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.
Your signal chain is quite complex, and you can have problems at every step, or even multiple problems. You have analog circuitry, into external ADC, through a PIC, into SRAM, back through the PIC, at some point employing a highly nonlinear filter, out through UART and into hyperterminal. Debugging this involves baby steps, which pretty much means you need to eliminate all the shortcuts you took getting to this point.
Where I would start would be to verify everything one step at a time. Start by sampling a CONSTANT voltage, then a sine wave out of a function generator, and make sure you understand what you see.
Once that makes sense to you, LOOK at your analog input with an oscilloscope, and make sure you understand what you see with that. There is no substitute for this. There are reasons why we use bench instrumentation, and this is one of them.
Next, find a way to get rid of all your post-sampling processing, and look at the data in as raw a state as you can. You are doing highly nonlinear processing. When you do this sort of stuff, when it doesn't work you go back and look at the whole process with a microscope.
I suspect you might have an extremely noisy signal, you're aliasing it down by not sampling fast enough, and the non-linear processing is confusing the issue.
Best Answer
Why use PIC24+sram when the newish PIC32MZ DA series have 32MB of internal/stacked DDR? TI has some nice adc codecs that mesh well with i2s. While I understand trying to keep it under one roof, I think it is better to add an audio adc rather than sram. Typical micro adc's aren't really geared toward audio anyway.
I'd guess that by the time you find 4mb of sram you'll about be at the cost of the DA series, especially if you figure the extra pcb layout time and layer count.
The current errata does limit ddr to 0-70C, but 32MB is real nice, it opens up lots of possibilities.