CODE
% LightningFFTs2
clf
clc
if (~exist('AL10','var')) (1)
load Lightning.mat
end
x=input('Input Lightning Data
Variable: '); (2)
COMMENTS
(1)
Loads data file
containing lightning data.
Lightning.mat can be
downloaded off the Cosmiac
wiki site.
(2)
Input lightning data
variable name (e.g. AL2,
AL10)
(3)
Computes period and
length of signal which is
then used to find frequency
in variable “hertz”
(4)
Fourier Transform of
lightning signal
(5)
Plots semi-logarithmic
graph of frequency versus
magnitude of the Fourier
Transform
(6)
Plots two vertical
lines that specify 30-300 MHz
frequency range
(7)
Table of antenna factor
values. Antenna factor can be
seen on the wiki site.
(8)
Used to define domain
of signal that needs to be
attenuated by antenna factor.
T=1/2.5e9;
N=length(x); (3)
k=0:N-1;
X=fft(x(:,2)); (4)
magX=abs(X);
hertz=k*(1/(N*T));
figure(1) (5)
semilogy((hertz(1:N/2)),magX(1:N/2)
),...
title('Magnitude of X(k)'),...
xlabel('Hz'),ylabel('|X(k)|'),
grid
hold on
plot([3e7;3e7],[10^4;10^4],'r','LineWidth',2)
plot([3e8;3e8],[10^4;10^4],'r','LineWidth',2) (6)
hold off
a=hertz;
b=magX;
tab=[30e6 12.5;
75e6 6; 90e6 8;
14;...
135e6 14.5;
180e6 15; 195e6
17.5;...
225e6 16.5;
16; 270e6 17.5;
20];(7)
45e6 11; 60e6 12;
105e6 13; 120e6
150e6 14; 165e6 14;
17.5; 210e6
240e6 16.5; 255e6
285e6 18; 300e6
subdomain=[30e6,300e6]; (8)
xsub=N*T*subdomain(1):N*T*subdomain
(2);
xbefore=1:N*T*subdomain(1);
end_x=size(x)/2;
xafter=N*T*subdomain(2):end_x;
xi=linspace(0,300e6,length(xsub));
pp=interp1(tab(:,1),tab(:,2),'pchip
','pp'); (9)
yi=ppval(pp,xi);
figure(2)
semilogy(abs(X(xsub)))
title('Magnitude of X(k)'),...
xlabel('Hz'),ylabel('|X(k)|'),
grid (10)
figure(3)
sig_af=abs(X(xsub))+yi’; (11)
phase_af=angle(X(xsub));
total_sig=phase_af./sig_af;
complex_corrected=sig_af.*(cos(phas
e_af)+1*i.*(sin(phase_af)));
plot(abs(sig_af))
title('Signal minus Antenna
Factor'),...
xlabel('Magnitude of
X(k)'),ylabel('|X(k)|'), grid (12)
[maxX_k,maxloc]=max(abs(sig_af));
[minX_k,minloc]=min(abs(sig_af));
(13)
xsub=N*T*subdomain(1):N*T*subdomain
(2);
signal = [ ...
X(1:N*T*subdomain(1)-1); ...
complex_corrected; ...
X(N*T*subdomain(2)+1:500e3);
...
X(500e3:-1:N*T*subdomain(2)+1);
...
complex_corrected(size(complex_corr
ected,1):-1:1); ...
X(N*T*subdomain(1)-1:-1:2); ...
]; (14)
sig=ifft(signal); (15)
figure(4) (16)
subplot(2,1,1)
plot(1:size(x),x)
title('Signal')
xlabel('Time')
ylabel('Volts')
grid on
subplot(2,1,2)
(9)
Creation of polynomial
function used to define
antenna factor
(10)
Semi-logarithmic plot
of 30-300 MHz region
(11)
Correcting signal using
antenna factor
(12)
Plot of 30-300 MHz
region after antenna gain or
loss is considered
(13)
Returns minimum and
maximum values of X(k) in the
30-300 MHz region
(14)
Reconstruction of
original signal with antenna
factor taken into account in
the frequency domain
(15)
Inverse Fourier
Transform of corrected signal
(16)
Plots of original
signal and corrected signal
plot(real(1:size(sig),sig))
(17)
Maximum intensity of
electric field
[v,loc]=max(sig);
correct_sig=real(sig(loc100:loc+100,:));
(18)
Impedance of free
space: Z0=120π Ω
E_max=max(sig); (17)
(19)
z0=120*pi; (18)
(20)
Calculates time length
of the corrected signal. The
code then calculates the
energy of the signal by
numerical integration and the
power of the signal
noise=[x(1:4e5) x(6e5:1e6)];
energy_noise=trapz(real(noise.^2))/
z0; (19)
time_sig=length(x)*(x(2)-x(1));
energy_sig=trapz(real(correct_sig.^
2))/z0-energy_noise;
power_sig=energy_sig/time_sig; (20)
fprintf('\nMaximum value of X(k):
%f dBV \n',maxX_k)
fprintf('\nLocation of Maximum dBV:
%f Hz \n',maxloc)
fprintf('\nMinimum value of X(k):
%f dBV \n',minX_k)
fprintf('\nLocation of Minimum dBV:
%f Hz \n',minloc)
fprintf('\nMaximum Intensity of EField: %f volts/meter \n',E_max)
fprintf('\nAverage Power of EField: %f Watts \n',power_sig)
fprintf('\nEnergy: %f Joules
\n',energy_sig)(21)
R=input('\nInput "1" to exit
program and close plots: ');
if R==1
close all
end
Calculates noise energy
(21)
Returns maximum and
minimum frequency and their
locations, maximum intensity,
and average power and
displays them on the command
window