# Aliasing and low-pass filtering question

Discussion in 'Electronic Basics' started by MRW, May 15, 2007.

1. ### MRWGuest

Hello,

Can someone please para-phrase the following?

"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"

I cannot picture this properly.

Thanks!

2. ### Rich GriseGuest

These guys explain it a lot better than I can:
http://en.wikipedia.org/wiki/Aliasing

Have Fun!
Rich

3. ### David L. JonesGuest

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 when in fact you
are just seeing an aliasing artifact caused by a 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:
http://en.wikipedia.org/wiki/Aliasing
and some of the links might help explain it better, like this one:
http://burtonmackenzie.blogspot.com/2006/07/i-cant-drive-55.html

Dave.

4. ### MRWGuest

Thanks! That seems clearer now.

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.

5. ### John FieldsGuest

---
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.

6. ### Ben JacksonGuest

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:

1. 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.

2. 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.

3. (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
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
where many of the same considerations apply.

7. ### Bob MastaGuest

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
http://www.daqarta.com/dw_0haa.htm

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
http://www.daqarta.com/dw_0hdd.htm

(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
www.daqarta.com
Scope, Spectrum, Spectrogram, Signal Generator

8. ### Guest

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".