I believe I understand how tuning a radio with an analog tuner works: turning the dial physically changes the length of the antenna, which determines which broadcast wavelength will resonate in the antenna and get picked up. In contrast, what is the mechanism that makes a digital tuner work? My guess is it'll be some clever little circuit that somehow selects a resonant frequency by changing the amount of current going through it (or something like that).
[Physics] How does a digital radio tuner work
antennaselectronicsradio
Related Solutions
In the microwave band here are multi-element detectors, but at longer wavelengths the telescope is a single pixel.
Yes it does take a while to build up an image, but radio pictures aren't usually very large - not the millions of pixels of an optical/IR image.
One big advantage of radio telescopes is that you can combine telescopes 1000s of km apart to create an image with the resolution of a single dish that large ( you can just about do this in the optical with 100m separation now)
You know about the interference pattern you get with two slit? If you picture the two telescopes as the two slits and you interfere (electrically) the signals to form the fringe pattern. You can then calculate the shape of the light source - a single point will produce the classic fringe pattern, 2 close points will produce a slightly different pattern etc.
edit: Building an optical 'radio' telescope - the original English solution and the rather more impressive Teutonic result (if you have a lot more $$$)
Consider the incoming electric field of the radio waves. This field is a superposition of all broadcasts from stations near your receiver. The job of the receiver is to pick out one of these transmissions and turn it into sound.
AM radio
Now consider an AM radio station transmitter. Suppose the sound wave that station wants to transmit is represented by a function of time $m(t)$ where here $m$ is for "message". Note that $m(t)$ includes all information about the sound, i.e. it includes frequency, amplitude... everything. In an AM transmitter, we use a circuit to multiply $m(t)$ by a sinusoid, creating the transmitted signal $$s(t) = m(t) \cos(\Omega t)$$ where here $s$ stands for "signal" and $\Omega$ is called the "carrier frequency". Here we see the reason for the term Amplitude Modulation (AM): the message is a modulation of the amplitude of the carrier wave.
You can use trig identities or Fourier analysis to see that the spectral content of $s(t)$ is in the range $\Omega \pm \delta \omega$ where $\delta \omega$ is the highest frequency in $m(t)$. The carrier frequency $\Omega$ might be in the tens of MHz range. On the other hand, the actual message $m(t)$ would absolutely never have any frequencies above around 20 kHz because that's the upper range of human hearing. In real life, $m(t)$ doesn't use up the full 20 kHz; useful speech and music don't need our full hearing range.
So now we see that the transmitted signal $s(t)$ is contained within some relatively narrow bandwidth, i.e. maybe a 10 kHz band centered at 10 MHz. Therefore, a tuned circuit with a $Q$ of around 1,000 and centered at $\Omega$ picks up $s(t)$ but mostly nothing else.$^{[a]}$ Of course, we also have to enforce that the various stations' carrier frequencies are separated by more than their $\delta \omega$'s so that nobody's transmissions overlap with anyone else's.
So, the output of our tuned circuit is roughly just $s(t)$! I say "roughly" because our tuned circuit isn't perfect, so we might pick up a bit of stuff from other transmissions, but since it's farther away from the center of our tuned circuit the amplitude is suppressed. Then, we just put the signal through a rectifier and a low pass filter so that the carrier oscillations are gone and we only get $m(t)$. That's it! Now we have the original sound message and we can put it into a speaker. We don't have to think about amplitude and frequency separately: we have the entire original sound waveform.
$[a]$: $Q$ is the center frequency divided by the bandwidth, so $$Q = 10 \text{MHz} / 10 \text{kHz} = 1,000 \, .$$
Best Answer
In the early days of radio, the resonance of the antenna in combination with its associated inductive and capacitive properties was indeed the item which "dialed in" the frequency you wanted to listen to. You didn't actually change the length of the antenna, but by changing the inductor (a coil) or capacitor connected to the antenna you tuned the resonance. The output signal is an alternating voltage, and by rectifying it with a diode (called a "crystal" then..) you could extract a signal modulated as a varying amplitude of the carrier wave. All this without any battery! :)
But actually the antenna in a normal modern radio is not the component that "dials in" the selected broadcast frequency. The antenna circuit should indeed have a resonance within the band of frequencies you are interested in but this wide-band signal is then mixed with an internally generated sinusodial signal in the radio in an analog component, this subtracts the frequencies and lets the rest of the radio operate on a much easily handled frequency band (called the intermediate frequency). It is in the mixer you tune the reception in a modern superheterodyne radio receiver. It is much easier to synthesize an exact mixing frequency to tune with than to change the resonance of the antenna circuit.
The rest is not really physics, but the difference between an analog and a digital radio comes in the circuits after this and basically an analog radio extracts a modulation from the intermediate frequency which is amplified and sent to the speakers or radio output. In a digital radio, the signal represents a digital version of the audio, just like a WAV or MP3-file on a computer is a digital representation which can be turned back into an analog signal you can send to a speaker. The benefit of this is that the digital signal requires (potentially) less bandwidth in the air so you can fit more signals in the same "airspace" and that the digital signal can be less susceptible to noise. I write "can", because unfortunately many commercial digital radio/TV stations don't do this to improve the viewing or listening quality but just to fit in more content.
Let me reiterate that in a "digital" radio, the component that selects the reception frequency is still analog but the mixing (tuning) frequency is digitally controlled and selected.
There is also a very interesting thing called Software Defined Radio, SDR, which is the principle where the intermediate frequency (or in some cases the antenna frequency directly) is turned into a digital signal and demodulated by a signal processor which is completely software-upgradeable. Since it is much easier to program new software than to solder electronic components around, this created large interest in the radio hobby community where you can completely change the properties of a radio receiver just by downloading someone else's software from the net or write a new one yourself.
If you include SDR, and apply it without any intermediate frequency (take the antenna directly to an analog/digital converter and into a signal processor), you do indeed have a purely software-way of tuning your source like you ask for, although this is not how the most common digital radios work currently.