# GEOPHYS 6001 Advanced Geophysical Data Analysis Worksheet The subject is Advanced Geophysical Data Analysis and Instructions are in the attachment. Geophys

GEOPHYS 6001 Advanced Geophysical Data Analysis Worksheet The subject is Advanced Geophysical Data Analysis and Instructions are in the attachment. Geophys 6001: Advanced Geophysical Data Analysis

Assignment 5 (10 points)

The purpose of this Matlab assignment is to general a square-wave (boxcar), which is made

up of a sum of odd harmonics.

Go through the Matlab instructions (g6001-L14-matlab-basics.pdf) first, then do the following

tasks. Submit all the figures you have created and explain your observations.

1.

Plot a sine function. To achieve this, you may first generate a time vector, then take

the sine of all the points.

? Here is my example to generate the first harmonic in Matlab (Please general your

own vector), plot

t=0:0.2:10;

y=sin(t);

plot(t,y);

2.

Sum the first and the third harmonics, plot.

?Matlab

y=sin(t)+sin(3*t)/3;

plot(t,y);

3.

Sum the first, third, and fifth harmonics, plot.

?Matlab

Y=sin(t)+sin(3*t)/3+sin(5*t)/5;

plot(t,y);

4.

5.

6.

Sum the first, third, fifth, seventh, ninth, 11th, 13th, 15th, 17th, and 19th harmonics, plot.

Sum a number of harmonics of your choice (at least 15 harmonics), plot.

Compare the above five plots and explain what you have observed. Who was right?

Fourier or Lagrange?

7. Perform the following in Matlab, explain the results.

t = 0:.02:3.14;

y = zeros(10,length(t));

x = zeros(size(t));

for k=1:2:19

x = x + sin(k*t)/k;

y((k+1)/2,:) = x;

end

plot(y(1:2:9,:)’)

title(‘The building of a square wave: Gibbs” effect’)

8. Perform the following in Matlab, explain the results.

surf(y);

shading interp

axis off ij

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