[cushychicken]

The folks who are telling you you’re wrong don’t understand Nyquist’s criterion very well. Curse those undergrad courses for only effectively teaching about Nyquist at baseband frequencies.

You can sample 100MHz of bandwidth at 1GHz just as you describe at 210MSPS. You’ll get everything in the 950-1050MHz band.

Trouble is, without an antialiasing filter, you’ll get every other band that’s a multiple of that sampling rate. The Nyquist criterion works at every multiple of the sampling frequency.

Bandpass filter your analog input appropriately from 950-1050MHz and you’re golden.

This is the way nearly every commodity Wi-Fi chip downsamples 2.4/5GHz raw RF. Sigma-delta ADCs are cheap, fast, and space efficient for die area using this method.

[femto]

The most fiendish application of this effect that I've seen is polyphase filtering. I can't remember the details, but at the time I can remember the wonder of understanding (in a lecture by fred harris) how most the logic was running at a low sampling rate yet the input was at a high rate. The mixing was done by aliasing.

Details here:

https://www.dsprelated.com/thread/7758/understanding-the-con...

https://s3.amazonaws.com/embeddedrelated/user/124841/fbmc_bo...

https://s3.amazonaws.com/embeddedrelated/user/124841/fbmc_ch...

[Sesse__]

Polyphase filtering is less crazy than it initially sounds. Conceptually, you can think of it as: I have this signal in frequency f. I want to resample it to frequency (b/a)*f, where a and b are integers. (You can also do polyphase filtering to resample of non-rational or varying ratios, by essentially approximating towards a rational, but let's ignore that for the moment.) a and b can be pretty large if you want, e.g. a=160,b=147 will downsample from 48 kHz to 44100 Hz.

So what you do to resample a signal (again conceptually), is: 1. Add <a> zeros between every input sample (which repeats the spectrum <a> times), 2. Apply a suitable (long!) FIR lowpass filter so that the signal is bandlimited, 3. Take every <b>-th sample (which doesn't cause any aliasing due to #2).

Now the core of the polyphase filtering idea: We don't need to actually calculate the FIR filter for the samples we don't want in #3. And most of the input values to the filter will be zero due to #1. So instead of storing all the zeros and stuff, we simply pick out every <a>-th tap of the FIR filter and use that on the input signal directly. But since a and b don't line up perfectly, this means we get a different subset of the FIR filter for every output sample; we have a time-varying filter (or a filterbank, if you want). You get <b> different such filters before you're back where you started.

[cushychicken]

Implemented a polyphase filter in Verilog once. I learned the hard way that it’s easy to mix in unwanted stuff into your polyphase chain if you’re not careful with your implementation.