument is a user-friendly tool that provides efficient analysis of signals, using different algorithms and variety of options and parameters. It includes different multimedia test signals (both 1D and 2D signals), but also there is an option for user-defined signals.

A unified approach for the estimation of instantaneous frequency and its derivatives for non-stationary signals analysis

A unified approach for the estimation of the first three phase derivatives of non-stationary signals is proposed in this paper. The possibility to accurately estimate phase derivatives is important in many applications dealing with objects velocity, acceleration and acceleration rate, such as the radar applications and mechanics. The estimation approach is based on definition of the complex-lag distribution. The proposed distribution is inspired by the concepts of complex analysis theory. The general form of distribution for the estimation of the first, second and third derivative of the phase is derived from the specific individual cases. The theoretical considerations are illustrated in the example with fast varying signal phase function.

FHSS signal sparsification in the Hermite transform domain

Signal sparsity is exploited in various signal processing approaches. The applicability ranges from compression, signal classification, coding, etc. Finding a suitable basis where the signal exhibits a compact (sparse) support is a challenging task and the result mainly depends on the signal nature. In this paper, we observed sinusoidally modulated signals appearing in wireless communications, namely the FHSS signals. As a sparsity domain, the Hermite transform domain is considered. The Hermite basis functions resemble the shapes of the FHSS signal components, and therefore these are considered as suitable for compact representation. In order to improve the sparsity of the observed signal components, we propose to employ a procedure for the Hermite transform optimization. As a result, the discrete Hermite functions better fit the signal components, producing just negligible errors between the original and optimized signal. The theory is verified by the experimental results. The procedure is tested on synthetic FHSS signal.