This is a video preview of the Fourier transform model presented on this blog before.

A tutorial explaining the creation of such a model was posted here too.

2011-06-17

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This is a video preview of the Fourier transform model presented on this blog before.

A tutorial explaining the creation of such a model was posted here too.

2011-06-17

Previous Post: A Rigid Gravitational Pendulum Model – video preview

Hi Tobi! So you have to describe a real (not imaginary or complex), 100 percent periodic signal with a simple formula? You need to use either a cosine transform (the formula will contain only cosines – since the signal is periodic), or it’s easier to just use a Fourier Transform because Fourier is readily available (the Fourier transform will be more complicated but it works for non-periodic signals too. If you chose to use cosine transform (which is the best option in your case), check Wikipedia for it. If the signal is periodic, you will only have harmonics at f, 2f, 3f, … Just put together, say 100-1000 periods (the more periods the more precise the results) and ran it through the Fourier calculator, or make yourself a very basic cosine transform calculator (not hard at all – I should really do this as a project on this site). Is the signal even? This refers to the symmetry of the signal. Google “even – odd signal”. For an even signal you only have DC plus even harmonics which makes the formula simpler. Let me know and I could help you further.

Tschüß

Hi,

I have some data points over 0°…360°. It is kind of distorted sinus form, but not exact. Repeating every 360°. How can I create a formula out of these x/y points?

Thank you!

Anant, Fourier transform is a type of measurement, it shows the distribution of certain frequency components in a signal. In general any program program is limited, which means it can process a certain maximum number of points. Universe is however infinite. You cannot characterize the whole universe with a limited tool. You need to specify the start and stop frequency based on your needs. Let’s say you are looking at the power network in a residence (apartment). If you are a power engineer, you might be interested to look at anything between, say 10 Hz and 1000 Hz. If you are a telecom engineer you might look between say 100MHz and 2GHz since there might be telecom information transmitted over the same power grid. So, both engineers use the same tool and look at the same signal except they are interested to diagnose different regions of the spectrum. Another way to think about it, think at FT as a microscope. Specifying the start and stop frequency is like specifying the magnification and the orientation (where exactly the microscope is pointing) of the microscope. Or in a hospital, a foot doctor will use an X-ray machine to image the foot, whereas hand doctor will use the same machine to image the hand of the same patient. As far as Fourier transform is concerned, you need to start wide at the beginning of the measurement and after you identified certain regions of interests, you redo the measurements on certain narrow areas of the signal spectrum.

Hi George

Thanks for this excellent tool.

I have few queries though.

How do we decide what are the Start_Freq and Stop_Freq?

Not really. I should completely redo the whole Fourier section.

Is your DFT template equivalent to the Lanczos approach?

… To be more precise: I need to define with respect to the epitrochoid curve center its point vectors as a function of their vector angle for given base and rolling circle radii and k factor. I hope you can help.

Congrats George on your strong continuing support for Excel 2003. I am completely with you on the dumb down issue in newer releases. Anyway, I need to accurately define the direct polar coordinates of epitrochoid curve points with respect to the epitrochoid center with given base and rolling circle radii as well as k factor. All formulas I can find relate to the rotation angle of the moving circle.

I tried your fantastic Fourier Transform Calculator, but the results seem inconclusive. Since you are quite a math wizard I thought you might be able to help, please.

Hi Zhen! In this case I’ve chosen 3 different random frequencies (in that particular input function – however there are three input functions you can select) that happen to be the values mentioned by you. It’s an arbitrary choice just to prove that the Fourier calculator works OK. I could have chosen 1, or 7, or 25 different frequencies or any other number. On the other hand I have a better Fourier calculator version (built almost exclusively in VBA) and I will need to publish it on the site. Plus I will also have courses soon. Cheers!

Hello George, Where are the other frequency ? Why 1.5Hz,1.2Hz,0.9Hz are integrated in the function formula ?

I couldn’t resist commenting. Perfectly written!

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When I say variable periods I mean create a mega series (2000 points) with a certain period between the 20 elementary series, then create more of these mega (fake) series with different periods. All these series are fairly close to each others. It’s more an optimization process using both visual clues and calculated clues.

My model tries to be a very basic implementation of a classic algorithm.

Try the following:

1. Plot the series and try to visually clean the ends (series of zeros?)

2. plot the about 100 points (less after cleanup) say, 20 times with variable periods and visually try to adjust the spacing to create a large series with a dominant fundamental freq.

3. Do the fourier calculations on the compound series and try to choose the one with the cleanest spectrum (largest power in the fundamental compared to the remaining spectrum). Keep finely adjusting the time distance between these 20 series until you reach a sweet spot. Use your eyes and common sense too. The tool is blind and should be used sparingly. People love black boxes but they rarely are the best solution. Also work on centering the series.