Do digital Anti Aliasing filters exist for traditional ADCs?

Do digital Anti Aliasing filters exist for traditional ADCs?

Not in the sense you are discussing. There are other forms of "aliasing", but you seem to be considering only analog to digital conversion. If the signal is already digital (so that you can filter it digitally), then it's already been aliased. It's too late.

Where usually do people put these filters?. On the IC for the ADC itself?

I'm sure you can find ADCs with integrated filters, but it's not the norm. Different designs have different filtering requirements. You may need a linear phase filter, or you may not. You may need very good performance, or you may need very low cost. You might not even need filtering at all, if you know what frequencies your analog signal can contain.

Are physically big filters (e.g. through hole capacitors, inductors and resistors) the norm?

Not really, for reasons of cost. You need bigger components if you need to handle more power. High power is not usually something you need to drive an ADC. It may also be that a particular design requires a high capacitance or high inductance that's attainable only through large components, but a good engineer will avoid it if possible. Much better to use a 2 cent SMT capacitor, than a 20 cent through-hole electrolytic, wherever possible.

Yes, many \$ \Delta \Sigma\$ converters have digital FIR anti-aliasing (and decimation) filters.

That's possible because of the architecture- they're actually oversampling and decimating down to the output sample rate. The advantage of a digital anti-aliasing filter is that it can easily be a high-order filter with a sharp cutoff frequency that is almost at the Nyquist rate of \$0.5\cdot F_S\$.

(See link below for above figure, Joe H.)

You still may need an analog (analogue) anti-aliasing filter ahead of the oversampling converter if there is any signal or noise content up there, but the demands on it are significantly relaxed. See, for example, the ADS1278 which is 64x or 128x oversampling.

The input to a digital filter will necessarily be something that's sampled at a certain rate. For the filter to do anything useful, that rate must be more than twice the desired cut-off frequency. Most analog-to-digital converters are designed to perform conversions at the desired output sample rate, and output sample rates are often chosen to be more than 2x the highest frequency of interest, but not by a huge amount. That somewhat limits the usefulness of digital filtering in many cases.

Some audio CODECs, however, do include digital filtering. I'm not sure exactly how everything is implemented internally, but one chip I've used was designed so that when used with an 8KHz sampling rate, it would apply a filter with a sharp cut-off at 3.5Khz, but signals above 5.5Khz would alias back to the baseband. That design allowed some slight simplification in the analog front-end; since it meant the analog pass band could extend up to 4.5Khz, rather than only up to 4KHz, giving the front-end an extra 500Hz to play with.

Conceptually, it shouldn't be difficult for an audio-frequency ADC to oversample internally so as to allow the analog pass-band to extend up another octave or two, and I think I've seen CODEC chips which do that, but I'm not familiar with them. It's worth noting that many delta-sigma converters have an inherent sampling rate which is much faster than their output sample rate, but produces samples with a lot of noise; the output of such converters is then digitally filtered to yield a digital audio stream at a much lower sample rate. I think that's how most cheap PC sound chips work, but I don't know the details.

ADCs

All the ADC anti aliasing filters that I'm aware of are analogue i.e. they filter the analogue signal before it is sampled. Because an ADC can have its conversion rate usually controllable from nearly DC to S\$_{MAX}\$ it doesn't make sense to have the filter built in to the device but I wouldn't preclude this happening on some devices.

Decimation

There are digital anti-aliasing filters and these are used (exclusively in the digital realm) to convert from a particular sample rate to a lower sample rate - aliasing can occur here just as it can on an ADC - for instance, you can't just throw away every other sample and hope to achieve digital sample decimation - you need to filter the signal to take account of the decimated sample rate, then throw samples away. Typically, you add two samples together and divide by two - this gets rid of out of band signals at the new lower rate. Everyone's done it or recognizes the idea.

DACs

To broaden my answer I thought I'd mention a filter required to linearize a DAC output. If you sample a sinewave at close to the maximum frequency (before hitting aliasing problems) then reconstructed the analogue value with a DAC, you would not get the same amplitude signal as the original analogue - this is because most (maybe all) tend to attenuate the signal output at the expence of producing a larger RMS content of out-of band sampling noise. In your minds eye, a low frequency signal that is quantized at a high rate will look pretty similar to the original input to the ADC - it'll have a small mushy element due to quantization but, as the input frequency approaches maximum, the "mushy" parts get bigger and bigger whilst the actual analogue value produced gets smaller and smaller and for this reason it's sometimes necessary to use an anti-sinc filter. Maxim's application note 3853 offers a decent explanation.