Multiple multidimensional morse wavelets

This paper defines a set of operators that localize a radial image in space and radial frequency simultaneously. The eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found. The eigenfunctions are optimally concentrated over a given region of radial space and scale space, defined via a triplet of parameters. Analytic forms for the energy concentration of the functions over the region are given. The radial function localization operator can be generalised to an operator localizing any L-2(R-2) function. It is demonstrated that the latter operator, given an appropriate choice of localization region, approximately has the same radial eigenfunctions as the radial operator. Based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude, orientation and phase structure of locally oscillatory signals. The full set of quaternionic wavelet functions are component by component orthogonal; their statistical properties are tractable, and forms for the variability of the estimators of the local phase and orientation are given, as well as the local energy of the image. By averaging estimators across wavelets, a substantial reduction in the variance is achieved

Embedded AM-FM Signal Decomposition Algorithm for Continuous Human Activity Monitoring

AM-FM decomposition techniques have been successfully used for extracting significative features from a large variety of signals, helping realtime signal monitoring and pattern recognition, since they represent signals as a simultaneous composition of amplitude modulation and frequency modulation, where the carriers, amplitude envelopes, and the instantaneous frequencies are the features to be estimated. Human activities often involve repetitive movements, such as in running or cycling, where sinusoidal AM-FM decompositions of signals have already demonstrated to be useful to extract compact features to aid monitoring, classification, or detection. In this work we thus present the challenges and results of implementing the iterated coherent Hilbert decomposition (ICHD), a particularly effective algorithm to obtain an AM-FM decomposition, within a resource-constrained and low-power ARM Cortex-M4 microcontroller that is present in a wearable sensor we developed. We apply ICHD to the gyroscope data acquired from an inertial measurement unit (IMU) that is present in the sensor. Optimizing the implementation allowed us to achieve real-time performance using less then 16 % of the available CPU time, while consuming only about 5.4 mW of power, which results in a run-time of over 7 days using a small 250 mAh rechargeable cell

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

Multirate Frequency Transformations: Wideband AM-FM Demodulation with Applications to Signal Processing and Communications

The AM-FM (amplitude & frequency modulation) signal model finds numerous applications in image processing, communications, and speech processing. The traditional approaches towards demodulation of signals in this category are the analytic signal approach, frequency tracking, or the energy operator approach. These approaches however, assume that the amplitude and frequency components are slowly time-varying, e.g., narrowband and incur significant demodulation error in the wideband scenarios. In this thesis, we extend a two-stage approach towards wideband AM-FM demodulation that combines multirate frequency transformations (MFT) enacted through a combination of multirate systems with traditional demodulation techniques, e.g., the Teager-Kasiser energy operator demodulation (ESA) approach to large wideband to narrowband conversion factors. The MFT module comprises of multirate interpolation and heterodyning and converts the wideband AM-FM signal into a narrowband signal, while the demodulation module such as ESA demodulates the narrowband signal into constituent amplitude and frequency components that are then transformed back to yield estimates for the wideband signal. This MFT-ESA approach is then applied to the various problems of: (a) wideband image demodulation and fingerprint demodulation, where multidimensional energy separation is employed, (b) wideband first-formant demodulation in vowels, and (c) wideband CPM demodulation with partial response signaling, to demonstrate its validity in both monocomponent and multicomponent scenarios as an effective multicomponent AM-FM signal demodulation and analysis technique for image processing, speech processing, and communications based applications