Approaches to wavelet-based denoising (or signal enhancement) have generally relied on the assumption of normally distributed perturbations. To relax this assumption, which is often violated in practice, we derive a robust wavelet thresholding technique based on the minimax description length (MMDL) principle. We first determine the least favorable distribution in the "-contaminated normal fami...

Time-frequency distributions (TFD’s), which indicate the energy content of a signal as a function of both time and frequency, are powerful tools for time-varying signal analysis. The lack of a single distribution that is “best” for all applications has resulted in a proliferation of TFD’s, each corresponding to a different, fixed mapping from signals to the time-frequency plane. A major drawbac...

Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly coherent redundant dictionaries. The cooperation takes place by ranking the partition units for their sequential stepwise approximation, and is realized by mean...

The notion of representing discrete-time electromagnetic pulse (EMP) signals using or-thonormal Laguerre sequences is introduced. The motivation for doing so is that EMP signals and Laguerre sequences are both characterized by decaying exponentials. It is shown that very eecient Laguerre representation of EMP signals is possible using this approach. Given a sequence x(n), its Laguerre expansion...

The fractional Fourier transform is a mathematical operation that generalizes the well-known Fourier transform. This operation has been shown to have physical and optical fundamental meanings, and it has been experimentally implemented by relatively simple optical setups. Based on the fractional Fourier-transform operation, a new space-frequency chart definition is introduced. By the applicatio...

Natural signals are often characterized by a complex timefrequency behaviour. These signals exist in many different applications and systems from underwater acoustic to audio signals with sound attacks or electrical systems with partial discharges and commutation switches, for example. There is a huge number of Time-Frequency (TF) methods that aim to characterize these signals in terms of first...

The Deoxyribonucleic Acid (DNA) which is a doublestranded helix of nucleotides consists of: Adenine (A), Cytosine (C), Guanine (G) and Thymine (T). In this work, we convert this genetic code into an equivalent digital signal representation. Applying a wavelet transform, such as Haar wavelet, we will be able to extract details that are not so clear in the original genetic code. We compare betwee...

Heart sounds and murmurs are timevarying signals that would best be analyzed using timefrequency analysis. Windowed Wigner-Ville distribution (WWVD) and smooth windowed Wigner-Vffle distribution (SWWVD) are used to obtain the timefrequency representation of the signal. Determination of parameter setting of WWVD and SWWVD will eliminate the cross-terms and improve time frequency representation. ...

Signals with a sparse representation are more easily analyzed and processed, thus the search for this representation has become the focus of intensive research. We aim to analyze an optimization principle for signal decomposition known as Basis pursuit; write a parametrizable library for its fast and efficient implementation, and test its suitability for practical applications such as signal an...