FFT data

[Drej]

Dear all

This is semi-related to an earlier thread. I have performed a Fast Fourier Transform on a set of acceleration data within Excel using the Analysis Toolpak -> Data Analysis -> Fourier Analysis (thanks, Michael!). Excel has produced a set of FFT data which is a series of complex numbers. Since there is very little documentation on this function within Excel, could someone cast light on the following:

- My input - acceleration - data is sinusoidal in nature (also only a single frequency) the maximum amplitude being 0.5g. The complex numbers (FFT data) produced from Excel on this data I have converted using (x^2+y^2)^0.5 where x+yi is the format of the complex number; this apparantly yields the "magnitudes of the FFT". However, the magnitude of the dominant frequency in the FFT is at least 10 times higher than the input - I don't understand why this is, but there must be a good reason why.

Would appreciate a potted summary of the complex output for FFT in Excel and any general remarks about FFTs.

Many thanks,

-- drej --

 

[hacksaw]

why are you using FFT on a single frequncy sinusoid?

 

[GregLocock]

There are many scaling decisions and factors to be made with an FFT. It is very likely that you have fallen foul of one of them. I strongly recommend that you read agilent's guide to signal analysis, mentioned in this forum's FAQ section.

I always analyse a known signal when using a new FFT algorithm just to check what calibration factors etc the author has used.





Cheers

Greg Locock

 

[Drej]

Because I am new to the subject, I used a single frequency and known magnitude to FFT so I would know exactly which frequency/magnitude should be picked up in the Transform. Crawl before you walk and all that.

-- drej --

 

[hacksaw]

you'll notice that the excel package only allows a data stream input with no indication of the time basis. in that sense it is a form of series analysis not and is not setup for fourier analysis in a rigorous sense. it works but your time interval is unity...and the amplitude of your spectra will be scaled by the number of elements in your data (more or less). believe there are a number of fft freeware packages out there that will take time based data and even wave files. they are not perfect but fun to play with.

 

[GregLocock]

I disagree. There is nothing in the Fourier analysis process that requires knowledge of the time base, since all the manipulation is done relative to one frame length.

Scaling the frequency axis is easy. The first line is at 0 Hz, each line thereafter is 1/T Hz higher, if the frame is T seconds long.

If there were N samples in the frame then only the first N/2 bins are needed for amplitude work, the second half are used to define phase.

The amplitude scaling in a digital FT is a design choice made by the programmer, Excel appears to use a factor based on the number of samples.



Cheers

Greg Locock

 

[hacksaw]

agreed in the case of disctrete analysis, in all other cases the transformation is from a spatial or time coordinate into a reciprocal space. never the less you have made a good point that the excel analysis is based on a discrete frame, what ever you choose it to be and that the scaling must be carried out...