What’s the Frequency, Kenneth?: Sublinear Fourier Sampling Off the Grid

We design a sublinear Fourier sampling algorithm for a case of sparse off-grid frequency recovery. These are signals with the form f(t)=∑kj=1ajeiωjt+ν^ , t∈Z ; i.e., exponential polynomials with a noise term. The frequencies {ω j } satisfy ω j  ∈ [η,2π − η] and min i ≠ j |ω i  − ω j | ≥ η for some η > 0. We design a sublinear time randomized algorithm, which takes O(klogklog(1/η)(logk + log( ∥ a ∥ 1/ ∥ ν ∥ 1)) samples of f(t) and runs in time proportional to number of samples, recovering {ω j } and {a j } such that, with probability Ω(1), the approximation error satisfies |ω j ′ − ω j | ≤ η/k and |a j  − a j ′| ≤ ∥ ν ∥ 1/k for all j with |a j | ≥ ∥ ν ∥ 1/k

Interpolation-based matrix pencil method for parameter estimation of dispersive media in civil engineering

International audienc

Automated Classification of Medical Percussion Signals for the Diagnosis of Pulmonary Injuries

Used for centuries in the clinical practice, audible percussion is a method of eliciting sounds by areas of the human body either by finger tips or by a percussion hammer. Despite its advantages, pulmonary diagnostics by percussion is still highly subjective, depends on the physician\u27s skills, and requires quiet surroundings. Automation of this well-established technique could help amplify its existing merits while removing the above drawbacks. In this study, an attempt is made to automatically decompose clinical percussion signals into a sum of Exponentially Damped Sinusoids (EDS) using Matrix Pencil Method, which in this case form a more natural basis than Fourier harmonics and thus allow for a more robust representation of the signal in the parametric space. It is found that some EDS represent transient oscillation modes of the thorax/abdomen excited by the percussion event, while others are associated with the noise. It is demonstrated that relatively few EDS are usually enough to accurately reconstruct the original signal. It is shown that combining the frequency and damping parameters of these most significant EDS allows for efficient classification of percussion signals into the two main types historically known as resonant and tympanic . This classification ability can provide a basis for the automated objective diagnostics of various pulmonary pathologies including pneumothorax