ComputeEtaTilde

 Compute eta pulse related quantities [1].

0001 function [eta_tilde, zeta_tilde]=ComputeEtaTilde(Para)
0002 % Compute eta pulse related quantities [1].
0003 
0004 % This file is part of WaveComBox: www.wavecombox.com and is distributed under the terms of the MIT license. See accompanying LICENSE file.
0005 % Original author: François Rottenberg, May 4, 2018.
0006 % Contributors:
0007 % Change log:
0008 
0009 M=Para.nSubcarriers/2;
0010 
0011 %% Pulse generation and pulse-related quantities
0012 [pulse, pulse10, ~] = GeneratePrototypePhydyas(M, Para.kappa);
0013 pulse=pulse.*sqrt(1/M);
0014 pulse10=pulse10.*sqrt(1/M);
0015 
0016 % eta's calculation
0017 P00=reshape(pulse.*sqrt(M),2*M,Para.kappa);
0018 D10=reshape(pulse10.*sqrt(M),2*M,Para.kappa);
0019 
0020 R00_10=conv2along1(P00,flipud(D10));
0021 S00_10=conv2along1(kron(fliplr(eye(2)),eye(M))*P00,flipud(D10));
0022 Uplus=kron(eye(2),eye(M)+fliplr(eye(M)));
0023 Uminus=kron(eye(2),eye(M)-fliplr(eye(M)));
0024 
0025 eta_10_10=1/2/M*trace(R00_10*R00_10'*Uplus+S00_10*S00_10'*Uminus);
0026 
0027 eta_tilde=eta_10_10/(2*M)^2;
0028 
0029 
0030 S00_00=conv2along1(kron(fliplr(eye(2)),eye(M))*P00,flipud(P00));
0031 R00_00=conv2along1(P00,flipud(P00));
0032 R10_10=conv2along1(D10,flipud(D10));
0033 S10_10=conv2along1(kron(fliplr(eye(2)),eye(M))*D10,flipud(D10));
0034 
0035 etaminusplus0011=1/2/M*trace(R00_00*R10_10'*Uminus+S00_00*S10_10'*Uplus);
0036 zeta_tilde=etaminusplus0011/(2*M)^2;
0037 
0038 end
0039