Analysis and decomposition of frequency modulated multicomponent signals

Frequency modulated (FM) signals are studied in many research fields, including seismology, astrophysics, biology, acoustics, animal echolocation, radar and sonar. They are referred as multicomponent signals (MCS), as they are generally composed of multiple waveforms, with specific time-dependent frequencies, known as instantaneous frequencies (IFs). Many applications require the extraction of signal characteristics (i.e. amplitudes and IFs). that is why MCS decomposition is an important topic in signal processing. It consists of the recovery of each individual mode and it is often performed by IFs separation. The task becomes very challenging if the signal modes overlap in the TF domain, i.e. they interfere with each other, at the so-called non-separability region. For this reason, a general solution to MCS decomposition is not available yet. As a matter of fact, the existing methods addressing overlapping modes share the same limitations: they are parametric, therefore they adapt only to the assumed signal class, or they rely on signal-dependent and parametric TF representations; otherwise, they are interpolation techniques, i.e. they almost ignore the information corrupted by interference and they recover IF curve by some fitting procedures, resulting in high computational cost and bad performances against noise. This thesis aims at overcoming these drawbacks, providing efficient tools for dealing with MCS with interfering modes. An extended state-of-the-art revision is provided, as well as the mathematical tools and the main definitions needed to introduce the topic. Then, the problem is addressed following two main strategies: the former is an iterative approach that aims at enhancing MCS' resolution in the TF domain; the latter is a transform-based approach, that combines TF analysis and Radon Transform for separating individual modes. As main advantage, the methods derived from both the iterative and the transform-based approaches are non-parametric, as they do not require specific assumptions on the signal class. As confirmed by the experimental results and the comparative studies, the proposed approach contributes to the current state of the-art improvement

Radon spectrogram-based approach for automatic IFs separation

The separation of overlapping components is a well-known and difficult problem in multicomponent signals analysis and it is shared by applications dealing with radar, biosonar, seismic, and audio signals. In order to estimate the instantaneous frequencies of a multicomponent signal, it is necessary to disentangle signal modes in a proper domain. Unfortunately, if signal modes supports overlap both in time and frequency, separation is only possible through a parametric approach whenever the signal class is a priori fixed. In this work, time-frequency analysis and Radon transform are jointly used for the unsupervised separation of modes of a generic frequency modulated signal in noisy environment. The proposed method takes advantage of the ability of the Radon transform of a proper time-frequency distribution in separating overlapping modes. It consists of a blind segmentation of signal components in Radon domain by means of a near-to-optimal threshold operation. The inversion of the Radon transform on each detected region allows us to isolate the instantaneous frequency curves of each single mode in the time-frequency domain. Experimental results performed on constant amplitudes chirp signals confirm the effectiveness of the proposed method, opening the way for its extension to more complex frequency modulated signals

A signal complexity-based approach for AM–FM signal modes counting

I segnali modulati in frequenza appaiono in molte discipline applicate, tra cui la geologia, la comunicazione, la biologia e l'acustica. Questi sono multicomponenti, cioè consistono in forme d'onda multiple, con frequenza specifica dipendente dal tempo (frequenza istantanea). Nella maggior parte delle applicazioni pratiche, il numero di modalità - che è sconosciuto - è necessario per analizzare correttamente un segnale; per esempio per separare ogni singolo componente e per stimare la sua frequenza istantanea. Il rilevamento del numero di componenti è un problema impegnativo, specialmente nel caso di modalità che interferiscono. L'approccio basato sull'entropia di Rényi si è dimostrato adatto per il conteggio delle modalità di un segnale, ma è limitato a componenti ben separate. Il presente documento affronta questo problema introducendo una nuova nozione di complessità del segnale. In particolare, lo spettrogramma di un segnale multicomponente è visto come un processo non stazionario in cui l'interferenza si alterna alla non interferenza. La complessità relativa alla transizione tra sezioni consecutive dello spettrogramma viene valutata mediante la Run Length Encoding. Sulla base di una legge di evoluzione tempo-frequenza dello spettrogramma, le variazioni di complessità sono studiate per stimare accuratamente il numero di componenti. Il metodo presentato è adatto a segnali multicomponente con modalità non separabili, così come ad ampiezze variabili nel tempo e mostra robustezza al rumore.Frequency modulated signals appear in many applied disciplines, including geology, communication, biology and acoustics. They are naturally 1multicomponent, i.e., they consist of multiple waveforms, with specific time-dependent frequency (instantaneous frequency). In most practical applications, the number of modes—which is unknown—is needed for correctly analyzing a signal; for instance for separating each individual component and for estimating its instantaneous frequency. Detecting the number of components is a challenging problem, especially in the case of interfering modes. The Rényi Entropy-based approach has proven to be suitable for signal modes counting, but it is limited to well separated components. This paper addresses this issue by introducing a new notion of signal complexity. Specifically, the spectrogram of a multicomponent signal is seen as a non-stationary process where interference alternates with non-interference. Complexity concerning the transition between consecutive spectrogram sections is evaluated by means of a modified Run Length Encoding. Based on a spectrogram time-frequency evolution law, complexity variations are studied for accurately estimating the number of components. The presented method is suitable for multicomponent signals with non-separable modes, as well as time-varying amplitudes, showing robustness to noise

A Fast and Robust Spectrogram Reassignment Method

The improvement of the readability of time-frequency transforms is an important topic in the field of fast-oscillating signal processing. The reassignment method is often used due to its adaptivity to different transforms and nice formal properties. However, it strongly depends on the selection of the analysis window and it requires the computation of the same transform using three different but well-defined windows. The aim of this work is to provide a simple method for spectrogram reassignment, named FIRST (Fast Iterative and Robust Reassignment Thinning), with comparable or better precision than classical reassignment method, a reduced computational effort, and a near independence of the adopted analysis window. To this aim, the time-frequency evolution of a multicomponent signal is formally provided and, based on this law, only a subset of time-frequency points is used to improve spectrogram readability. Those points are the ones less influenced by interfering components. Preliminary results show that the proposed method can efficiently reassign spectrograms more accurately than the classical method in the case of interfering signal components, with a significant gain in terms of required computational effort

On the time-frequency reassignment of interfering modes in multicomponent FM signals

The paper presents a first attempt to correct the time-frequency reassignment of a multicomponent signal having non separable individual components. In particular, the case of a 2-components signal has been investigated in depth. It has been proved that the integral (along frequencies) of the spectrogram is still a multicomponent signal with specific instantaneous frequencies. As a result, the spectrogram of this signal allows us to disentangle the frequencies and recover the missing information in the non separability region. Preliminary results show that the proposed method is able to correctly reassign the information in the interference region by separating the two individual components, with a very moderate computational effort

An iterative approach for spectrogram reassignment of frequency modulated multicomponent signals

In this paper, an evolution law for the modulus of the Short Time Fourier Transform, referred as spectrogram, of a frequency modulated multicomponent signal is proposed. Based on this result, an iterative reallocating method for the enhancement of spectrogram resolution is proposed. Compared to the standard reassignment method, the presented procedure allows us to obtain a time–frequency representation which better localizes the individual modes of a multicomponent signal even in the non separable case. The proposed method is computationally advantageous and robust to modes interference, then it could be employed for accurate instantaneous frequency estimation, which is a fundamental goal in applications dealing with non stationary signals such as radar, surveillance and audio signals

A fast and robust spectrogram reassignment method

The improvement of the readability of time-frequency transforms is an important topic in the field of fast-oscillating signal processing. The reassignment method is often used due to its adaptivity to different transforms and nice formal properties. However, it strongly depends on the selection of the analysis window and it requires the computation of the same transform using three different but well-defined windows. The aim of this work is to provide a simple method for spectrogram reassignment, named FIRST (Fast Iterative and Robust Reassignment Thinning), with comparable or better precision than classical reassignment method, a reduced computational effort, and a near independence of the adopted analysis window. To this aim, the time-frequency evolution of a multicomponent signal is formally provided and, based on this law, only a subset of time-frequency points is used to improve spectrogram readability. Those points are the ones less influenced by interfering components. Preliminary results show that the proposed method can efficiently reassign spectrograms more accurately than the classical method in the case of interfering signal components, with a significant gain in terms of required computational effort. View Full-Tex

A pde-Based Analysis of the Spectrogram Image for Instantaneous Frequency Estimation

Instantaneous frequency (IF) is a fundamental feature in multicomponent signals analysis and its estimation is required in many practical applications. This goal can be successfully reached for well separated components, while it still is an open problem in case of interfering modes. Most of the methods addressing this issue are parametric, that is, they apply to a specific IF class. Alternative approaches consist of non-parametric time filtering-based procedures, which do not show robustness to destructive interference---the most critical scenario in crossing modes. In this paper, a method for IF curves estimation is proposed. The case of amplitude and frequency modulated two-component signals is addressed by introducing a spectrogram time-frequency evolution law, whose coefficients depend on signal IFs time derivatives, that is, the chirp rates. The problem is then turned into the resolution of a two-dimensional linear system which provides signal chirp rates; IF curves are then obtained by a simple integration. The method is non-parametric and it results quite robust to destructive interference. An estimate of the estimation error, as well as a numerical study concerning method sensitivity and robustness to noise are also provided in the paper

Toward Isolation of Palytoxins: Liquid Chromatography Coupled to Low- or High-Resolution Mass Spectrometry for the Study on the Impact of Drying Techniques, Solvents and Materials

Palytoxin (PLTX) and its congeners are emerging toxins held responsible for a number of human poisonings following the inhalation of toxic aerosols, skin contact, or the ingestion of contaminated seafood. Despite the strong structural analogies, the relative toxic potencies of PLTX congeners are quite different, making it necessary to isolate them individually in sufficient amounts for toxicological and analytical purposes. Previous studies showed poor PLTX recoveries with a dramatic decrease in PLTX yield throughout each purification step. In view of a large-scale preparative work aimed at the preparation of PLTX reference material, we have investigated evaporation as a critical—although unavoidable—step that heavily affects overall recoveries. The experiments were carried out in two laboratories using different liquid chromatography-mass spectrometry (LC-MS) instruments, with either unit or high resolution. Palytoxin behaved differently when concentrated to a minimum volume rather than when evaporated to complete dryness. The recoveries strongly depended on the solubility as well as on the material of the used container. The LC-MS analyses of PLTX dissolved in aqueous organic blends proved to give a peak intensity higher then when dissolved in pure water. After drying, the PLTX adsorption appeared stronger on glass surfaces than on plastic materials. However, both the solvents used to dilute PLTX and that used for re-dissolution had an important role. A quantitative recovery (97%) was achieved when completely drying 80% aqueous EtOH solutions of PLTX under N2-stream in Teflon. The stability of PLTX in acids was also investigated. Although PLTX was quite stable in 0.2% acetic acid solutions, upon exposure to stronger acids (pH < 2.66), degradation products were observed, among which a PLTX methyl-ester was identifie

Structural studies and biological evaluation of T30695 variants modified with single chiral glycerol-T reveal the importance of LEDGF/p75 for the aptamer anti-HIV-integrase activities

Some G-quadruplex (GQ) forming aptamers, such as T30695, exhibit particularly promising properties among the potential anti-HIV drugs. T30695 G-quadruplex binds to HIV-1 integrase (IN) and inhibits its activity during 3′-end processing at nanomolar concentrations. Herein we report a study concerning six T30695-GQ variants, in which the R or S chiral glycerol T, singly replaced the thymine residues at the T30695 G-quadruplex loops. CD melting, EMSA and HMRS experiments provided information about the thermal stability and the stoichiometry of T30695-GQ variants, whereas CD and 1H NMR studies were performed to evaluate the effects of the modifications on T30695-GQ topology. Furthermore, LEDGF/p75 dependent and independent integration assays were carried out to evaluate how T loop modifications impact T30695-GQ biological activities. The obtained results showed that LEDGF/p75 adversely affects the potencies of T30695 and its variants. The IN inhibitory activities of the modified aptamers also depended on the position and on the chirality (R or S) of glycerol T loop in the GQ, mostly regardless of the G-quadruplex stabilities. In view of our and literature data, we suggest that the allosteric modulation of IN tetramer conformations by LEDGF/p75 alters the interactions between the aptamers and the enzyme. Therefore, the new T30695 variants could be suitable tools in studies aimed to clarify the HIV-1 IN tetramers allostery and its role in the integration activity