Apply Fourier Transform to Scanning Results of Metal of Length L

In summary, the speaker has a piece of metal with length L and has scanned it to obtain results in %FSH. They want to analyze the noise of the signal using a Fourier transform and ask for advice on how to apply it to the range of results. The expert suggests obtaining more data points and using the magnitude of the Fourier components instead of a FFT. They also explain how to extract the noise component from the signal and analyze it using statistical tests. The speaker asks for more information and the expert offers to share their worksheets for MathCAD. They also mention their experience with classified materials.
  • #1
hhh79bigo
48
0
Hi there,

I have a range of results from scanning a piece of metal of length L. The results from the scan are %FSH of the oscilloscope. I have to analyse the noise of the signal and thought I'd do this using a Fourier transform. Using the range of results as follows could you please tell me how I can apply Fourier to this?

Length RESULT
1---------0
2---------0
3---------0
4---------5
5---------0
6---------8
7---------0
8---------20
9--------- 0
10-------- 3
11---------0
12---------3
13---------5
14---------0
15---------65

Thankyou in advance

hhh79bigo
 
Last edited:
Mathematics news on Phys.org
  • #2
Data Points

I would try to obtain more data points if possible (50 minimum). Especially since you are trying to analyze noise. I would also suggest taking the magnitude of the Fourier components (Periodogram) instead of using a FFT. [itex]A(f) = \frac{2}{N} \cdot \sum\limits_{t = 0}^{n - 1} {x_t \cdot \cos (2 \cdot \pi \cdot f \cdot t)}[/itex] and [itex]B(f) = \frac{2}{N} \cdot \sum\limits_{t = 0}^{n - 1} {x_t \cdot \sin (2 \cdot \pi \cdot f \cdot t)}[/itex]. The magnitude is given by [itex]I\left| f \right| = \sqrt {\left[ {A(f)^2 } \right] + \left[ {B(f)^2 } \right]}[/itex]. What kind of information will you gain concerning the noise by looking at the signals spectrum? In a sense the spectrum is simply the distribution of harmonics in the signal. If you are interested I can tell you how to extract all the noise out of the signal and analyze it.
 
Last edited:
  • #3
Yes that would be great.

(By the way the info given is not the real results because the real results are classified!) :yuck:
 
  • #4
Yes that would be great.

(By the way the info given is not the real results because the real results are classified!) :yuck:

I need to be able to see if they are indicative of noise!

Thanks
 
  • #5
Signal Decomposition

If you just look at the signals spectrum it will hard to distinguish between harmonics from the noise and signal. Signals can be decomposed into typical two components. They are others but they are immaterial to this purpose. You can smooth a signal by using a moving average (see the link below). This process will remove all the noise from the original signal. The smoothed signal is know as the trend component. After you have removed the noise you must subtract the smoothed sequence of numbers from the original sequence of numbers. This will leave you with noise component of the signal. Once you have the noise component you can then run statistical test on the noise to determine properties of the noise and categorize what type of noise it is. Use a histogram to determine the distribution of amplitudes of the noise once you done that you can find the mean amplitude, variance of the noise, etc. You can also take the periodogram of the noise and normalize to it look at the distribution of frequencies. You can then analyze statistical properties also such as mean frequency percentage of frequencies bound in a region on the spectrum. If you are a MathCAD user I have created worksheets for this stuff. If you email me I will send it to you.

http://mathworld.wolfram.com/MovingAverage.html

On a second note. I know all about the classified thing. I have to walk through a metal detector, bomb detector, send all my hand carried items through a X-ray, and I even have to get my coffee cup scanned ever morning.
 

1. What is Fourier Transform and how is it applied to scanning results of metal of length L?

Fourier Transform is a mathematical technique used to decompose a signal into its underlying frequencies. It is used in signal processing and image analysis to identify patterns and extract useful information. In the context of scanning results of metal of length L, Fourier Transform can be applied to analyze the distribution of metals in a sample and identify any patterns or anomalies in the data.

2. Why is Fourier Transform useful in analyzing metals of different lengths?

Fourier Transform is useful in analyzing metals of different lengths because it allows us to break down the signal into individual frequencies, making it easier to compare and analyze different lengths. This can help in identifying any differences or similarities between metals of different lengths and understanding their properties.

3. Can Fourier Transform be used to analyze other properties of metals besides length?

Yes, Fourier Transform can be used to analyze other properties of metals besides length. It can be applied to analyze the composition, structure, and density of metals, as well as their electrical and thermal properties. This makes it a versatile tool for studying various aspects of metal materials.

4. What are the limitations of using Fourier Transform in metal analysis?

One limitation of using Fourier Transform in metal analysis is that it assumes the signal to be periodic, which may not always be the case in real-world scenarios. Additionally, Fourier Transform may not be able to accurately capture very high or very low frequency components in the signal, leading to potential errors in the analysis.

5. Are there any alternatives to using Fourier Transform in metal analysis?

Yes, there are alternative techniques to Fourier Transform that can be used in metal analysis. Some examples include wavelet transform, short-time Fourier transform, and spectroscopy techniques. Each of these methods has its own advantages and limitations, and the choice of technique will depend on the specific research question and data being analyzed.

Similar threads

Replies
6
Views
1K
Replies
13
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • General Math
Replies
2
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
927
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
Replies
2
Views
950
Back
Top