Question
Transcribed Text
Problem 1
The solar radiation for Tucson, Arizona has been tabulated as,
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Radiation
144
188
245
311
351
359
308
287
260
211
159
131
assuming each month is 30 days long, fit a sinusoid to this data. Use the results to predict the radiation
on the 15th of October.
Problem 2
The periodic triangular wave function f(f) is defined as
n
for
n
2
2
for "
f(t)
2
2
n
Find the Fourier coefficients 80.9 28 and b, bb and approximate the periodic triangular wave
function by the Fourier series. Plot the first four approximations along with the triangular wave.
f(t)
"
f(t)=-t
*
2
n
7
"
2
"
t
2
n
2
T
T
2
2
Problem 3
Given the function of time,
k astf(t) iza
ac-a
Find the amplitude spectrum of f(t), IP(w) and graph both functions.
Problem 4
Compare the continuous Fourier Transform tothe discrete Fourier Transform for the function,
Use 64 sampling points, ie N=64 and a scaling factor of T=0.25 so that NT=16. Graph the real and
imaginary comparisons for separately. Consider the modified form of the discrete Fourier Transform
with wo 2itw,
N-1
Fk
n-0
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function main()clear all
close all %empty variables in memory then close all windows, pictures etc start fresh
options=odeset('RelTol',1e-12,'AbsTol', 1e-12);
time1=8147; %time it takes for earth to do one revolution in seconds
mu=3.986004415*10^5;
r0=[6678.1363, 0, 0];
v0=[0, 7.725760634075587,0];%
[propagatedtime,propagatedposvel] =ode45(@(t,x)twobody(t,x,mu),[0, time1],[r0, v0]',options);
N=length(propagatedtime); %length of the vector propagatedtime
size(propagatedposvel)
plot3(propagatedposvel(:,1),propagatedposvel(:,2),propagatedposvel(:,3))
% we plot the values x,y,z in 3d
hold on
xlabel('x')
ylabel('y')
zlabel('z')
disp('-------Part 3----------')
options=odeset('RelTol',1e-12,'AbsTol', 1e-12);
a=propagatedposvel(N,:) % propagatedposvel is of size N times 6...
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