×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Fourier Analysis and Synthesis

Fourier Analysis and Synthesis

Fourier Analysis and Synthesis

(OP)
I'm a software engineer working on a project to plot harmonic waveforms from source data. I do this using a Fourier approximation - taking harmonic numbers, magnitudes and phases as input, and deriving magnitudes to be plotted against time.

I use the following equation:
f(t) = sigma (from n =1 to 50) ansin(n * omega0 * t + thetan)

where:
  an          = nth magnitude
  n            = harmonic number
  omega0  = fundamental frequency (2*pi*f)
  t            = time
  thetan    = nth phase

Basically, this is a simplified equation which allows me to construct (or to use more technical terms: do a Fourier synthesis) harmonic waveforms  for up to 50 harmonics.

What I need to be able to do is work backwards (i.e. do a Fourier analysis) and take the derived magnitudes (from the Fourier synthesis), put them into an equation which determines the original data going into the equation (or an approximation of it anyway). Does anyone know how to go about this or sites that talk about this?

RE: Fourier Analysis and Synthesis

Why not do an FFT?  It produces the same type of results and allows you take the inverse transform of filtered data to determine the magnitude of the components.

TTFN

RE: Fourier Analysis and Synthesis

I have found several good sources of theoretical information about Fourier analyses by doing a google search on the internet.  I haven't save the URL's but you should also have success.

If your data is in digital form, as from a digital meter, the FFT would be more appropriate.

RE: Fourier Analysis and Synthesis

(OP)
At the moment, I pass in real values (i.e. magnitudes and phases) into the above equation which produces real values as output to use in a time plot.

My data is not in digital form so what technique is best to go with? Basically, I'm a bit confused with all the terminology i.e. Discrete Fourier Transform, Fast Fourier Transform, Chirp Z Transform. As I said at the top, I'm a software engineer and I have a reasonable mathematical background but I don't really have any physics or electrical engineering knowledge. So any other advice would be very welcome!

RE: Fourier Analysis and Synthesis

Where does your frequency magnitude/phase data come from?
Can you describe a little more about the frequency magnitude/phase data that you have available as a starting point... where did it come from, what form is it in?

RE: Fourier Analysis and Synthesis

(OP)
The magnitude/phase data describe various electrical power system elements. So for a busbar element the magnitude is the voltage (in volts) and for other elements it is the current (in amps). It's in polar form. Does this help describe the data (I'm not really sure what else I can say about it!)?

RE: Fourier Analysis and Synthesis

If it's not in digital form, how are you doing the Fourier analysis.  Surely, you're not using an analog computer?

TTFN

RE: Fourier Analysis and Synthesis

Try
http://aurora.phys.utk.edu/~forrest/papers/fourier/index.html
"An Introduction to Fourier Theory" by Forrest Hoffman.

If you use Mathcad, there is a Mathcad Electronic Book "Theory and Problems of Electric Circuits" from Shaum's Outline Series that has a good explanation of trigonometric and exponential fourier analysis (non-discrete).  There are also some Mathcad worksheets on Fourier analysis in the Mathcad Library.

RE: Fourier Analysis and Synthesis

(OP)
IRStuff,
So far I have only done a Fourier Synthesis using the equation at the top of this post. What I'm trying to find out is how to do Fourier Analysis with the data I currently have.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources