Hi.

I have a question... I want to design an antialiasing filter and later
do an A/D conversion (undersamplig).

The signal (at IF) is at 44MHz and the bandwidth is 1MHz. How can I
design the antialiasing filter for undersampling with that information
?

Thanks

Hern=E1n S=E1nchez
HJ4SZY

"Hernán Sánchez" wrote in message
oups.com...
"The signal (at IF) is at 44MHz and the bandwidth is 1MHz. How can I
design the antialiasing filter for undersampling with that information?"

Slap a bandpass filter that's 1MHz wide at 44MHz around the signal input path.
Sample at something better than 2MHz (depending on how ideal your bandpass
filter is -- realistically you'll probably need to sample at 2.5MHz or
better... and things are simpler if you could manage to sample at 4MHz so that
44MHz ends up translated directly to DC rather than some offset).

Hi.

Thanks for your answer... so, the basic idea is to design a filter at
the frequency of IF (44MHz in this case) with a bandwidth equal to the
BW of the data (1Mhz in this case)... am I right ?

Thanks

Hern=E1n S=E1nchez
HJ4SZY

"Hernán Sánchez" wrote in message
oups.com...
"Thanks for your answer... so, the basic idea is to design a filter at
the frequency of IF (44MHz in this case) with a bandwidth equal to the
BW of the data (1Mhz in this case)... am I right ?"

Yes, that's it!

Oh...be a little careful here! If you have a filter centered at 44MHz
and 1MHz wide, even with perfect "brick wall" attenuation below 43.5
and above 44.5, it would be very bad to sample at 4MHz, or any
frequency whose harmonic landed in the passband. That is because you
will not be able to distinguish (with 4MHz sampling) between a signal
in your IF at 44.1MHz or 43.9MHz. Both will come out aliased by the
sampling to 0.1MHz.

For a more practical example, let's say you manage to find or build a
filter with acceptable flatness from 43.5 to 44.5, and acceptable
attenuation below 42.5 and above 45.5. (Acceptable means that whatever
signals appear there will be attenuated enough to not cause trouble if
they alias into the ADC's output in the desired 1MHz passband.) Then
you can, at best, use a sampling frequency whose harmonic is at
43.0MHz, and whose sampling frequency is at large enough so that the
sampling freq harmonic which lies on the other side of the IF filter
passband won't let signals alias into the output passband. So maybe
you could use 3.071429Mhz sampling, which has a harmonic at 43MHz,
alisaing 43.5-44.5 down to 0.5-1.5, and the the next harmonic at
46.07MHz is more than 1.5MHz above upper frequency where the filter
gives good enough attenuation to prevent aliases. (Good luck building
a filter like that with acceptable performance from practical inductors
and capacitors, unless you don't need much alias protection!)

If you have trouble seeing this, draw some pictures of what goes on in
the frequency domain. Remember that you get nominally the same ADC
response from a signal x kHz above the effective sampling rate
(harmonic of the ADC sample rate) as you do from a signal x kHz below,
and remember that you get response from signals x kHz away (above or
below) the 11th harmonic just the same as the 10th harmonic or the 12th
harmonic, with perfect sampling. So, do NOT let in frequencies that
would let you see the same response from two different inputs...be sure
to filter out those freqs that would give you the same response. (That
applies to noise, too...don't let multiple copies of amplifier noise
alias all down to the ADC output.)

Yes, you WILL end up with your desired passband aliased to something
like 0.5MHz to 1.5MHz. But you can do whatever you want to that with
digital signal processing. (You can also do I and Q sampling
[quadrature sampling] just like you can do I and Q mixing, but you'll
have the same problems with sideband rejection degraded by imperfect
quadrature phase and amplitude matching.)

Cheers,
Tom

Oooops. Correction. That 3.07MHz sampling frequency will NOT work for
the example filter I gave, because the harmonic at 46.07 will alias the
range from 45.57 to 44.57 into the 0.5-1.5MHz output band. And 44.57
to 45.5 does not have acceptable attenuation. Better use instead a
4.3MHz sampling, so that the 10th harmonic converts the desired band to
0.5-1.5MHz, and the 11th harmonic at 47.3 converts the highest
unprotected frequency, 46.5MHz, to 1.8MHz, which is above the output
band of interest.

Cheers,
Tom

Grrr. Gremlins struck again. Should read, "...and the 11th harmonic
at 47.3 converts the highest unprotected frequency, 45.5MHz, to 1.8MHz,
which is above the output band of interest."

Wow... it's more complicated that I thought.. So, what you are saying
is that I must do "mixing" with all the harmonic frequencies, almost to
the 11th harmonic to find the right frequency that don't generate a
mixing signal (with the IF signal) at the 0 - 1MHz range ?

Thanks

Hern=E1n S=E1nchez

Assuming that you have a bandpass filter that allows your desired band
to pass (say 43.5 to 44.5MHz), and that has enough attenuation outside
some band (say 42.5 to 45.5MHz) to protect against aliases, then the
only harmonics of the sampling frequency that are of interest are the
first one below the passband, and the first one above the passband.
That is assuming that you don't have a harmonic of the sampling
frequency inside the passband, which I explained would be bad because
you can't distinguish between a signal xx.xxkHz above that harmonic and
a signal xx.xxkHz below that harmonic.

You can list some specific rules. Try this:

Define four frequencies for your filter:
f1 = frequency below which attenuation is great
enough that you can ignore signals there.
f2 = bottom edge of the passband, where
attenuation is small enough that signals are OK.
f3 = top edge of the passband, like f2, so signals
between f2 and f3 are all OK
f4 = frequency above which attenuation is great
enough that you can ignore signals there.
So, f1f2f3f4.
(in the example above, f1=42.5MHz, f2=43.5MHz, f3=44.5MHz and
f4=45.5MHz. But the passband does not have to be symmetrical; f4 could
have been 46.5MHz for example, and the equations below will still
work.)
Define the sampling frequency = fs
Then there are two possibilities that will work:
(1) a harmonic of fs, call it n*fs, falls below (f1+f2)/2,
and (n+1)*fs-f4 f3-n*fs. In that case, the band
from f2 to f3 will be aliased down to the band
from f2-n*fs to f3-n*fs. In fact, each frequency
f in the passband will alias (mix) to f-n*fs.
OR
(2) (kind of the mirror image of (1)) a harmonic of
fs, call it m*fs, falls above (f3+f4)/2, and
m*fs-f2 f1-(m-1)*fs. In that case, each
frequency f in the passband will alias to m*fs-f.
In other words, the output spectrum will be
flipped compared with the input: lower freqs
in the input spectrum will be at the higher end
of the output (digitized) spectrum.

In both (1) and (2), the first requirement as I've stated them is so
that nothing on the other side of the sampling harmonic from the
passband is big enough to cause trouble in the output frequency range.
The second requirement insures that nothing aliased by the harmonic on
the other side of the passband from the harmonic doing the work will
cause trouble in the output passband. But bewa the digitized
output may very well contain frequencies which lie outside the
passband, because your analog filter on the passband does not cut them
off sharply enough to get rid of them. You can use DSP algorithms (FIR
or IIR filters, for example) to do a good job getting rid of the
remainder that you might not want in the output.

Cheers,
Tom

(Sure hope I got all those inequalities right! I trust someone will
double-check them and let us know if they are wrong...)

Yes, the input signal will try to "mix" with ALL the harmonics of the
sampling frequency. You must pick the sampling frequency so that the
desired signals mix down to the output you want and also no other
signals that may be present can also mix down to the output you want.
That is where the anti-aliasing BANDPASS filter helps by restricting
the possible input signals.

Mark