cp's OEIS Frontend

A300727 Decimal expansion of the total harmonic distortion (THD) of the sawtooth signal filtered by a 2nd-order low-pass filter.

%I A300727 #19 Mar 12 2018 03:48:28
%S A300727 1,8,1,1,4,1,6,1,3,7,9,3,8,2,9,0,0,4,0,8,0,2,1,8,1,0,5,5,8,1,3,0,1,6,
%T A300727 7,8,4,4,3,8,9,2,8,3,5,1,5,9,5,6,3,5,3,8,9,1,1,5,5,6,0,6,0,8,6,2,6,4,
%U A300727 1,4,1,9,5,6,3,6,7,9,2,4,7,3,1,6,9,8,0,7,9,1,7,9,2,7,4,4,1,6,2,1,2,2,4
%N A300727 Decimal expansion of the total harmonic distortion (THD) of the sawtooth signal filtered by a 2nd-order low-pass filter.
%C A300727 See formula (34) in Blagouchine & Moreau link.
%H A300727 I. V. Blagouchine and E. Moreau, <a href="http://dx.doi.org/10.1109/TCOMM.2011.061511.100749">Analytic Method for the Computation of the Total Harmonic Distortion by the Cauchy Method of Residues.</a> IEEE Trans. Commun., vol. 59, no. 9, pp. 2478-2491, 2011. <a href="http://iblagouchine.perso.centrale-marseille.fr/IEEE-TCOM-2011-061511-100749.php">PDF file</a>.
%F A300727 Equals sqrt(Pi*(cot(Pi/sqrt(2))*coth(Pi/sqrt(2))^2-cot(Pi/sqrt(2))^2*coth(Pi/sqrt(2))-cot(Pi/sqrt(2))-coth(Pi/sqrt(2)))/((cot(Pi/sqrt(2))^2+coth(Pi/sqrt(2))^2)*sqrt(2))+(1/3)*Pi^2-1).
%e A300727 0.1811416137938290040802181055813016784438928351595635...
%p A300727 evalf(sqrt(Pi*(cot(Pi/sqrt(2))*coth(Pi/sqrt(2))^2-cot(Pi/sqrt(2))^2*coth(Pi/sqrt(2))-cot(Pi/sqrt(2))-coth(Pi/sqrt(2)))/((cot(Pi/sqrt(2))^2+coth(Pi/sqrt(2))^2)*sqrt(2))+(1/3)*Pi^2-1), 120)
%t A300727 RealDigits[Sqrt[Pi*(Cot[Pi/Sqrt[2]]*Coth[Pi/Sqrt[2]]^2-Cot[Pi/Sqrt[2]]^2*Coth[Pi/Sqrt[2]]-Cot[Pi/Sqrt[2]]-Coth[Pi/Sqrt[2]])/((Cot[Pi/Sqrt[2]]^2+Coth[Pi/Sqrt[2]]^2)*Sqrt[2])+(1/3)*Pi^2-1], 10, 120][[1]]
%o A300727 (MATLAB) format long; sqrt(sqrt(pi*(cot(pi/sqrt(2))*coth(pi/sqrt(2))^2-cot(pi/sqrt(2))^2*coth(pi/sqrt(2))-cot(pi/sqrt(2))-coth(pi/sqrt(2)))/((cot(pi/sqrt(2))^2+coth(pi/sqrt(2))^2)*sqrt(2))+(1/3)*pi^2-1))
%o A300727 (PARI) s2=sqrt(2);
%o A300727 A=Pi/s2;
%o A300727 B=1+2/(exp(2*A)-1)
%o A300727 C=1/tan(A);
%o A300727 sqrt(Pi*(B^2*C-B*C^2-C-B)/((C^2+B^2)*s2) + Pi^2/3 - 1) \\ _Charles R Greathouse IV_, Mar 11 2018
%Y A300727 Cf. A247719 (Pi/sqrt(2)), A300690, A300713, A300714.
%K A300727 nonn,cons
%O A300727 0,2
%A A300727 _Iaroslav V. Blagouchine_, Mar 11 2018