Finding Fundamental Period of x(t) with 2 Exponentials

In summary, the formula for finding the fundamental period of x(t) with 2 exponentials is T = 2π/|ω|, where ω is the frequency of the exponential term in x(t). The existence of the fundamental period can be determined by the frequencies of the exponentials, with the fundamental period not existing if the frequencies are different and existing if they are the same or have a common multiple. This formula can be used for any function with 2 exponentials as long as the frequencies are the same or a common multiple. Negative frequencies do not affect the calculation of the fundamental period, as they can be treated as positive frequencies with the same magnitude. However, this formula cannot be used for functions with more than
  • #1
EvLer
458
0
I can't get my answer match up with correct answer in the book:
i need to find fundamental period of this signal:

x(t) = 2 cos(10t + 1) - sin(4t -1)

i used formula for cosine Acos(wt + a) = ... that gives two exponentials... so I got pi/10 instead of pi for answer...
any help is appreciated
 
Physics news on Phys.org
  • #2
x(t) = 2 cos(10t + 1) - sin(4t -1)

Is there an [itex]\omega[/itex] missing in this forumla?

The +1 and -1 are phase shifts.

10 and 4 share a gcf of 2.

IIRC, there may be a relationship between gcf and the fundamental frequency.
 
  • #3


It is important to note that there are different methods for finding the fundamental period of a signal, and the results may vary depending on the approach used. It is also possible that there may be a mistake in the book's answer.

In this case, it appears that you have used the formula for cosine in the form of Acos(wt + a), which gives two exponentials. However, this formula is used for a single cosine term, not a combination of cosine and sine terms. Therefore, it may not give the correct result for this particular signal.

One way to approach this problem is to rewrite the signal in terms of a single exponential term using Euler's formula. This would result in a complex exponential with a fundamental period of 2pi/10, which is equivalent to pi/5. This may be the correct answer according to the book.

Another approach could be to use the formula for the fundamental period of a sum of two sinusoidal signals, which is given by 2pi/LCM(w1,w2), where LCM is the least common multiple of the frequencies w1 and w2. In this case, the fundamental period would be 2pi/LCM(10,4) = pi/5, which is once again equivalent to pi/5.

Overall, it is important to carefully consider the methods and formulas being used when finding the fundamental period of a signal, and to double check the calculations for accuracy. If there are discrepancies between your results and the book's answer, it may be helpful to consult with a colleague or instructor for further clarification.
 

What is the formula for finding the fundamental period of x(t) with 2 exponentials?

The formula for finding the fundamental period of x(t) with 2 exponentials is T = 2π/|ω|, where ω is the frequency of the exponential term in x(t).

How do I know if the fundamental period of x(t) with 2 exponentials exists?

If the exponentials in x(t) have different frequencies, then the fundamental period does not exist. However, if the frequencies are the same or have a common multiple, then the fundamental period exists.

Can I use the same formula to find the fundamental period for any function with 2 exponentials?

Yes, the same formula can be used to find the fundamental period for any function with 2 exponentials, as long as the exponentials have the same or a common multiple frequency.

What happens if the exponentials in x(t) have a negative frequency?

If the exponentials in x(t) have a negative frequency, then the fundamental period will still be positive. In this case, the negative frequency can be treated as a positive frequency with the same magnitude.

Can I use this formula to find the fundamental period for functions with more than 2 exponentials?

No, this formula is specifically for functions with 2 exponentials. For functions with more than 2 exponentials, the fundamental period must be found using other methods, such as finding the least common multiple of the exponential frequencies.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
5
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
  • General Math
Replies
33
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
7
Views
859
  • Engineering and Comp Sci Homework Help
Replies
3
Views
826
Replies
3
Views
699
  • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
990
  • General Math
Replies
7
Views
898
Back
Top