Cut off frequency of anti aliasing filter

[atferrari]

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.

 

[misterT]

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.

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

If your highest frequency of interest is F, you need a sample frequency of at least twice the signal frequency: fS > 2*F
All frequencies above fS/2 will be aliased to lower frequency by the sampling process. This is why you need a low-pass filter with cut-off frequency fS/2.

Sampling frequency and highest frequency of interest are two different things. In practice, the sampling frequency needs to be much higher than the theoretical Nyquist rate. This makes low-pass filter design easier.

 

[atferrari]

How to decide sampling rate then, and cut-off frequency based on it?

Sampling frequency and highest frequency of interest are two different things. In practice, the sampling frequency needs to be much higher than the theoretical Nyquist rate. This makes low-pass filter design easier.

Now things start to make sense.

a) Going by her examples, my fS/2 should be around 5*F thus fS about 10*F (to accomodate those factors of ~0.2). Isn't that excesive?

In audio, as far as I know, sampling rate is just 2.2*F, right?

b) Mister T, could you guide me where to look at for how those factors are calculated?

 

[misterT]

I don't think I can explain it better than Bonnie Baker does in her paper. Important frequencies are the cut-off and stop frequencies of the filter. Cut-off frequency must be equal (or greater) than the highest frequency of interest and the stop frequency must be lower than fS/2.

If your highest frequency of interest is F, then you choose that to be your filters cut-off frequency. Following Bonnie's example (12bit ADC and 5th order butterworth) your fS needs to be:

Fcutoff = F = 0.18 * fS/2
<=> fS = 11.1*F

So yes, your calculation was correct. Important thing here was also the 74dB signal to noise ratio of the 12bit ADC.

Maybe you can tell us more about your design. What kind of signal are you sampling and what is the resolution and speed of your ADC?

 

[crutschow]

An important factor in the amount of anti-alias filtering required is the value of undesired signal/noise about F and fS/2. That determines the order and type of filter you need to achieve your desired S/N of the sampled signal.

Standard audio CDs use a 2.2*F value but that is mostly to minimize the amount of digital data on the disc. Other digital recording methods, such as Super Audio CD, use a much higher sample ratio to minimize anti-alias filter requirements and improve the fidelity over standard CDs.

 

[atferrari]

What I am trying

So yes, your calculation was correct.

Good to hear that.

Maybe you can tell us more about your design. What kind of signal are you sampling and what is the resolution and speed of your ADC?

I programed a micro with a FIR alogirthm and am going to test it with this signal: https://www.electro-tech-online.com...ignal-to-test-a-fir-filter.116825/#post958378

Signal frequency would be around 350 to 400 Hz. Vpp =2V.

DAC is the 10-bit one from the 18F452. With 4 MHz Xtal I managed to get a sampling period of 268 usec (fS> 3500 Hz) for 31 taps. Sure there is leeway with such a low frequency signal.

But I am still intrigued where she got those factors from. Maybe they come from plain trial and error just by designing with (diferent values*fS). Filterlab from Microchip has one section specifically for antialiasing filters.

 

[crutschow]

But I am still intrigued where she got those factors from. Maybe they come from plain trial and error just by designing with (diferent values*fS). Filterlab from Microchip has one section specifically for antialiasing filters.

It's not trial and error. Read my previous post. The needed filter is determined by the amount of noise/signal outside the passband and the signal S/N ratio you need. This can be calculated if you know how to calculate noise levels.