The thing that allows for all this SDR magic is something called the Fast Fourier Transform, and its inverse. This little bugger is a way to convert all those bins that get loaded by the A to D converter into waveforms, and to de-convert waveforms back to bins for array manipulation or modulation.
The way I think about this is imagine you have a cucumber. You get that widget from Ronco called the slice-o-matic and that cuts your cucumber up into a million little cucumber slices. Then you jam all the slices back together. By golly it still looks like a cucumber!!!, but it really isn't the same cuecumber. Its a million slices of cucumber recombined to look like a cucumber. As far as your eye is concerned its a friggin cucumber, but it is really a bunch of slices. This is how FFT works. it takes a bunch of discrete data and jams them all together to make audio that sounds just like analogue audio.
TV actually works like this. If you watch a running back tearing down the field at the stadium its all real time. If you watch it on TV its really a bunch of discrete scans, scanned fast enough that the discreteness dissappears into the persistance of your visual perception. Thought has a certian speed based on how fast the neural network can conduct. The speed of thought is called the P300. It's actually probably slower than P300, but neuroscientists like to talk about that over wine and cheese (neuroscientists are a snotty lot, when I was doing chemistry and physics it was beer (by the keg if you please) and pizza. In fact my old boss had pizza bake-offs where we tried to devise man's best pizza. We would all keep track of our recipe's and once a month we would all meet and bake a bunch of pizza trying to improve pizza science! All that science made us damn thirsty. Good excuse for a party). P300 is the speed an impulse can travel down a neuron and in the fastest neuron that is 300 m/s for the alpha motor neurons. You can't react any faster than the neurons can conduct, and conduct in a coordinated way. Like the speed of light it is a boundary that you can approach but can not cross. So now you have some really good cocktail info and you can look like the smartest guy in the room.
The sampling rate needed to completely characterize an analogue signal is determined by the Nyquist Shannon sampling theorem. Basically you have to sample at least twice the highest frequency of what ever analogue signal you are sampling and you have all the data you need. In other words once you chop the cucumber into critically thin enough slices, it really doesn't improve resolution to chop further, (and pretty soon you'd wind up with cucumber mush anyway).
here are a couple of pretty good short wikipedia articles on these two concepts
http://en.wikipedia.org/wiki/Fast_Fourier_transform
http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem
What I have presented actually considerably over simplifies the reality. The point of the blog is to try and provide some understanding of how this thing works in practical terms for people who are not mathematicians. Its of course hard in a few hundred words to do justice to a concept like this especially without resorting to mathematics. I've been told by more than one person when I discussed the idea of this blog: "Good Luck!" When I started Ham Radio I didn't understand what a "Tank Circuit" did. I was 7 when I first heard the words, but just hearing the words was the start of understanding. I rad those words in the Novice test license manual and there was a little schematic. Why, the tank was between the tube and the antenna! So: It's a start :)
I think Flex-co should include a Cap Snaffler along with every order for snaffling caps of all sizes!!! It really really works!!!
Actually it is true this radio does really really work.
73
