Analyzing Sinusoidal Parameters and Identifying N in Complex Numbers Summation

[Bob Busby]

Homework Statement

I'm given that the sum from k = 0 to N-1 of e^(j*2*pi*k/N) + 0. Then there's some code.

tt = 0:1:1000;
xx = 0*tt;
for kk=5:11
xx = xx + 99*cos(0.006*pi*tt + 0.25*pi*kk);
end
plot(tt,xx), title(’SECTION of a SINUSOID’), xlabel(’TIME (sec)’)

The plot made from the vector xx is a single sinusoid, which can be written as A*(omega_0t + phi). I need to use the identity above and analyze the code to determine the parameters for the sinusoid in the vector xx. Also, I need to identify the value of N needed to apply the identity.

Homework Equations

the sum from k = 0 to N-1 of e^(j*2*pi*k/N) + 0

The Attempt at a Solution

I think the value of N should be 2/.25 but I don't see how to apply the identity since there are only 11-5 sinusoids being summed.

 

[KataKoniK]

Can you provide more information about the context of this problem? It seems like there may be some missing information or steps that need to be clarified in order to fully understand and analyze the code and determine the parameters for the sinusoid.