Could you do DDS of comprehensible radio signals with an Arduino? Maybe with some filtering.
You can spit out data words with bitstreams at the full clock rate with the SPI controller (and some trickery), which is a square wave of up to 8MHz. You can get 10MHz (20mbps) if you use a 20MHz crystal.
AM radio is 525 kHz to 1705 kHz with like a 10kHz bandwidth. FM radio is 88 to 108 MHz with like a 200kHz bandwidth and ±75 kHz deviation.
The mechanisms for these two bands would be quite different.
For AM, we would be synthesizing more or less the frequency we actually want, but with different amplitudes (and unwanted harmonics). A 530kHz cycle is 1.89 μs, about 30 bit times. That should give us something like 10 or 15 distinct amplitudes, maybe 4 bits. Not as good as magnetic tape, but probably enough for comprehensibility.
For FM, we can’t hope to get close to the actual carrier frequency; instead, we can hope that our square waves are square enough and well-timed enough to have harmonics up there. We may be able to improve the situation by reshaping them (say, with a Schmitt trigger) to sharpen the edges. At 8MHz, though, you can’t get very narrow variation of frequencies. At 4MHz, your 23rd and 25th harmonics would be within the FM band. But I’m not convinced you can do an adequate job unless you’re actually bending the Arduino’s own clock.
Bending the clock might not be that hard, though, especially if we’re running on the internal 8MHz RC oscillator for a change. Keep in mind we’re looking for a deviation of less than 75kHz out of about 100MHz: 0.075%. And it doesn’t even have to be very linear. It just has to be roughly controllable.
(The numbers hereafter are from the ATtiny2313 datasheet.)
The OSCCAL register on the ATtinies can adjust the internal oscillator speed, but only by increments of about 1% (about 2% at the high end of the frequency range) which would take you to an entirely different radio station. However, the oscillator frequency also varies with Vcc in a much more subtle fashion. So maybe by putting a resistor on the Vcc lead we could vary the Vcc between, say, 1.8V and 5V, by varying the current drawn by the chip and therefore the voltage across the resistance. The voltage coefficient of frequency varies on both sides of zero over the voltage range, but it seems to be usably large in many places. For example, going from 2V to 2.5V, eyeballing the chart, it looks like the frequency at 25° declines from about 8.02MHz to about 7.99MHz, a 30kHz variation (0.375%), about 60Hz/mV (0.00075%/mV). This means that by varying the voltage by 100mV we can vary the frequency over the appropriate range.
Active supply current Icc increases with Vcc; over that range, it varies from 1.3 mA at 2V to 1.8 mA at 2.5V, supposedly. Idle supply current is about 0.3 mA to 0.5 mA over that range, so you can generate a proportionately large variation in current just by executing instructions. If we want 1mA to vary our current by 100mV, then we want about 100Ω of resistance.
We can’t be sourcing 20mA of FM signal, because the resulting current and thus voltage and thus frequency variation would overwhelm the signal we are trying to generate. We might be able to sink it, though, with the output load being connected between an output pin and Vcc.
Scott Harden reports that he is able to get good results transmitting 1MHz square waves with a class-C amplifier consisting of a 2N7000, a resistor to Vcc, a couple of coupling capacitors, and modulating the signal into the transistor’s drain below the resistor with an audio signal. But he was just generating square waves. If I understand it right, this seems like it might be a useful alternative to direct digital synthesis, maybe using a filtered PWM output.