Why analog anti aliasing filter is used before analog to digital converter when there is already a digital filter after ADC?

Question

Normal data acquisition consist of:

1. Analog anti aliasing filter( Sampling frequency : $5\textrm{ kHz}$)
2. ADC - Digital Filter - (Sampling : 200K samples /sec)
3. Digital low pass filters Filters
4. DAC

Questions:

1. My question is why analog anti-aliasing filter is used when their is already a digital low pass filters after ADC to prevent anti aliasing.

2. If analog anti-aliasing filter have sampling frequency $5\textrm{ kHz}$ , the system will not take frequency greater than $2.5\textrm{ kHZ}$,

   • then why ADC frequency is $200\textrm{ kHz}$?
   • Doesn't analog anti-aliasing filter sampling frequency limit overall system frequency ?

Answer 1

Question 1: The anti-aliasing filter before the ADC is exactly for the purpose of rejecting high frequencies, that will become lower frequencies (i.e. aliasing) after the ADC. The digital lowpass after the ADC cannot help here, as the aliasing has already happened. Consider this example:

• Your ADC has a sampling frequency of Fs=100kHz.
• Your input signal is a sum of two sine waves, with frequencies 10kHz and 220kHz.
• After ADC you would find two sine waves: one at 10kHz, one at 20kHz (220kHz-2*Fs).
• Hence, you have aliasing occured, and no digital lowpass can remove this aliasing.

Question 2: Without more information on the system this cannot be answered. However, here are some thoughts:

• filter of 5kHz requires a sampling frequency of at least 10kHz (ideally). You state you only need 2.5kHz. I think you mix something here.
• in reality, no anti-aliasing filter is a perfect low-pass, hence its cutoff-frequency does not mean, that higher frequencies are perfectly blocked. Instead, they are more and more attenuated. To cope with non-ideal anti-aliasing filters, the sampling frequency should be higher than 2 times the cutoff. However, 200kHz from your example occurs still quite high for me.

Answer 2

The higher the sample rate, to easier (and thus cheaper) it is to make the analog low-pass filter required to prevent aliasing (to limit aliasing to below your required noise floor). Making a filter with a sharp transition band is more costly. Often a much higher sample rate is cheaper to implement than a slightly sharper low-pass filter.