Signal Processing and the Duffing ODE

In summary, the conversation revolves around two attached plots and the question of whether the signal was correctly reconstructed. The solution from the Duffing ODE is shown in signal.pdf and the FFT in pow.pdf. The main frequency observed is shown in the FFT plot. After some troubleshooting, it is discovered that the issue was with the sampling rate being incorrect. The conversation ends with a mention of using a dual signal to check the accuracy of the FFT.
  • #1
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

  • pow.pdf
    26.1 KB · Views: 186
  • signal.pdf
    182.3 KB · Views: 205
Physics news on Phys.org
  • #2
NVM, I figured it out. Thanks though.
 
  • #3
So what was it sampling rate wrong?
 
  • #4
Yep! Only took me all afternoon to figure it our lol
 
  • #5
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.
 
  • Like
Likes member 428835
  • #6
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?
 

1. What is signal processing?

Signal processing is a field of science that deals with analyzing, modifying, and synthesizing signals. A signal is a physical quantity that varies with time or space, such as sound, images, or electrical signals. Signal processing involves techniques and algorithms for extracting useful information from signals, removing noise, and enhancing signal quality.

2. What is the Duffing ODE?

The Duffing ODE (ordinary differential equation) is a mathematical model that describes the behavior of a damped, driven oscillator. It is used in signal processing to analyze nonlinear systems, such as chaotic systems. The equation takes the form of x'' + δx' + αx + βx^3 = γcos(ωt), where x represents the displacement of the oscillator, δ is the damping coefficient, α and β are nonlinear coefficients, γ is the driving force, and ω is the frequency of the driving force.

3. How is signal processing used in analyzing the Duffing ODE?

Signal processing techniques, such as Fourier analysis and spectral analysis, are used to analyze the behavior of the Duffing ODE. These techniques allow us to understand the frequency components of the signal and how they are affected by the nonlinear coefficients. Additionally, signal processing can be used to identify chaotic behavior in the system and predict its future behavior.

4. What are some real-world applications of signal processing and the Duffing ODE?

Signal processing and the Duffing ODE have a wide range of applications in various fields, including physics, engineering, biology, and economics. Some examples include analyzing vibrations in mechanical systems, studying brain activity in neuroscience, predicting stock market fluctuations, and understanding the dynamics of chemical reactions.

5. What are the challenges in using signal processing for the Duffing ODE?

One of the main challenges in using signal processing for the Duffing ODE is dealing with the nonlinear nature of the equation. This can make it difficult to extract useful information from the signal and predict the behavior of the system. Additionally, the presence of noise in the signal can also complicate the analysis and require advanced signal processing techniques to filter out the noise.

Similar threads

MATLAB Creating and recovering a frequency shift in time domain in MATLAB
    • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
1K
Digital Electronics: Image Frequencies & Nyquist/Shannon Theorems
    • Electrical Engineering
Replies
7
Views
3K
How to simulate multipath signals?
    • Electrical Engineering
2
Replies
43
Views
4K
How to measure the time dependent correlation of two signals
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
Some questions about Fourier transformation
    • General Math
Replies
13
Views
2K
Problems regarding signal sampling
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Op-amp compensation of cascade fudges audio signal oddly
    • Electrical Engineering
Replies
3
Views
793
How can background be separated from 1D data with data smoothing/filtering?
    • General Math
Replies
6
Views
2K
Tips/recommendations for continuing my learning in DSP?
    • STEM Academic Advising
Replies
6
Views
1K
EE/Math electives for signal processing
    • STEM Academic Advising
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top