In the spatial frequency domain of interest here, a minimum of two pixels are required to sample one line pair (comprising one dark and one bright section of a pattern), resulting in a Nyquist frequency
of 38 lp/mm for the digital images analyzed in this work.
For 10 Hz (left column), our method has performance issues due to the signal being sampled at the Nyquist frequency
. SymPy's RL method does not have this limitation because it requires the original equation and the evaluation time (t), ignoring any sampling.
The Maximum frequency for THD calculation is Nyquist frequency
. The frequency is taken in the X-axis and the magnitude is taken in the Y-axis.
Given the model, the spectral limits, the spatial origin, and the phase, [S.sub.E] and [S.sub.O] are estimated up to the Nyquist frequency
from the whole data set.
Remember the DFT is mirror-symmetric to the Nyquist frequency
[f.sub.s]/2 = 10 so that the first amplitude A1 becomes
Choosing a convex piece from the set [A.sub.i], i = 1,2, and 3 in the frequency range below Nyquist frequency
B, its counterpart above B will be a concave one from the set [A.sub.i'], i = 4,5, and 6.
We find that the new MTS method may be more stable than the Courant-Friedrichs-Levy-Nonlinear (CFLN) due to the damping it exhibits at the Nyquist frequency
. The MTS method also utilizes very few steps in order to evolve the solution compared to the ICN, RK3, RK4, and the CFLN.
In the frequency spectrum of this up-shifted function, the centre peak-to-null width of the main lobe [18For window length L of 200 and Nyquist frequency
of 250 kHz (corresponding to the sampling rate of 500 kS/s), this main lobe width is 2.5 kHz.
It can be clearly observed that 6th order half differentiator based on PSOGA Hybrid optimized differentiator, namely, [G.sub.HYBR_3rd_6](z), outperforms all other proposed half differentiators with RME (dB) of the order of [less than or equal to] -40 dB in range of 0.46 [less than or equal to] [omega] [less than or equal to] 3 n radians of complete Nyquist frequency
. Third order half differentiator [G.sub.HYBR_3rd_3](z) outperforms Al-SKG rule based half differentiator with RME (dB) of [less than or equal to] -27.92 dB in 0.77 [less than or equal to] [omega] [less than or equal to] 1.7 radians and [less than or equal to] -36.26 dB in 2.1 [less than or equal to] [omega] [less than or equal to] 3 [pi] radians of complete range.
For more information about [S.sub.g], it is a complex vector with Nyquist frequency
([f.sub.Ny]=fs/2, the highest frequency can be observed according to sampling theorem) as the axis of symmetry, and the symmetrical elements conjugate each other.
The spectrum reconstruction algorithm is based on the theory of combining L independent representations of each echo signal; each channel samples the echo with 1/L the Nyquist frequency
Figure 5(a) shows the IF versus Ft of a scenario where the antennas are spaced at a distance (d = [lambda]) that is to mean, double of the spatial frequency sampling or Nyquist frequency
* energy at frequencies higher than the Nyquist frequency
. Elimination by using suitable sampling rate;
Therefore, in order for us to process the data we will need to down-shift the RF signal below the Nyquist frequency
in hardware before any digital processing can occur.
Any sampling frequency, [f.sub.S], selected for data acquisition (having a period [P.sub.S]) implies a corresponding Nyquist frequency
([f.sub.N]) that is half the sampling frequency.