Abstract - University of Arizona



Fast Fourier Transformation of Vibration Signals using Microsoft EXCEL

Mohammed Aref

(mdaref120@)

Department of Information Technology

Salalah College of Technology (SCOT)

Salalah, Sultanate of Oman

Abstract

One needs to do signal analysis for a variety of situations. The Fast Fourier Transformation is the mainstay of vibration signal analysis as it is the most time saving algorithm. It is a computational algorithm which computes Fourier Transformation of discrete data. This can be done by several of the packages available. We chose to use the Microsoft Excel as it is very widely available. Microsoft Excel is a wonderful and easily available application which can be used for implementing this algorithm. The experiments show that this method is capable to find the Fourier Transformation of the vibration signals.

Background

The Science laboratories supposed to be made up of three components, namely data gathering, Analysis and conclusions. Many experiments need high speed data collection, like the study of sound or vibration signals. We know that vibrations are the fluctuations of a mechanical system about an equilibrium position. To analyze the data may need some sophisticated mathematical techniques like FFT. The Fast Fourier transform (FFT), which is an efficient adaptation of Fourier’s work, is regularly used to analyze sound waves. Here we are trying to do it using MS-Excel, which is easily available application software mostly in every personal computer. The hardware and software available with the computers can be used for some experiments without any additional expenses. The microphone and the sound card provide a means for data gathering and the spreadsheet Excel provides a means of data analysis.

Design

We have used the microphone and sound card, along with the PC oscilloscope program Winscope downloaded from internet to study sound in time and frequency domain as shown in the fig 1. This experiment carries out two phases, the first is to acquire the data, second process the acquired data using MS-Excel. For this experiment the data source is computer speaker. That the .wav file is played and at the same time sound data recorded with help of setup shown in fig 1. The captured data has been transferred to Microsoft Excel oscilloscope for Windows, which is a Windows application. We are grateful to Konstantin Zeldovich for providing Winscope program free of cost on internet. MS-Excel spreadsheet provides quite a powerful environment for such experiments. We are in process of developing many other experiments using sound card. Here we would like to be able to measure the signal as a function of time at a specific data acquisition rate, which depends on the nature of the observed signal.

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Fig 1: Schematic experimental setup

MS-Excel provides the FFT tools. One can access it from the tools menu as by opening Data analysis. If in case data Analysis does not appear in the tools menu, so it can be access from Add-Ins menu by adding Analysis Toolpak as Fourier Transform is a part of it. Finally Fourier Analysis can be select from Data Analysis list. Excel works with discrete data and has a build in Fast Fourier Transform Algorithm. The important and basic requirement is that the number of points to be transformed must be always 2n. To make exactly with the same number of samples points if needed can add zeros.

An FFT operation involves complex numbers. In excel, such a number can be represented as -19.085527+.66697647i. The Wave data we are getting is –real number, just complex number with no imaginary parts. The computer sound card captures the data by 22050Hz sampling rate. Here we have got 512 sample points in the table shown in fig 2. By plotting the graph of derive points (FFT values) and Signal Amplitude column the resultant picture shown in fig 3. Actually, there are a lot of things to be borne in mind when doing this, but this simple example does illustrates the method and shows its potential.

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Fig 2: Reconstructed Signal values from Sampled Points using MS-Excel

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Fig 3: Fast Fourier Transformation using MS-Excel

Conclusions

It is seen that PC with microphone, sound card, winscope program and MS-Excel spreadsheet provides quite a powerful environment for such experiments. We are in process of developing many other experiments using sound card.

References:

1. “Using Sound to Analyze Hardware Operation: A Progress Report”, Robert Karns Henry, East Tennessee State University

2. FFT Spectrum Analyzer Applet , United Kingdom

3. “Digital Data Acquisition and Analysis”, Department of Physics, Northeastern University

4. “Sound Analysis using FFT”, Dr. Mohammed Iqbal, Department of Physics, India.

5. Ronald N. Bracewell, "The Fourier Transform," Scientific American, June 1989, pp. 86-95.

6. “Mechanical Vibrations” , S. Graham Kelly, McGraw-Hill International Editions, Mechanical Engineering Series

7. The Zoom FFT by Bores Signal processing , Surrey

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