# Analog anti-aliasing filter design - stopband attenuation

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#### Jo999

##### Newbie level 3
Hi,

I have to design an anti-aliasing filter. The parameters I have are:

Sampling frequency: 50kHz
Voltage range: +-2v, so 4 volt range
Bits: 14

Passband: 2kHz
Noise: 5E-4v (minimum detectable signal)

Looking around, it seems that the noise of my system will determine what attenuation I should have at half the sampling frequency. I asked the demonstrator for my class how to determine the minimum attenuation required for the system and he said that the signal at half the sampling frequency should be less than the SNR of the system so that when the frequency components above half the sampling frequency 'fold back', it will be less than the overall noise.

Only thing is, I can't figure out how to compute what the attenuation should be at half the sampling frequency given these values. It seems logical to me that before you calculated that, you would have to know what the strength of your signal was above these frequency components. If you don't have high frequency signals, no point attenuating what isn't there...

If you could shed some light, I would be grateful, especially if it has maths to back it up.

Regards,

Jo

#### FvM

##### Super Moderator
Staff member
It seems logical to me that before you calculated that, you would have to know what the strength of your signal was above these frequency components. If you don't have high frequency signals, no point attenuating what isn't there...

Apparently the exercise problem is assuming a non-zero aliasing signal... At worst casde, it's full level (4 Vpp). The assumption should be sufficient to solve the problem.

#### Jo999

##### Newbie level 3
Apparently the exercise problem is assuming a non-zero aliasing signal... At worst casde, it's full level (4 Vpp). The assumption should be sufficient to solve the problem.

Hmm, sorry, I don't think I phrased that well enough. The worst case noise allowed is 0.0005 V. I think that since this noise will be spread out quite wide in the frequency domain you can't filter it all away and therefore there will be some aliasing...

I found an equation that says the dynamic range specifies the minimum attenuation, and another that says the SNR of my system is going to be 78.06dB, but I don't know what this implies.

#### FvM

##### Super Moderator
Staff member
Yes, -78 dB is just another expression for 5e-4/4.

In fact, your initial description sounds clearer than the latest. But in simple terms, you want 78 dB stopband attenuation for the lowest expectable alias frequency, which is 48 kHz in your case.

#### crutschow

In fact, your initial description sounds clearer than the latest. But in simple terms, you want 78 dB stopband attenuation for the lowest expectable alias frequency, which is 48 kHz in your case.
How did you arrive at 48kHz? The alias frequencies are anything above 1/2 the sample frequency or 25kHz.

If the SNR of the system is 78dB then worst-case you would want a LP filter with 78dB minimum of attenuation at 25kHz and above for the anti-alias filter.

#### FvM

##### Super Moderator
Staff member
The passband is 2 kHz. Components above this frequency are present in the data stream and can be filtered in the digital domain. Components between 25 and 48 kHz are aliased as 25 downto 2 kHz and can be digitally filtered as well. Only components above 48 kHz are aliased into the passband and need to be fully suppressed.

#### Jo999

##### Newbie level 3
Aah, I see. That required a little pondering as to what you mean, but I see. So both crutschow and FvM are right, the first case is assuming I am not doing any digital filtering and the second case is assuming that I am doing filtering. In this case, the 'folded back' frequencies from 48 - 50kHz will interfere with the desired data and must be suppressed as much as possible (I think with probably a FIR filter since we need linear phase here). Thanks guys, this really helps!

#### crutschow

The passband is 2 kHz. Components above this frequency are present in the data stream and can be filtered in the digital domain. Components between 25 and 48 kHz are aliased as 25 downto 2 kHz and can be digitally filtered as well. Only components above 48 kHz are aliased into the passband and need to be fully suppressed.
You misunderstand the nature of the aliased signals. The aliased frequencies are like beat frequencies, generating the sum and difference of the two frequencies. The aliased frequencies are mirror folded around the 25kHz point. For example, a noise frequency of 26kHz will generate the aliased difference frequency of 1kHz into the passband and cannot be digital filtered. Thus anything above 25kHz must be analog filtered.

#### FvM

##### Super Moderator
Staff member
You misunderstand the nature of the aliased signals. The aliased frequencies are like beat frequencies, generating the sum and difference of the two frequencies. The aliased frequencies are mirror folded around the 25kHz point. For example, a noise frequency of 26kHz will generate the aliased difference frequency of 1kHz into the passband and cannot be digital filtered. Thus anything above 25kHz must be analog filtered.
Excuse me, but that's clearly wrong. Mirror folded around the 25kHz point (fs/2, also called Nyquist frequency) is right, but it works different: f2 = fs - f1. 26 kHz is e.g. aliased at 24 kHz. A brief explanation is given here https://en.wikipedia.org/wiki/Aliasing

#### crutschow

Excuse me, but that's clearly wrong. Mirror folded around the 25kHz point (fs/2, also called Nyquist frequency) is right, but it works different: f2 = fs - f1. 26 kHz is e.g. aliased at 24 kHz. A brief explanation is given here https://en.wikipedia.org/wiki/Aliasing
Yes, you are correct. My error was confusing fs/2 with fs as regarding the foldback frequencies.

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