# Fourier Transform

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

hhh79bigo

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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. $A(f) = \frac{2}{N} \cdot \sum\limits_{t = 0}^{n - 1} {x_t \cdot \cos (2 \cdot \pi \cdot f \cdot t)}$ and $B(f) = \frac{2}{N} \cdot \sum\limits_{t = 0}^{n - 1} {x_t \cdot \sin (2 \cdot \pi \cdot f \cdot t)}$. The magnitude is given by $I\left| f \right| = \sqrt {\left[ {A(f)^2 } \right] + \left[ {B(f)^2 } \right]}$. 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.

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Yes that would be great.

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

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

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.