Digital Origami in Software Defined Radio

Foundations of Amateur Radio

As a quick recap of what I've discussed before, a Software Defined Radio is a tool that essentially measures the voltage at the base of an antenna system and sends that to a computer for processing.

The faster you measure, or sample, the better the representation of what's coming in via the antenna. The traditional view is that you need to sample at least twice as high as the highest frequency you want to represent.

You may also recall that an antenna system doesn't just receive a single frequency, the one your radio is tuned to, but all frequencies.

So, if you need to build a software defined radio from scratch, your first question might be: What do I want to listen to?, followed by: Which sample rate do I need?

If we were to answer the first question with HF, say up to 50 MHz, the answer would be something like a sample rate of 100 MHz, so you can capture any signal up to 50 MHz.

So, twice the highest frequency as the one you care about, that's the short way of waving your hands about and ignoring any little inconvenient side effects.

Like, what happens to signals above 50 MHz?

First of all, your antenna system will still receive those signals to more or lesser degree, they don't just vanish because your sampling tool isn't interested in anything over 50 MHz.

The second thing that happens is that the signals between 50 and 100 MHz will turn up backwards between 0 and 50, so you'll effectively hear 51 MHz at 49, 55 MHz at 45 and so on.

As a neat little side-effect, for those reversed signals, an upper side band signal will turn into a lower side band signal and vice-versa, but I'll leave that for another time. In case you're wondering, yes, this can be a desired effect.

The signals between 100 and 150 MHz will also turn up where they're not welcome, 105 MHz becomes 5, 110 MHz becomes 10 and so on.

A different way to picture that is to think of a tri-fold birthday card. Lay it flat on the table, put a 0 in the top left, 50 at the first fold, 100 at the second fold and 150 in the top right. You're looking at 0 to 150 MHz.

Now fold it up.

You'll notice that 0 and 100 are in the same place and 50 and 150 are also in the same place. If you need more detail, put some in-between numbers, 25 MHz, 75 MHz and 125 MHz and you should see what's happening.

I've seen it described as digital origami and it is. The technical term is called aliasing and it's also referred to as folding. It happens in day-to-day life as well. If you've ever seen a wheel running backwards on television or on a film, that's an example of folding.

If that's not enough, this phenomenon repeats itself, 150 to 200 MHz is overlapped in reverse, 200 to 250 MHz overlaps normally and so on.

You might come to the conclusion that your magic SDR isn't so magic any more, now you have all this other stuff turning up that you don't want to hear. So what do you do?

One approach is to increase the sample rate, but as I've explained, it doesn't make the problem go away.

But here's the thing: If you were to sample at say 200 MHz, you'd be perfectly fine with any signal up to 100 MHz.

Now here's the kicker.

If you filter out anything above 50 MHz, and as long as there's nothing left by the time you get to 100 MHz, you're good to go, no more unwanted information, no more aliasing or folding.

Essentially what you've just done is created a thing called a bandwidth limited system. You've essentially removed anything above 100 MHz and now your sampling is working as planned and all of the stuff I've said about sampling at least twice the maximum frequency applies.

Yes, there's more, but I'll get to that another time, but to give you a taste, what happens if you want to use the same SDR to listen to the 2m band?

I'm Onno VK6FLAB