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Fast Fourier transform FFT

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dlopezb:
   Hi Dave,

  I studied electronics over 15 years ago when Internet in Spain was just a dream so I had to deal with so many datasheet books, and it was crazy to find some items. My laboratory is really basic, but now I have a RIGOL :-) and its excellent.  I always worked with analog oscilloscopes so there are so many new functionality, just unbelievable.  One of this functionalities is the FFT for frequency analysis. I am not sure to understand all the power of the FFT and it would be great if you can explain how to use it and in which situations is useful.

   Thanks in advance and best regards,

PD: Please find attached my laboratory :-)

hans:
FFT stands for Fast Fourier Transform. So, it's a fast way of doing Fourier Transform. Fourier Transform is used to transform a (periodic) signal between the time base (which you can see on the normal oscilloscope screen) and the frequency base (a plot where you can see all the containing frequences).

If you put on a 1kHz signal on your channel and let it run a FFT it will show 1 line at 1kHz. It will also show the amplitude, which you can determine by it's height. Note that this is in the decibel scale. I think it's 0dB if your signal originally went top-top in your normal oscilloscope screen. The big advantage of this type of measuring is you can see how much noise a signal has, how your mixers and other signal transforming circuits work.

For example. If you make a FM stereo coder you have 2 audio channels (the audio for the left and the right speaker) and an output (MPX channel). In the past FM has been used to be received by mono radio's. It was just connecting the received audio signal up to a speaker. If you want to send out stereo, you need 2 different channels; L and R. Because you can't just leave away the R (or the L) channel, they made a dual side band at 38kHz with L-R, the mono sound or L+R on the normal band and added a pilote tone of 19kHz (which shouldn't be of that high amplitude). It would look something like this, except the SCA band:


If you would make a mixer that computes the L+R sound, the L-R sound, a 19kHz pilot tone and a DSB modulator (to make the L-R a 38kHz band where the signal folds out from the 38kHz point), you will need such a tool as FFT to verify it's functionality. We had to make this device for a college project, where it was very important to see even the smallest signals which are basically invisible on the normal scope screen. If you see a signal of -50 dB or even less in the FFT screen, that's something of 10000x as small as 0dB. Might not seem important, but it will when you are going to mix signals or amplify them.
edit: I believe it was also a rule that the 38kHz was supposed to be damped, otherwise you would have to put like 25% or even more of the transmitting power into that signal. So ,  we did find an IC (MC1496) that could suppress the carrier, but it performed disappointing. In these terms I am speaking about a carrier signal of a few millivolts against 2Vpp of the original audio signal. We could see it on FFT screen very clearly, no way we see that on the time base. Still though, we expected the carrier signal to be in the regions of -65dB, because that's what the specified for a much higher frequency.

There are a lot of books about Fourier Analysis but I won't recommended buying those. The reason is because they are all very theoretic and I think you should look for the practical usage of this first. I think you will find it a lot used in telecommunications and signal processing. Most of these books will describe a bit of it and also how it works.
edit:: Oh yeah, I know that DSP book and it's indeed worth a read. It's more focussed on digital signals, but those require the same theory.

tecman:
A bit more explanation.  Hans did a good job, but a few more details.  Fourier series math explains that any waveform, no matter how complex, is made up of a series of sine wave signals.  The amplitude, frequency and phase of each of these sine waves, when combined, will result in the final waveform.

So the output of an FFT is most commonly displayed as a frequency response curve.  Amplitude, or power, vs frequency.  FFT, as was explained, is a mathematical method to generate this frequency plot from a signal input.  FFT required far fewer calculations that the long method FDT (discrete fourier transform) and allows analyzers to plot the results in near real time. 

The RIGOL has FFT functionality, but it is somewhat limited.  It does not display as much of the frequency spectrum as is of interest.  Also the ability to get detailed information seems to be limited by the amplitude resolution.

It is nice as a feature, but not overly useful for FFT analysis.

Go to:  http://www.home.agilent.com/agilent/facet.jspx?cc=US&lc=eng&k=an+243&sm=g

and download AN 243.  It is a good reference

Paul


wd5gnr:
As the previous poster mentioned, the FFT is a way to map the time domain to the frequency domain. So when your scope is in the "normal" mode it is plotting time (x axis) vs voltage (y axis). In FFT mode it is plotting frequency (x axis) vs magnitude (y axis).

While I agree a lot of books are theoretical, there is a freebie you can download that is quite good. I got a hardcopy of it from analog devices awhile back but if you don't mind PDF: http://www.dspguide.com/

Very good and very practical. However, just to use your scope, here's a few basic things:

1) You can only measure to 1/2 of your sampling rate (Nyquist limit).

2) Each "tick" in the frequency domain is basically a sine wave at that frequency. So if you feed a square wave (like your probe calibrator) into the FFT you will find out that a square wave is the same as a sine wave at the frequency of the square wave plus the sum of the odd harmonics (technically to infinity, but in real life, just a few harmonics added together gets you pretty square). It is instructive to use a spreadsheet or a program like SciLab or MatLab to make sine waves at say, 1kHz, 3kHz, 5kHz, 7kHz, etc. and add them together.

I've attached what my calibrator looks like on the FFT. Notice on the left hand edge is just "0 Hz" garbage. Then there is a big spike at 1kHz, 3kHz, etc. The center line is on 7kHz.

3) In actuality, for the transform to work you should have infinitely fine sampling that goes from the beginning of time to the end of time. But none of that is practical. So instead you have a discrete FT -- you sample at certain points for a finite period of time. That produces little errors. The "Window" is a way to make the "abrupt edges" less significant. Different windows have different characteristics (like a filter, do you want flat passband, steep skirts, or no phase shift -- pick one or two but not all 3).
Rectangle is basically no window. If you set your scope up and flip through the windows you'll see the "blips" get steeper, but remember you are introducing other errors too.

That's about all I can think of at the moment you NEED to know for something like this. The DSP book is worth a read. Not so much math and very practical.

Al W.
http://www.hotsolder.com

saturation:
Buenas dias, nice lab! photo.


--- Quote from: dlopezb on May 13, 2010, 08:47:07 pm ---
   Thanks in advance and best regards,

PD: Please find attached my laboratory :-)


--- End quote ---

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