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In many mechanical, electrical, and general physical systems evolving over time or space, spectral analysis methods as Fast Fourier Transform (FFT), Short Term Fourier Transform (STFT), Power Spectrum Density (PSD) plays a very important…
We describe a new and efficient technique which we call sideband or phase-modulation searching that allows one to detect short period binary pulsars in observations longer than the orbital period. The orbital motion of the pulsar during…
The "theoretical limit of time-frequency resolution in Fourier analysis" is thought to originate in certain mathematical and/or physical limitations. This, however, is not true. The actual origin arises from the numerical (technical) method…
In recent years diode laser sources have become widespread and reliable tools in magneto-optical spectroscopy. In particular, laser-driven atomic magnetometers have found a wide range of practical applications. More recently, so-called…
In the framework of linear optics, light fields do not interact with each other in a medium. Yet, when their field amplitude becomes comparable to the electron binding energies of matter, the nonlinear motion of these electrons emits new…
We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type. The modulation frequency of the forcing is assumed to be…
Most radio signals can be described as a form of sinusoidal carrier modulation. These signals have the property that when observed over a sufficiently short period of time, the waveform is approximately sinusoidal, exhibiting constant…
Spectra derived from fast Fourier transform (FFT) analysis of time-domain data intrinsically contain statistical fluctuations whose distribution depends on the number of accumulated spectra contributing to a measurement. The tail of this…
Spectrotemporal encoding of optical quantum information is emerging as a powerful tool in quantum information technology. Processing of spectrotemporal information has recently been demonstrated in multi-mode quantum memories, based on…
We investigate the sideband spectra of a driven nonlinear mode with its eigenfrequency being modulated at a low frequency (< 1 kHz). This additional parametric modulation leads to prominent antiresonance lineshapes in the sideband spectra,…
Periodic signals in electrical and electronic equipment can cause interference in nearby devices. Randomized modulation of those signals spreads their energy through the frequency spectrum and can help to mitigate electromagnetic…
Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…
To obtain the initial pressure from the collected data on a planar sensor arrangement in photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…
A strong phase modulated coupling field leads to an amplitude modulation of a probe field in an electromagnetically induced transparency process. Time vs. detuning plots for different modulation frequencies reveals a transition between an…
The time-modulated array is a simple array architecture in which each antenna is connected to an RF switch that serves as a modulator. The phase shift is achieved by digitally controlling the relative delay between the periodic modulating…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…
Heart and respiration rate measurement using Doppler radar is a non-contact and non-obstructive way for remote thorough-clothing monitoring of vital signs. The modulated back-scattered radar signal in the presence of high noise and…
It is shown that the direct Fourier synthesization of light beams allows one to create polarity-asymmetric waves, which are able, in the process of nonlinear interaction with a medium, to break its inversion symmetry. As a result, these…
In scientific inquiry of small scale energy and transition events, the effect of an observer on the measurement can be substantial. Similarly, the methods of observation can create entirely different understandings of the system behavior,…
Consider quantum harmonic oscillator, perturbed by an even almost-periodic complex-valued potential with bounded derivative and primitive. Suppose that we know the first correction to the spectral asymptotics $\{\Delta\mu_n\}_{n=0}^\infty$…