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Sonography techniques use multiple transducer elements for tissue visualization. Signals detected at each element are sampled prior to digital beamforming. The required sampling rates are up to 4 times the Nyquist rate of the signal and…
Analyzing the internal loss characteristics and multimodedness of (integrated) optical devices can prove difficult. One technique to recover this information is to Fourier transform the transmission spectrum of optical components. This…
Nonlinear distortion experienced by signals during their propagation through optical fibers strongly limits the throughput of optical communication systems. Recently, a strong research focus has been dedicated to nonlinearity mitigation and…
Oscillation synchronization phenomenon is widely observed in natural systems through frequency modulated signals, especially in biological neural networks. Frequency modulation is also one of most widely used technologies in engineering.…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
Optical turbulence modelling and simulation are crucial for developing astronomical ground-based instruments, laser communication, laser metrology, or any application where light propagates through a turbulent medium. In the context of…
Nonadiabatic change of the control field or of the low-frequency coherence allows for an almost instantaneous change of the signal field propagating in a thick resonant absorber where electromagnetically induced transparency is realized.…
In a number of data-driven applications such as detection of arrhythmia, interferometry or audio compression, observations are acquired indistinctly in the time or frequency domains: temporal observations allow us to study the spectral…
Temporal diffraction from rapidly time-modulated materials can generate new frequency components not present in an incident wave. In such an experiment, the spectral extent of these new frequencies is determined by the rate of modulation…
Linear (spectro) polarimetry is usually performed using separate photon flux measurements after spatial or temporal polarization modulation. Such classical polarimeters are limited in sensitivity and accuracy by systematic effects and…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to…
Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
The problem of joint estimation of power spectrum and modulation from realizations of frequency modulated stationary wideband signals is considered. The study is motivated by some specific signal classes from which departures to…
Uniform quantization is a topic that has been extensively studied. However and although an analytical description of quantization noise has been proposed, most descriptions of the spectral properties of quantization error resort to…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…