Anti-aliasing ADC samples

If you want to analyze frequency content to 500 kHz, the design of a "brick wall" low pass filter makes the filter design extremely difficult. If you sampled at 10 MHz, your low pass filter just needs to supply the proper rejection at nearly 20x your frequency of interest making the analog filter very simple. The digital filtering would be applied to the high sample rate to deliver the necessary "brick wall" filter and deliver your signals of interest up to 500 kHz without significant aliasing or other distortions that an analog filter would typically produce.

It's the oversampling that allows digital filters to deliver such great performance for antialiasing. The analog filter is still needed, it's just so much simpler.

There is a way to digitally filter a signal without suffering from aliasing. It is called the bi-linear z transform method. You design an analog filter, and then transform it to a digital filter by substituting (2/T)[(1-z^-1)/(1+z^-1)] for s, where T is the sampling interval. Actually, the (2/T) factor is not necessary, but most books on DSP include it. The resultant filter will have better attentuation performance than the corresponding analog filter prototype. The transformed filter suffers from "frequency warping". You compensate for this by pre-warping the critical frequencies before you design the analog prototype filter. Neither the phase vs frequency curve nor the step response of the digital filter will match the correspondimg phase and step response characteristic of the analog prototype filter. Any book that covers digital filtering will have a section on the bilinear z-transform. See, for example, "Therory and Application of Digital Signal Processing" by Rabiner and Gold.

But aliasing still needs to be addressed at the analog level. You can only get a digital filter to work on frequencies below Nyquist. I think the original question was whether digital filters could get rid of the aliazing problems without use of any external analog filters. I'm happy to be mistaken.

Man, this is revolutionary!

Do you mean I can sample a baseband signal with frequencies extending to f0 at a sampling frequency of f0, and have no aliasing, just by using a bilinear filter?

That is _so cool!_

Maybe I'm missing something in your explanation?

regards PN2222A

I have never seen anybody claim that you can get around aliasing the way you describe.

The only thing I have heard of is "digital down-converting" where you bandpass filter a signal so that all that is left is that portion of the signal from, say, Fs to 1.5 * Fs. Then the signal is aliased, but can still be reconstructed correctly since the number of times it has "wrapped" is known.

It could also be 1.5 * Fs to 2 * Fs. The only constraint is that the signal must still occupy a bandwidth of less than Fs/2 when it is actually sampled.

And of course, if the signal is known to have no frequency content outside of the aforementioned band, then no filter is necessary.

--Mac

First you have to understand what aliasing means. IF you sample at 1MHz but only want to use audio frequencies up to 20kHz, aliasing doesn't disturb unless it is folded back into 0 - 20kHz. This means you only need to care that at 980kHz and above no signal goes into the ADC which is above say -90dB or whatever noise floor you are digitizing.

All those aliased frequencies between 500k and 980k can be eliminated digitally when downsampling, but anything in the bandwidth of interest can not be eliminated later.