I need to design an antialiasing filter.

After reading a lot on them I found AN699 from Microchip by Bonie Baker which is clear enough except in one point:

When deciding on the transition band of the filter, given fS (sampling frequency) she states that fcut-off of the filter can be made much lower than fS/2.

To that, in page 5 she gives this specific examples:

Assuming a 5th order filter is used in this example:

fCUT-OFF = 0.18fS /2 for a Butterworth Filter
fCUT-OFF = 0.11fS /2 for a Bessel Filter
fCUT-OFF = 0.21fS /2 for a Chebyshev Filter with
0.5dB ripple in the pass band
fCUT-OFF = 0.26fS /2 for a Chebyshev Filter with
1dB ripple in the pass band

My questions:

Isn't contradictory that the filter has a cut-off frequency much lower than most of the frequencies of interest?

Accepted that the above is correct, how does she gets those coefficientes which apear as dependent of the filter's order? Up to now they seem drawn from a magic hat...

What I decide first? Order of the filter or cut-off frequency? Chicken or egg dilemma.

Sorry but this is my first time I face this subject.

Any help is appreciated.

 

Isn't contradictory that the filter has a cut-off frequency much lower than most of the frequencies of interest?

No, and it doesn't. Let me explain: A sampling system, such as an A-to-D converter can not know the frequency of a sine wave that occurs at any higher than 1/2 the sampling frequency (Fs/2). For example, when you look at a sine wave that is sampled exactly once every cycle, it looks just like DC because the waveform is sampled in exactly the same phase every time. We say the signal is "Aliased" to DC. And other frequencies look liked frequencies they are not. The purpose of the anti-aliasing filter is to filer out the signals above Fs/2. Since real life filters do not have vertical skirts (the skirts are also called the "transition band", you have to place the corner frequency at an even lower frequency than Fs/2 so that the amplitude of unwanted frequencies is low enough by the time the rolloff gets to Fs/2.

So to summarize, you don't want anything over Fs/2 because it is uncertain information, and you have to loose some more data at frequencies below that because real world filters are not ideal.

Accepted that the above is correct, how does she gets those coefficientes which apear as dependent of the filter's order? Up to now they seem drawn from a magic hat...

I am sure those numbers are based on the shape of the slope of the skirt and the desired amount of attenuation.

What I decide first? Order of the filter or cut-off frequency? Chicken or egg dilemma.

I would recommend first deciding what kind of filter characteristics you can tolerate -that is function of what you are going to do with the data -can you tolerate a lot of ripple in the passband, for example? After you select the type of filter you want to use decide the needed bandwidth. Then its a matter of setting clock frequency to the highest you can afford to use (as an example, there might be a power consideration) and the distance (in octaves) between the needed bandwidth and FS/s will tell you how many poles you will need.

 

Thanks Dick for your time.

My mistake was thinking that fcut-off = fS/2. There was no leeway for the transition band. Just by increasing the sampling rate I can accomodate it between both values.

Rereading the AN found that she says so.