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?
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
TTFN
RE: Fourier Analysis and Synthesis
If your data is in digital form, as from a digital meter, the FFT would be more appropriate.
RE: Fourier Analysis and Synthesis
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
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
RE: Fourier Analysis and Synthesis
TTFN
RE: Fourier Analysis and Synthesis
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
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.