"To avoid aliasing, an analog low-pass filter is placed at the input before the sampler. The low-pass filter determines the highest frequency of the FFT analyzer. Because the rate at which signals can be represented without error is one half the maximum sampling rate, signals are often cut off at a lower frequency to provide sampling rates greater than twice the maximum frequency components. Typically the cutoff of the low-pass filter is 2.5 times less than the maximum sampling rate of the analyzer. This determines the maximum frequency component."
The part that I'm especially confused at is: "Because the rate at which signals can be represented without error is one half the maximum sampling rate, signals are often cut off at a lower frequency to provide sampling rates greater than twice the maximum frequency components"
If you have say a 1KHz sample rate then you cannot sample any signal greater than half that (500Hz). If you do, input frequencies *higher* than 500Hz will appear as frequency artifacts *lower* than 500Hz. You will think you are looking at a real signal 500Hz. This is why most analog to digital converters will have an anti-aliasing filter at around half the sample rate on the input.
You might like to start here:
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and some of the links might help explain it better, like this one:
The text is actually in regards to a spectrum analyzer. For our project, I was assigned by my professor to find a spectrum analyzer that can work all the way up to 16GHz and get a quote. I didn't know these things were that expensive.
Is it possible to still use a spectrum analyzer that works all the way up to 3GHz using an input signal of up to 16GHz? I was thinking of a mixer and vco to step down the frequency to something below 3GHz, but I'm not aware of any such modules for spectrum analyzers.
--
In some old western movies the spokes of wagon wheels would be going
fast enough that in one frame one spoke would be caught vertical,
while in the next frame the next spoke would be caught a little
counter-clockwise from vertical, giving the appearance that the
wagon wheels were rotating backwards.
At higher speeds, the first spoke would be caught at vertical while
the next spoke would be caught a little clockwise from vertical,
giving the impression that the wheel was rotating much more slowly
than it really was.
The "cut off" frequency of a filter is not a brick wall. Typically it's specified as the point with 3dB of loss. If your anti-aliasing filter has Fco = 1/2 FS, then there are a few issues:
Your signal at 1/2 FS is at half the amplitude of the signal in the rest of your passband (3dB point), so if it's an important frequency it will be attenuated.
No filter is a brick wall, so Fco + epsilon is near 3dB down, but it is aliasing back to Fco - epsilon, which it will be large enough to interfere with your signal of interest.
(if you are really nit-picky) The phase response of your filter will probably also be changing around your cutoff frequency, which will matter if you care about the phase output of the FFT.
What you really have to consider is how much you want to attenuate the aliases (stoppband attenuation of your filter), how much of your signal is important (your passband, but still beware of how passband is defined), and how wide the transition band is. You will want FS to be at least twice the start of your *stop*band, which is beyond the transition.
If you look on google groups you can find a thread from a while back where I asked essentially the same question but about DAC reconstruction filters, where many of the same considerations apply.
Depending on what you are doing, you may very well be able to use signals that are higher than half the sample rate. This is called undersampling. It's typically used where you are only interested in a narrow band of frequencies, not the entire spectrum down to DC. You still get aliasing, but if you know for certain that the input signal is within a certain frequency range, you can interpret the aliased spectrum properly.
The input signal bandwidth must be less than half the sample rate, so in your case less than 3/2 GHz or 1.5 GHz. Better if it is quite a bit less, to avoid confusion at the band edges. For example, if it only contains components between 15 and
16 GHz, the bandwidth is only 1 GHz so that should work OK. Note that you will have to bypass the anti-alias filter on the 3 GHz analyzer.
The aliased signal "folds over" the spectrum limits at the Nyquist frequency (half the sample rate) and at DC (zero Hz). A signal that is a little above Nyquist will be mirrored downward. For example, a 1.6 GHz signal will be mirrored about the 1.5 GHz Nyquist and appear at 1.4 GHz. As the input goes higher, the alias appears lower until it hits zero, where it "bounces back". So an input of 3 GHz will alias to 0, and 3.1 GHz will alias to
0.1 GHz. This pattern repeats for higher inputs.
I have some examples (at audio frequencies) in the discussion of aliasing at
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If you want to play around with aliasing to get a feel for how it works, you can use the Daqarta signal generator and the example at
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(Note that the signal generator is free, even though Daqarta itself is $29. When the trial period expires, the signal generator and all the analysis features continue to work. You can use it this way for as long as you like.)
Best regards,
Bob Masta D A Q A R T A Data AcQuisition And Real-Time Analysis
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Scope, Spectrum, Spectrogram, Signal Generator Science with your sound card!
A 3GHz SpecA would not be useful with direct 16GHz signals. You can devise a mixer/VCO bit to bring down bands of interest narrower than 3 GHz. To get accurate results you will also need to calibrate the setup. Some analyzers allow calibration of the external mixer. But perhaps it is better to spend more time measuring the device of interest, rather than the setup. Companies like Agilent make whole families of SpecA's that have 1GHz,
2GHz, even 26GHz input range. Try Googling for "8563E rental".
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