Mathematical Formula: Prony Analysis ~ A= { A i } n i=1 ∈R n (equation 1) ~ a= { a i } n i=1 ∈R +¿ n ¿ (equation 2) e n ( γ ) ≈ ∑ i=1 n A i e −a i γ −p e ( γ ) (equation 3) p e ( γ) ≈ ∑ i=1 n A i e −a i γ (equation 4) e n,p = ∑ j−1 p μ j ¿ γ' j −γ j ∨ ¿ q ¿ (equation 5) ∑ i=1 n A i e −a i γ ' j ¿ p e ( γ ) ,j=1,2 ,….,p (equation 6) Prony Approximation E ( 2 nxn) .A =P ( 2nx 1) (equation 7) E ( pxn) .A=P ( px1) (equation 8) Higher Order Moment of Error Rates M k =E ¿ (equation 9) P e = ∑ i=1 p A i ∅ γ (−a i ) (equation 10) E [ p ¿¿ e ( γ ) ¿¿ 2 ]= ∑ i=1 p A i 2 ∅ γ ( −2 a i ) +¿ 2 ∑ i=2 p ∑ j=1 i−1 A i A j ∅ γ ( −a i −a j ) ¿¿¿ (equation 11) Bollinger Bands B 1 =− P e ( γ )( √ M 2 log ( 1−∝ )) −1 (equation 12) B 2 =− P e ( γ )( √ M 2 log ( 1−∝ )) (equation 13)
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