H−N heteronuclear NOE data were acquired with interleaved, unenhanced and enhanced (3 s H excitation period) spectra.
So spectrum utilization η period in an ideal periodical spectrum sensing system is obtained as: eta^{period}_{ideal} = frac{bar{T}_{H}^{d}}{bar{D}_{H}} = 1-f_{sens}W, (47).
A post-processing of the period-3 spectrum signal is performed to smooth the signal, detect the period-3 spectrum peaks, and locate the boundaries of the protein-coding regions.
The proposed method also uses the nucleotide distribution variance which has less computational cost than the Fourier transform to extract the period-3 spectrum.
The dynamic representation scheme assigns numerical pairs to the nucleotides to emphasize the effect of the nucleotides that have a stronger participation in the period-3 spectrum.
The proposed method uses a dynamic representation scheme to convert DNA sequences into a numerical form, and then it uses the nucleotide distribution variance to calculate the period-3 spectrum.
Then, according to Eqs. (57) and (58), we can derive the utilization of the spectrum (eta ^{period}_{noise}) in a periodical spectrum sensing system in a noisy environment as: eta^{period}_{noise} = frac{bar{T}}{bar{D}_{H}}=frac{frac{1}{f_{sens}W}-1}{frac{1}{f_{sens}W}+frac{P_{f_{1}} }{ 1-P_{f_{1}})^{ 1-P_{f_{
As the linear modulated signal s(n) is almost cyclostationary signal according to [19], then it is almost-periodic [18, 19] and consequently it can be considered as deterministic during a period of spectrum sensing.
In this context, a necessary and sufficient condition depending upon the coupling gains, sampling period, and spectrum of the Laplacian matrix, is established for achieving consensus.
It can be expressed as the expected value (Eleft {T_{i}^{loss} left | text {sensing stage} right.right }) of all wasted durations in one period of spectrum sensing which denotes as (bar {W}_{loss}): Eleft{T_{i}^{loss} right}= bar{N}Eleft{T_{i}^{loss}left|text{sensing stage}right.right} = bar{N} bar{W}_{loss}, (54).
