et us assume that $A_{ij}$ is the power received (expressed in dBm)by the frequency band $F_{i}$ at the time $T_{j}$. We have represented the data collected during our spectrum measurement by using a N $ imes$ M matrix designed by L. The matrix L is defined as:
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[ L = [A(F_i,T_j)]= egin{bmatrix} A_{F_1T_1} & A_{F_2T_1} & cdots & A_{F_nT_1} \
A_{F_1T_2} & A_{F_2T_2} & cdots & A_{F_nT_2}\ vdots & vdots & ddots & vdots \
A_{F_1T_m} & A_{F_2T_m} & cdots & A_{F_nT_m} end{bmatrix}
]
Where i=1,2, $cdots$, n and j=1,2, $cdots$, m.
%$F_{start} leg F_{i} leg F_{stop}; i=1,2, cdots, n$
%$T_start leg T_{j} leg T_stop; j=1,2, cdots, m$
In order to determine the occupancy of a spectrum $F_i$, we have first to
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C is the matrix of classification and it is defined as follows. $C=[A_c(F_i,T_j)]$ where $A_c(F_i,T_j)$ is obtained by applying the hypothesis test described in equation ef{eq:hypothesistest}. egin{equation} label{eq:hypothesistest} A_c(F_i,T_j)= egin{cases} 1 & quad ext{if} quad A(F_i,T_j) geq lambda \ 0 & quad ext{if} quad A(F_i,T_j) <lambda \ end{cases} end{equation}. Step 2. This step describes the computation done in order to find the duty cycle of data taken during a specific interval of time and the duty cycle of the each frequency band for a specific interval of time. Step 2.1. Let us denote by D the duty cycle of the overall data taken during the spectrum monitoring. egin{equation} label{Genral duty cycle} DC=frac{sum_{i=1}^n sum_{j=k}^q A_c(F_i,T_j)}{n imes (r-k+1)} end{equation} Step 2.2. This step describes the computation done in order to find the duty cycle of each frequency point for a specific interval of time. egin{equation} label{frequency i duty cycle} DC_{f_{i}} =frac{sum_{j=k}^q A_c(F_i,T_j)}{r-k+1}