I had the “opportunity” to spend many hours alone with my own thoughts over the last month. I spent much of the time imagining how I would transmit a signal if I were wanting to contact aliens. What I came up with may not be particularly novel since I am not a signal processing expert but hopefully this writing won’t upset my grad school professors on the subject too much.
We start with a repeating signal to give us a method of synchronizing clocks between locations. A more capable civilization might modulate the wavelet of a pulsar but my soft human meat brain likes to imagine a sine wave to serve as this timing wave. From this wave we can easily detect a frequency (f) and express it as a period (T).
My idea from there is to capture the residual fluctuations over the wave and average them. For symmetrical waves like sinusoidal waves the first half of the wave can be added to the second half (half-period residual modulation detection). But in general any given wavelet would be differenced from the next to produce a set of residuals (full period residual modulation detection).
As far as I know this is not something that can be accomplished with analog signal processing. The signal must be stored for at least the full period T and then combined with the next wavelet instance. The collection and storage of the signal will have a certain bitrate, which must be higher than the timing wave. It is not clear to me what bitrate would be the ideal choice for a given timing frequency. Bigger always seems better but I remain uncertain how to encode universally interpretable information in a time series, regardless of the bitrate. One ideal would be to transmit a signal with similar meaning at multiple bitrates - a lower resolution vs a higher resolution of the same meaning. Could the antenna bandwidth characteristics somehow imply an ideal bitrate? Maybe there is something to be figured related to the maximum throughput or channel capacity of the proposed signal processing paradigm. Or perhaps using a known distance to the transmitter could give you a sense of what sampling frequency would be reasonable to expect.
Anyway, this is how I would get started if I was leading a new SETI project. Aim something at a pulsar and start crunching on this.
