Fourier Coefficient Amplitude: Is Infinity Possible?

  • Thread starter Thread starter magnifik
  • Start date Start date
  • Tags Tags
    Amplitude Spectra
AI Thread Summary
The discussion centers on the possibility of achieving an infinite amplitude for a Fourier coefficient, specifically in the context of the signal sin(w0t) over the interval from 0 to T/2. The derived coefficient formula leads to an infinite result for F1, raising questions about its validity. It is argued that an infinite coefficient would not allow for the proper reconstruction of the original signal, as it would result in an infinite product with the sinusoid. Therefore, the conclusion is that the coefficient must be incorrect, as it contradicts the requirement for a well-behaved original signal. The conversation emphasizes the importance of finite coefficients in Fourier analysis for accurate signal representation.
magnifik
Messages
350
Reaction score
0
Is it possible to have an infinite value for the amplitude of a Fourier coefficient?

The signal is sin(w0t) from 0 to T/2. My resulting coefficient formula was
Fn = 2/[4pi(1-n)] + 2/[4pi(1+n)]
so for F1 i got infinity ... is this possible?
or is coefficient just wrong?
 
Physics news on Phys.org
This solution cannot be correct, because if you add the Fourier components up, you will get infinity multiplied by a sinusoid. Does that reconstruct the original signal in the designated range? No, and it must for such a well-behaved original signal.
 

Similar threads

Engineering Reconstruct a signal by determining the N Fourier Coefficients
Replies
6
Views
5K
Phase and amplitude spectrum of signal
Replies
14
Views
3K
Comp Sci Plot periodic function with Fourier coefficients
Replies
3
Views
2K
Fourier series neither odd nor even
Replies
3
Views
6K
Power of first three harmonics of periodic signal
Replies
1
Views
1K
Comp Sci Harmonic Amplitudes - 3rd & 101st
Replies
13
Views
2K
Understanding MIT's applet on sound with Fourier coefficients
Replies
3
Views
1K
Engineering MATLAB Exercise on DFT
Replies
1
Views
2K
Finding Fourier Coefficients: 0's and Questions
Replies
9
Views
3K
Engineering Question - Calculating Coefficients for 2nd Order Transient Analysis
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top