Journal of Electrical and Computer Engineering

Research Article

Analysis of the Consecutive Mean Excision Algorithms

Table 3

Detection alternatives for the CME and FCME algorithms as a function of the relative height of the 𝑖 th lobe 𝛼 𝑖 , 𝑖 = 1 , … , 𝑛 , and threshold multiplier 𝑇 . The used functions are 𝑓 ( π‘˜ , 𝑗 ) (7), 𝑔 ( π‘˜ , 𝑗 ) (9), and 𝑓 𝐹 ( 𝑓 ) (11). Alternatives for the detection: all the lobes are detected (a1) at the same time, (a2) one-by-one, and (a3) other possible alternations. Alternative β€œimpossible detection” gives general limits when the signal is detectable and when it is not.
CME algorithm FCME algorithm
(a1) 𝛼 𝑛 > 𝑓 ( 0 , 𝑛 ) 𝛼 𝑛 > 𝑇 βˆ’ 1
1 < 𝑇 < 𝑔 ( 0 , 𝑛 ) 𝑇 < 𝛼 𝑛 + 1
(a2) 𝛼 π‘˜ + 1 > 𝑓 ( π‘˜ , 1 ) and 𝛼 π‘˜ + 1 < 𝑓 ( π‘˜ , 2 ) for all π‘˜ β€”*
𝑔 ( π‘˜ , 2 ) < 𝑇 < 𝑔 ( π‘˜ , 1 ) for all π‘˜ β€”*
(a3) 𝛼 𝑖 > 𝑇 𝑓 𝐹 ( π‘˜ ) βˆ’ 1 and 𝛼 𝑖 + 1 < 𝑇 𝑓 𝐹 ( π‘˜ ) βˆ’ 1 βˆ— βˆ—
𝑔 ( 0 , 𝑛 ) < 𝑇 < 𝑔 ( π‘˜ , 2 ) ( 𝛼 𝑖 + 1 + 1 ) / 𝑓 𝐹 ( π‘˜ ) < 𝑇 < ( 𝛼 𝑖 + 1 ) / 𝑓 𝐹 ( π‘˜ ) βˆ— βˆ—
Impossible detection 𝛼 𝑖 < 𝑓 ( 0 , 1 ) 𝛼 1 < 𝑇 𝑓 𝐹 ( π‘˜ ) βˆ’ 1
𝑇 > 𝑔 ( 0 , 1 ) 𝑇 > ( 𝛼 1 + 1 ) / 𝑓 𝐹 ( π‘˜ )
*Cannot be detected one-by-one.
**Lobes 𝑆 1 π‘Š 1 , … , 𝑆 𝑖 π‘Š 𝑖 are detected.