other-side-of-d-moon
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Integration MATLAB QUESTION
Dear friends, i am really in trable, i am trying to find the specific attenuation due to rain but i have problem in my code and i am asking you your help. My problem is in the last command which is an integration operation, and i am sure you will do your best for helping me. The link below is for the equations and it's followed by the code.
https://www.mediafire.com/view/u7ktl5tj5jy700u/nnnn.png
radius = 1;
nMax = 40; % maximum mode number
No=8*10^3; %m^ -4
R1=140; %rainfall rate=1mm/hr
AS1=8.2*R1^-0.21;
N1D=No*exp(-AS1*radius*1e-3);
% mode numbers
mode = 1:nMax;
frequency = 6e9;
% speed of light
c = 299792458.0;
lambda = c / ( frequency ) ;
for n=1:10;
n2 = (2*n+1);
% radian frequency
w = 2.0*pi*frequency;
% wavenumber
k = w/c;
% conversion factor between cartesian and spherical Bessel/Hankel function
s = sqrt(0.5*pi/(k*radius));
% compute spherical bessel, hankel functions
[J(mode)] = besselj(mode + 1/2, k*radius); J = J*s;
[H(mode)] = besselh(mode + 1/2, 2, k*radius); H = H*s;
[J2(mode)] = besselj(mode + 1/2 - 1, k*radius); J2 = J2*s;
[H2(mode)] = besselh(mode + 1/2 - 1, 2, k*radius); H2 = H2*s;
% derivatives of spherical bessel and hankel functions % Recurrence relationship, Abramowitz and Stegun Page 361
kaJ1P(mode) = (k*radius*J2 - mode .* J );
kaH1P(mode) = (k*radius*H2 - mode .* H );
% Ruck, et. al. (3.2-1)
An = -((1i).^mode) .* ( J ./ H ) .* (2*mode + 1) ./ (mode.*(mode + 1));
% Ruck, et. al. (3.2-2), using derivatives of bessel functions
Bn = ((1i).^(mode+1)) .* (kaJ1P ./ kaH1P) .* (2*mode + 1) ./ (mode.*(mode + 1));
Qt = (lambda^2/2*pi)*sum(n2).*sum(real(An + Bn));
end
Co1=4.343*No;
================================================== ============
NOW SHOULD BE THE INTEGRATION OPERATION
Dear friends, i am really in trable, i am trying to find the specific attenuation due to rain but i have problem in my code and i am asking you your help. My problem is in the last command which is an integration operation, and i am sure you will do your best for helping me. The link below is for the equations and it's followed by the code.
https://www.mediafire.com/view/u7ktl5tj5jy700u/nnnn.png
radius = 1;
nMax = 40; % maximum mode number
No=8*10^3; %m^ -4
R1=140; %rainfall rate=1mm/hr
AS1=8.2*R1^-0.21;
N1D=No*exp(-AS1*radius*1e-3);
% mode numbers
mode = 1:nMax;
frequency = 6e9;
% speed of light
c = 299792458.0;
lambda = c / ( frequency ) ;
for n=1:10;
n2 = (2*n+1);
% radian frequency
w = 2.0*pi*frequency;
% wavenumber
k = w/c;
% conversion factor between cartesian and spherical Bessel/Hankel function
s = sqrt(0.5*pi/(k*radius));
% compute spherical bessel, hankel functions
[J(mode)] = besselj(mode + 1/2, k*radius); J = J*s;
[H(mode)] = besselh(mode + 1/2, 2, k*radius); H = H*s;
[J2(mode)] = besselj(mode + 1/2 - 1, k*radius); J2 = J2*s;
[H2(mode)] = besselh(mode + 1/2 - 1, 2, k*radius); H2 = H2*s;
% derivatives of spherical bessel and hankel functions % Recurrence relationship, Abramowitz and Stegun Page 361
kaJ1P(mode) = (k*radius*J2 - mode .* J );
kaH1P(mode) = (k*radius*H2 - mode .* H );
% Ruck, et. al. (3.2-1)
An = -((1i).^mode) .* ( J ./ H ) .* (2*mode + 1) ./ (mode.*(mode + 1));
% Ruck, et. al. (3.2-2), using derivatives of bessel functions
Bn = ((1i).^(mode+1)) .* (kaJ1P ./ kaH1P) .* (2*mode + 1) ./ (mode.*(mode + 1));
Qt = (lambda^2/2*pi)*sum(n2).*sum(real(An + Bn));
end
Co1=4.343*No;
================================================== ============
NOW SHOULD BE THE INTEGRATION OPERATION
Last edited: