Kevin Reid's blog

Just about a year ago, I acquired a 3D printer.

I've been casually reading about the progress of hobbyist 3D printing since the RepRap days, but sometime in late 2017 I decided to seriously consider whether I should get one for myself. I'd already purchased items from printing services (i.materialise and Shapeways), both existing and of my own design, and that experience taught me that I wanted to do more and to iterate cheaper and faster. As a sanity check, I made a list of further things I thought I could make with one — not general themes but specific items to solve problems I had. That list was immediately filled with ten or so items, so I bought one.

I purchased a Prusa i3 MK3 kit printer (despite, at the time, uncertainty about whether the MK3 design was flawed as a lot of people were reporting quality and reliability issues), set it up in April 2018, and have been printing things ever ever since (with very little trouble).

I've been posting my designs on Thingiverse (pictures there) and on Github — rather, those that I have declared finished and documented. There's another 30 or so that aren't published, yet.

(You can also see hints of some other ‘new hobbies’ in what I've been posting, but I'm overly fond of putting things in chronological or at least dependency order.)

Background

In software-defined radio, there are well-established ways of visually representing the signal(s) in the entire bandwidth available from the hardware; we create a plot where the horizontal axis is frequency (using the Fourier transform to obtain the data). Then either the vertical axis is amplitude (creating an ordinary graph, sometimes called panorama) or the vertical axis is time and color is amplitude (creating a waterfall plot).

Here is an example of ShinySDR's spectrum display which includes both types (y=amplitude above and y=time below):

A further refinement is to display in the graph not just the most recent data but average or overlay many. In the above image, the blue fill color in the upper section is an overlay (both color and height correspond to amplitude), the green line is the average, and the red line is the peak amplitude over the same time interval.

We can see signals across an immensely wide spectrum (subject to hardware limitations), but is there a way to hear them meaningfully? Yes, there is, with caveats.

What's pictured above is a small portion of the band assigned to aviation use — they are used primarily for communication between aircraft in flight and air traffic control ground stations. The most significant thing about these communications is that there are a lot of different frequencies for different purposes, so if you're trying to hear “what's in the area”, you have to monitor all of them.

The conventional solution to this problem is a scanner, which is a radio receiver programmed to rapidly step through a range of frequencies and stop if a signal is detected. Scanners have disadvantages: they will miss the beginning of a signal, and they require a threshold set to trade off between missing weak signals and false-triggering on noise.

An alternative, specific to AM modulation (which is used by aircraft), is to make a receiver with very poor selectivity: the ability to receive only a specific channel and ignore other signals. (Historically, when RF electronic design was less well understood and components had worse characteristics, selectivity was a specification one would care about, but only if one lived in an area with closely-spaced radio stations — today, every receiver has good selectivity.)

I'm going to explain how to build an unselective receiver in software, and then refine this to create spatial audio — that is, the frequency of the signal shall correspond to the stereo panning of the output audio. This is the analogue of the spectrum display in audio.

Of course, this is an AM receiver and so it will only make intelligible sound for amplitude-modulated signals. However, many signals will produce some sound in an AM receiver. The exception is that a clean frequency-modulated (FM) or phase-modulated signal will produce silence, because its amplitude is theoretically constant, but this silence is still audibly distinct from background noise (if the signal is intermittent), and transmitted signals often do not have perfect constant amplitude.

Implementation

A normal software AM demodulator has a structure like the following block diagram (some irrelevant details omitted). The RF signal is low-pass filtered to select the desired signal, then demodulated by taking the magnitude (which produces an audio signal with a DC offset corresponding to the carrier).

In order to produce an unselective receiver, we omit the RF filter step, and therefore also the downsampling — therefore demodulating at the RF sample rate. The resulting real signal must be low-pass filtered and downsampled to produce a usable audio sample rate (and because the high-frequency content is not interesting; see below), so we have now “just” swapped the two main components of the receiver.

This simple change works quite well. Two or more simultaneous AM signals can be received with clear stereo separation.

One interesting outcome is that, unlike the normal AM receiver, the audio noise when there is no signal is quieter (assuming AGC is present before the demodulator block in both cases) — this conveniently means that no squelch function is needed.

The reason for this is obvious-in-hindsight: loosely speaking, most of the noise power will be at RF frequencies and outside of the audio passband. In order to have a strong output signal, the input signal must contain a significant amount of power in a narrow band to serve as the AM carrier and sideband. (I haven't put any math to this theory, so it could be nonsense.)

Adding stereo

In order to produce the spatial audio, we want the audio signal amplitude, in a single stereo channel, to vary with frequency. And that is simply a filter with a sawtooth frequency response. The signal path is split for the two stereo channels, with opposite-slope filters. (AGC must be applied before the split.)

An undesired effect is that near the band edges, since the filter has a steep but not perfectly sharp transition from full-left to full-right, there is a lot of slope detection (output from frequency-modulated signals) that does not occur anywhere else. Of course,

This design can of course be applied to more than two audio channels; using surround sound would avoid the need for steepness of the filter at the edges and map the inherently circular digitized spectrum to a circular space, so it's worth trying.

Notes

I've implemented this in ShinySDR (and it is perhaps the first novel DSP feature I've put in). Just click the “AM unselective” mode button.

Some “directions for future research”:

As I mentioned above, this is useless for listening to FM signals. Is some technique which can do the same for FM? Naïvely creating an “unselective FM receiver” seems like it would be a recipe for horrible noise, because to a FM demodulator, noise looks like a very loud signal (because the apparent frequency is jumping randomly within the band, and frequency maps to amplitude of the output).

If we declare that the output need not be intelligible at all, is there a way to make a receiver that will respond to localized signal power independent of modulation? Can we make an unmodulated carrier act like an AM signal? (CW receivers do this using the BFO but that is dependent on input frequency.)

I have really failed to get around to blogging what I've been doing lately, which is all software-defined radio. Let's start fixing that, in reverse order.

Yesterday, I went to a Bay Area SDR meetup, “Cyberspectrum” organized by Balint Seeber and gave a presentation of visual representations of digital signals and DSP operations. It was very well received. This video is a recording of the entire event, with my talk starting at 12:30.