sampling theoremFourier transformation theoryZak basisband limited signalscoherent state systemsHeisenberg-Weyl groupThe Poisson Summation Formula and the sampling theorem for band limited signals, well known in
We prove that in the low noise limit minimizing the distortion is equivalent to minimizing the noise amplification. We derive several asymptotic scaling laws for distortion and noise amplification. They depend on properties of the state space reconstruction, such as the sampling time and the ...
In order to unambiguously determine the frequency of the piecewise constant IF signal, a number of frequencies, N, greater than a number stipulated by the sampling theorem will be required. The distance to the reflecting surface is then determined using the frequency of the IF signal in a ...
small‐gain theoremThis paper studies the event-triggered control problem for nonlinear systems with partial-state feedback.We consider a general class of control systems that are transformable into an interconnection of two input-to-state stable(ISS)subsystems with the sampling error as the external...
J2. Using the Nyquist-Shannon sampling theorem, the required temporal resolutionδtshould be\(\delta t\le \frac{1}{2{{\Delta }}\omega }\). The spatial resolutionδθandδϕcan be determined with the argument that the nodal structure of spherical harmonic basis in Eq. (2) must be...
For the integration over the Brillouin zone (BZ) of the primitive unit cell, we employed a Monkhorst–Pack grid with a dense k-point sampling of 11 × 11 × 11, which provides a comprehensive representation of the reciprocal space.Data availability All data generated or analyzed during this ...
We applied EMD to decompose the EEG signal into a finite number of intrinsic mode functions (IMFs). Each IMF represents a narrow-band amplitude and frequency-modulated signal. In our study, the sampling frequency of the raw EEG signal is ~ 120 Hz, we found the frequency range for ...
habenula regions. To resolve the dynamics of GCaMP6s, image stacks were acquired at 2Hz, which allowed us to resolve frequency components up to 1Hz based on Nyquist sampling theorem. Each 100-μm stack consisted of 26 slices with 4 μm between two adjacent slices. The resting state of ...
According to the sampling theorem, only the first M=N/2 harmonic components are considered significant. The 13 frequency-domain features derived from these components are listed in Table A-2. Table A-2. Features extracted from the frequency-domain values of a segment NameMeaningExpressionName...
In thermoelectric, phase interface engineering proves effective in reducing the lattice thermal conductivity via interface scattering and amplifying the density-of-states effective mass by energy filtering. However, the indiscriminate introduction of pha