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For simplification within the algorithms the mask function p_m_ILT is normalized to 1 Hz reference bandwidth:
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| body | ${{p}_{n\_ILT}}={{p}_{m\_ILT}}(\Delta f)-10{{\log }_{10}}\left( \frac{b}{1Hz} \right)$ |
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(Eq. 110)
The bandwidth b is the bandwidth used for the emission mask. The total received interfering power emission_ILT can easily be calculated by integration over the receiver bandwidth from to
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| body | $powe{{r}_{ILT}}=10{{\log }_{10}}\left\{ \int\limits_{a}^{b}{{{10}^{\left( {{p}_{n\_ILT}}(\Delta f)/10 \right)}}}d\Delta f \right\}$ |
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(Eq. 111)
with p_n_ILT denoting the normalized mask in dBm/Hz. Using 1 Hz reference bandwidth the integral can be replaced by a summation
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| body | $powe{{r}_{ILT}}=10{{\log }_{10}}\left\{ \sum\limits_{i=a}^{b}{{{10}^{\left( {{p}_{n\_ILT}}(\Delta {{f}_{i}})/10 \right)}}} \right\}$ |
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(Eq. 112)
where power_ILT is given in dBm.
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The total interfering power relative to carrier 
can be calculated by integration over the receiver bandwidth from 
to 
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| body | $emission\_re{{l}_{ILT}}=10\log \left\{ \int_{a}^{b}{P_{rel}^{linear}\left( \Delta f \right)d\Delta f} \right\}=10\log \left\{ \int_{a}^{b}{{{10}^{\frac{P_{rel}^{dBc}\left( \Delta f \right)}{10}}}d\Delta f} \right\}$ |
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(Eq. 113)
with 
denoting the normalized user-defined mask in dBc/Hz.
This mask is expressed as an array of N+1 points 
and assumed linear between these points.
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| body | $P_{rel}^{dBc}\left( \Delta f \right)={{P}_{i}}+\frac{\Delta {{f}_{{}}}-\Delta {{f}_{i}}}{\Delta {{f}_{i+1}}-\Delta {{f}_{i}}}\left( {{P}_{i+1}}-{{P}_{i}} \right)$ |
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(Eq. 114)
This leads to:
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| body | $emission\_re{{l}_{it}}=10\log \left\{ \sum\limits_{i=0}^{N-1}{\int_{\Delta {{f}_{i}}}^{\Delta {{f}_{i+1}}}{{{10}^{\frac{P_{rel}^{dBc}\left( \Delta f \right)}{10}}}d\Delta f}} \right\}$ |
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(Eq. 115)
where:
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| body | $\Delta {{f}_{0}}=a={{f}_{VLR}}-{{f}_{ILT}}-{{B}_{VLR}}/2$ |
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(Eq. 116)
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| body | $\Delta {{f}_{N}}=b={{f}_{VLR}}-{{f}_{ILT}}+{{B}_{VLR}}/2$ |
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(Eq. 117)
Intermediate calculation
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Eventually:
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| body | $\begin{align} & emission\_rel_{i}^{dBc}=\int_{\Delta {{f}_{i}}}^{\Delta {{f}_{i+1}}}{{{10}^{\frac{P_{rel}^{dBc}\left( \Delta f \right)}{10}}}d\Delta f} \\ & emission\_rel_{i}^{dBc}={{10}^{\frac{{{P}_{i}}}{10}}}\int_{\Delta {{f}_{i}}}^{\Delta {{f}_{i+1}}}{{{\left[ {{10}^{\frac{{{P}_{i+1}}-{{P}_{i}}}{10\left( \Delta {{f}_{i+1}}-\Delta {{f}_{i}} \right)}}} \right]}^{\left( \Delta {{f}_{{}}}-\Delta {{f}_{i}} \right)}}d\Delta f} \\ & emission\_rel_{i}^{dBc}=\frac{{{10}^{\frac{{{P}_{i}}}{10}}}}{{{K}^{\Delta {{f}_{i}}}}}\int_{\Delta {{f}_{i}}}^{\Delta {{f}_{i+1}}}{{{K}^{\left( \Delta {{f}_{{}}}-\Delta {{f}_{i}} \right)}}d\Delta f},\quad K={{10}^{\frac{{{P}_{i+1}}-{{P}_{i}}}{10\left( \Delta {{f}_{i+1}}-\Delta {{f}_{i}} \right)}}} \\ & emission\_rel_{i}^{dBc}=\frac{{{10}^{\frac{{{P}_{i}}}{10}}}}{{{K}^{\Delta {{f}_{i}}}}}\left[ {{e}^{\ln K}} \right]_{\Delta {{f}_{i}}}^{\Delta {{f}_{i+1}}}=\frac{{{10}^{\frac{{{P}_{i}}}{10}}}}{\ln K}\left[ {{K}^{\Delta {{f}_{i+1}}-\Delta {{f}_{i}}}}-1 \right],\quad \ln K=\frac{\ln 10}{10}.\frac{{{P}_{i+1}}-{{P}_{i}}}{\Delta {{f}_{i+1}}-\Delta {{f}_{i}}} \\ & \\ \end{align}$ |
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(Eq. 118)
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| body | $emission\_rel_{i}^{dBc}=\frac{10}{\ln 10}\frac{{{10}^{{{P}_{i+1}}}}-{{10}^{{{P}_{i}}}}}{{{P}_{i+1}}-{{P}_{i}}}\left( \Delta {{f}_{i+1}}-\Delta {{f}_{i}} \right)$ |
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(Eq. 119)Eventually:
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| body | $emission\_re{{l}_{ILT}}=10\log \left\{ \frac{10}{\ln 10}\sum\limits_{i=0}^{N-1}{\frac{\left( P_{i+1}^{linear}-P_{i}^{linear} \right)\left( \Delta {{f}_{i+1}}-\Delta {{f}_{i}} \right)}{\left( P_{i+1}^{dBc}-P_{i}^{dBc} \right)}} \right\}$ |
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(Eq. 120)