High-Resolution Sparse Representation of Micro-Doppler Signal in Sparse Fractional Domain

A frequency domain method for scattering problems with moving boundaries

“…According to Floquet's theory [37], they can be written as φ(τ ) = e iµτ p(τ ), with p a π-periodic function and µ the associated Floquet's exponent. Let us remark that the function φ(−τ ) is also solution to the equation (18). Whenever φ(τ ) and φ(−τ ) are linearly independent, the general solution writes [1] as…”

“…In the automotive industry, micro-Doppler sensing has recently been proposed [23,31,36,38] for the contactless detection of vital signs like breathing of infants left alone on the back seat of overheating cars. The engineering of such very high frequency radar sensing devices entails dealing with multiple challenges, as for instance the analysis of random body movements and vehicle vibrations [23,31,38,39,40,43], leading to radar signatures that can be classified for example by deep learning techniques [7,8,18]. In order to design these new sensors, an adequate full realistic simulation of the underlying high frequency scenarios is crucial.…”

A MultiHarmonic Finite Element Method for Scattering Problems with Small-Amplitude Boundary Deformations

“…However, in the case of a small deformation of the moving interface, an accurate approximate formulation can be used to simplify the calculations. Indeed, a careful analysis developed in [22] for the one-dimensional case, and formally extended to higher-dimensional problems, shows that the following simplified weak formulation (14) provides an accurate approximate solution v of u 0 that satisfies (12). More precisely, the formulation writes: for a fixed time t > 0, find…”

“…To give a more rigorous understanding on how these approximation lead to (14) as a correct approximation of ( 12), let us write the application Φ t with a small smooth perturbation 1 under the form…”

“…In the automotive industry, micro-Doppler sensing has recently been applied with success [17,24,27,29] to the contactless detection of vital signs, in particular for the breathing of children left alone on the back seat of overheating cars. Difficult challenges are then related to this kind of applications as for example the analysis of random body movements or vehicle vibrations [17,24,29,31,32,33] that can be classified thanks to their radar signature by deep learning techniques [3,4,14]. In the development life cycle of these new sensors, a full realistic simulation of the high frequency scenarios is therefore needed.…”