ARLA/CLUSTER: Foundations of Amateur Radio #205: SDR Sample Rates: How fast is fast enough?

[João Costa > CT1FBF]

If you measure the voltage at the base of an antenna and record the
readings, you end up with a collection of numbers that represent the
voltage over time. These numbers, or samples, can be used to represent the
antenna signal inside a computer.

An antenna system voltage is an example of an analogue signal, continuous
over time, the recorded readings, the samples are an example of digital,
discrete and intermittent.

It's possible to reconstruct an analogue signal from digital samples and
that's exactly what Software Defined Radio or SDR is all about.

The process of sampling essentially converts a continuous signal into an
intermittent one. As recording separate samples implies, there is loss of
information in this conversion.

For example, if you sample once a minute, you'd represent a continuous
signal as 60 samples per hour, probably enough to reconstruct where you've
driven in your car along the highway, but hardly enough to reconstruct the
route through the middle of the city, let alone represent an antenna signal
that varies millions of times per second.

So, how often do you need to record a sample?

Turns out that if you sample at least twice as fast as the highest
frequency you're representing, you're good to go.

So, for sound, the human ear can hear about 20 kHz, so more than twice
that, explains some of why a CD is sampled at 44 kHz.

If you want to represent the 20m band, up to 14.350 MHz, you need at least
a sample rate that's double that, or 28.7 MHz.

As an aside, there are other ways to look at this problem. If you managed
to move the 20m band down to 0, then you'd only need at least a sample rate
of 700 kHz to do this.

Let me say that in a different way.

The width of the 20m band is 350 kHz. So sampling it would require at least
twice that, or at least 700 kHz. Moving frequencies around is something
that we've been doing in traditional radios for a long time. The technique
uses one or more frequency mixers. This means that combining some
traditional radio tools with an SDR gives you even more options.

Truth be told however, this idea of moving the band with one or more mixers
is becoming less important as technology improves and there are plenty of
reasons not to use this. I'll talk about that at another time.

So, the first takeaway is that to sample a continuous signal and be able to
represent that signal accurately requires a sample rate that's at least
twice as high as the highest frequency in the continuous signal.

Without going into the actual proof of this, consider a sine wave that
oscillates at 1 Hz. If you sample it at anything less than 2 Hz, you'll end
up with some cycles being sampled only once, which isn't enough to
represent the sine wave. If you sample it at exactly 2 Hz, you'll have two
samples on every cycle, but if you happen to sample when your signal is 0,
all you'll ever measure is 0. By sampling at a rate greater than 2 Hz, you
overcome that limitation.

I'll make brief mention of another phenomenon, that of over sampling. An
interesting thing happens if you sample twice, three times or more than the
minimum sample rate. In short, the higher sample rate improves the dynamic
range, noise performance and filtering, all very useful when you are
processing radio signals. Cheaper and cheaper hardware are making this very
attractive and it explains some of the reasons why SDR manufacturers are
using sample rates that far exceed double the highest frequency being
sampled, for example, the Flex-6600 samples at 245.76 Mega Samples Per
Second, or Msps, even though the maximum receive frequency is between 30
kHz and 54 MHz.

In case you're wondering, yes, I'm leaving out a lot of detail here, one
thing at a time.

The opposite, under sampling, has its uses as well, but I'll also leave
those for another time.

The second takeaway is that higher sample rates are used to reduce cost,
increase performance and reduce component count.

Some of what I've talked about can be explored with the popular RTL-SDR USB
dongle which is actually a mass produced commodity digital television
receiver, made in the millions and accessed directly thanks to the combined
efforts of many different people. If you'd like to start to play, $25
should get you a dongle and most of the software you can start to
experiment with is free. Check out rtl-sdr.com to get started.

If you'd like to get in touch, please do, cq  vk6flab.com.

I'm *Onno VK6FLAB*
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