Fourier Analysis and Synthesis

[EngineeringNewbie]

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) a_nsin(n * omega₀ * t + theta_n)

where:
a_n = nth magnitude
n = harmonic number
omega₀ = fundamental frequency (2*pi*f)
t = time
theta_n = 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?

 

[IRstuff]

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

 

[jghrist]

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.

 

[EngineeringNewbie]

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! ;-)

 

[electricpete]

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?

 

[EngineeringNewbie]

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!)?

 

[IRstuff]

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

 

[jghrist]

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.

 

[EngineeringNewbie]

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.