Signal Processing and the Duffing ODE

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Discussion Overview

The discussion revolves around the reconstruction of a signal derived from the Duffing ordinary differential equation (ODE) using Fast Fourier Transform (FFT). Participants explore the accuracy of the signal reconstruction and the implications of sampling rates on the results.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant presents plots of a signal from the Duffing ODE and questions the correctness of the signal reconstruction using FFT.
  • Another participant suggests that the issue may have been related to the sampling rate.
  • A later reply confirms that the participant resolved the issue after realizing the sampling rate was incorrect.
  • One participant mentions the Nyquist frequency as a common source of confusion when working with FFT plots.
  • Another participant reflects on their experience with FFT in MATLAB, noting the importance of verifying the FFT results by using dual sine curves.
  • One participant expresses that returning to a pure sine wave should yield accurate results, indicating a method for troubleshooting FFT issues.

Areas of Agreement / Disagreement

Participants generally agree that the sampling rate was a critical factor in the signal reconstruction issue, but the discussion includes multiple perspectives on how to approach and verify FFT results.

Contextual Notes

Limitations in the discussion include potential assumptions about the sampling rate and the definitions of frequency constraints, as well as the unresolved details of the reconstruction process.

Who May Find This Useful

Readers interested in signal processing, particularly those working with FFT and the Duffing ODE, may find the discussion relevant.

member 428835
Hi PF!

Attached are two plots: signal.pdf is a solution from the Duffing ODE, and plots vertical displacement over time, both the raw signal (blue) and the reconstructed signal from an FFT (red). I've also shown a zoomed in view so you can see how oscillatory the signal is.

pow.pdf plots the FFT, showing one main frequency observed.

My question is, have I correctly reconstructed this signal? Sure look like I've done something terribly wrong, but perhaps I have not?
 

Attachments

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NVM, I figured it out. Thanks though.
 
Yep! Only took me all afternoon to figure it our lol
 
There that's frequency constraint aka the Nyquist frequency that always gets me.

When we first did FFT plots in MATLAB we constructed a dual signal by adding two sine curves and then checking to see that the FFT got the spectrum right.
 
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jedishrfu said:
There that's frequency constraint aka the Nyquist frequency that always gets me.

When we first did FFT plots in MATLAB we constructed a dual signal by adding two sine curves and then checking to see that the FFT got the spectrum right.
That's ultimately how I figured out what was wrong actually...take it back to a pure sine wave and it better be 100% accurate right?
 

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