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Phase and Magnitude of a Cosine 
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#1
Nov712, 04:45 PM

P: 1

1. The problem statement, all variables and given/known data
Graph the magnitude and phase of the function: H(w) = cos(3w) 2. Relevant equations None 3. The attempt at a solution So here's the thing, I understand how to graph the phase and magnitude of any sort of function like X(w) = A*exp(wt). In that case, the magnitude would just be X(w) = A and the phase would be w. However, I'm not sure how to apply that to graphing a cosine. I know that it doesn't have any imaginary portions (I think), so the magnitude would be just the absolute value of the function, which would be the cos function with a period of (2*pi)/3 but with all the negative parts flipped over the xaxis. Using Matlab, I see that this is indeed the case: However, I don't understand how to get the phase graph or why it is like it is: Could someone explain this to me? Thanks in advance! 


#2
Nov712, 08:14 PM

HW Helper
Thanks
P: 5,243

It seems you are thinking of the case where the exponent is imaginary. But it isn't imaginary in the example you show here. This sort of phase comparison — of signals of differing frequencies — is relevant to PLLs. 


#3
Nov712, 11:09 PM

P: 296

H(w) changes sign at some w. The magnitude only shows size so sign change has to be reflected in the phase.



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