Each gate pulse was incident into an SFG-NLC at a different angle; therefore, each SFG pulse was output to a different direction under a phase-matching condition with keeping a time delay corresponding to a time slot interval.
where N p is the number of the detected paths between the track-side BS and the wireless gateway on the train, α n, Ф n, Δf n, and τ n are the averaged fading amplitude, phase shift, Doppler frequency shift, and time delay corresponding to the n th path, respectively.
Then we can get the critical value of time delay corresponding to every fixed positive root ω i ′ of Eq. (17): τ i ′ ( j ) = 1 ω i ′ arccos f 1 ∗ ( ω i ′ ) + 2 j π ω i ′, i = 1, 2, …, k, j = 0, 1, 2, ….
where σ is the bistatic backscattering coefficient of the point target P, t delay = (r T t,t 0T,r 0T) + r R(t 0T,r 0T))/c is the time delay corresponding to the time it takes the signal to travel the transmitter-target-receiver distance, c is the speed of light, and T S is the synthetic aperture time for the point target P.
For subsequent analysis, we considered the time delay corresponding to a 90% decrease of mutual information between the maximal value at τ = 0 and a reference minimal value (i.e., the average value for large time delays, 100 < τ < 200 measured in samples).
A delay corresponding to a 20 Hz coupling was used to select long range couplings in the HMBC experiment.
where contains the possible delays corresponding to the dictionary columns.
This results in different ranges (that is, group delays) corresponding to very similar heights.
where is a diagonal matrix with the elements of vector on its main diagonal, and contains the possible delays corresponding to the dictionary columns for the channel from the th transmitter to the th receiver.
Table 1 shows the time delays corresponding to three known source locations: 1. Case I: source positioned at a point on the line that passes through the two microphones.
The trivial equilibrium of a controlled van der Pol Duffing oscillator with nonlinear feedback control may lose its stability via a non-resonant interaction of two Hopf bifurcations when two critical time delays corresponding to two Hopf bifurcations have the same value.
