Spectral Analysis – a Fourier transform tutorial – part #5

This part of the tutorial demonstrates the Fourier transform operation in a few cases of periodic and aperiodic signals, such as an AM signal, an FM signal, a rectangular nonrepetitive signal and a cardinal sinus signal. The last slide contains an application to the scaling property of the Fourier transform on a nonrepetitive time signal. It actually shows that spreading a signal in the time domain shrinks its spectrum and viceversa.

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This article has 9 Comments

  1. Hi George, I did create a sinus function with amplitude of 20 and frequency of 200Hz then I used the built-in FFT function in Excel the results I have got were different than what I expect, i.e, amplitude of 18 instead of 20, and the frequency 29Hz rather than 200Hz, I couldn’t figure it out why. I did use your template for the same function, the amplitude was 0.6 and the frequency 29. So both calculation gave different answers. Shall I send you the files? you may have the answer for that ? PS: my knowledge in this area are very limited. By the way your template is it DFT or FFT ?

  2. Yes, you definitely need to try. I am a little sceptical about applying the FT at counting steps but it would be interesting to experiment it on the data. Take data and put it in excel. Also do both integration and derivation on the original data and run different tests on all these stacks of data. These are just some wild guesses. You need to practically experiment with this yourself. Also if you have more time you could look into Kalman filters but also try various simple filters (low pass, high pass, band pass, FIR, IIR). All of there are easy and fun to implement in Excel. Your original idea with a simple threshold might work satisfactorily though. Play with a basic moving average filter before thresholding to get rid of noise. Good luck, George

  3. Great work keep it up! I’m currently working on examining accelerometer data from walk trips and thinking of using this technique to count steps. Do you think that is an effective technique for that purpose? I would use the amplitude values above certain threshold levels to identify step counts.

  4. Tarek, go to the “About” page on the top menu. There is a “Contact me at:” on that page.

  5. Hi George, Sorry I can’t see the email address!

  6. Tarek, firstly this site is for fun and inspiration only. Please don’t take anything from here to be used to design something that might put people’s life at risk. I am an electrical engineer and I do all of these things for fun myself since the life out there in industry can be quite boring. Within the next couple of years I will get to very advanced stuff here, and CFD and FEA will be prime subjects. I can help you with the FT. FFT and DFT (discrete) do the same thing just FFT saves some time. In your case you don’t mind if the computation takes 2 seconds or 5 seconds to plot a chart so just use DFT. To begin with, my worksheet is good enough, you just need to extend the number of time points to accommodate 38000. Sure, send me the file (in the About there is an email address) but keep working on it yourself too. Let’s keep the communication on the comment section – HERE. I need comments. Cheers, George

  7. Hi George,
    Thank you for your reply. Just to give you an idea about the problem that I am facing. I have 8m /s airflow of over a hard disk and I am looking to find out if the airflow is inducing the vibration of the disk. I did a transient computational fluid dynamics (CFD) simulation of the air flow over the disk, as results I have the pressure as function of time. I have been advised to record the pressure on different points and use the FFT to calculate the amplitude vs frequency, the sound level pressure (SPL) vs frequency. At this stage I will focus on analysing the data recorded on points before moving to surfaces. The outcome of the FFT calculation based on CFD analysis will be then compared to Finite Element Analysis (FEA). If the amplitudes are intersecting at the same frequencies, then that would answer my question about the cause of the disk vibration.

    Example of the data:

    time [s] Point 1 (Pressure) [Pa] Point 2 (Pressure) [Pa] Point 3 (Pressure) [Pa]
    0.00001 2.78E-04 4.61E-04 1.21E-05
    0.00002 1.45E-01 2.91E-02 -5.91E-04
    0.00003 -2.05E-02 2.99E-02 -3.65E-03
    0.00004 3.05E-01 3.79E-02 -9.40E-03
    0.00005 -5.18E-02 -1.02E-02 -1.61E-02
    0.00006 9.85E-01 1.15E-01 -9.77E-03
    0.00007 3.41E+00 5.79E-01 -1.57E-02

    I have 38000 sampling data. I can send you the data if want.
    I really appreciate your help.

    Tarek

  8. Tarek, due to my busy schedule I don’t promise anything but I will try. Please define your problem. Is a 3D surface? What is SPL? Do you have a function of pressure function of time (history)? George

  9. Hi,

    Thank you for the spreadsheet. I would like to ask you question. I have pressure times histories over a surface. I would like to calculate the SPL and the amplitudes by using the FFT. Could you please show me how to do it. Thank you in advance. Tarek

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