I am not sure at this point. I remember I used a weird scale factor (It must be a multiple of 10) in order for the chart to fit better.
I need to delete the whole thing and redo it from scratch. Just calculate the average (DC of the function over the window of interest) and that should be fourier value of zero frequency. Then correct the model.
Cheers!

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!

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

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.

… 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!

How do I map the magnitude of the fourier back to the amplitude of the input wave? The magnitude seems to be normalized or scaled of some form.

I am not sure at this point. I remember I used a weird scale factor (It must be a multiple of 10) in order for the chart to fit better.

I need to delete the whole thing and redo it from scratch. Just calculate the average (DC of the function over the window of interest) and that should be fourier value of zero frequency. Then correct the model.

Cheers!

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!

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 George

Thanks for this excellent tool.

I have few queries though.

How do we decide what are the Start_Freq and Stop_Freq?

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.

Is your DFT template equivalent to the Lanczos approach?

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

… 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.

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

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!

I couldn’t resist commenting. Perfectly written!

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