[<<][math][>>][..]Wed Jun 10 15:35:37 CEST 2009

What is nice about the SD form is the ease at which it can be integrated into mixed analog/digital electronics. In fact, it can be attached directly to a set of speakers, or any analog circuit with low-pass characteristic. However, I wonder if moving to an edge-only representation will make things simpler. This will give a pure FM representation of a signal: value directly proportional to square wave frequency. It eliminates an element from the data representation: the width of a pulse. This is essentially an arbitrary component and can be easily reconstructed later. The important question is: does it make things really simpler? Let's re-interpret the elementary operations explored in [1] in terms of square wave signal. FM signals are trivially generated from an accumulator as the accumulator's MSB. Converting an FM signal to analog can be done in many ways [2], but the simplest ways seem to convert the edge signal back to a pulse signal either unclocked using a one-shot, or clocked using a bit delay. Since a signal's value is directly proportional to the density of transitions, addition is represented by the XOR operation. The advantage here is that addition is "dumb". There is no gating required as in the pulsed case. This seems simpler, but just as the pulse representation, this might lead to loss of information due to aliasing. However, the form of aliasing is different and consists of glitches. Proper "de-glitching" needs some clocked logic, and can only be done exactly if there is room in the output signal (if signals don't change during de-glitching pulse width). This brings us back to the complexity of dealing with bit slots as in the SD case. Attenuation could be implemented statistically as "selectively forgetting" to toggle the switch. There isn't much difference here. So, it looks like most operations can again be implemented using simple logic gates, conditionally on the uncorrelated nature of the input signal. I'm not really convinced about this since it seems to be harder to qualify: the extra work that needs to be done in a clocked/pulsed representation seems to bring at least some order that is harder to reconstruct in the FM case. The FM case however is probably simpler to interface to special puropose (non-clocked) analog circuits. Conclusion: FM representation is in some respects simpler, but harder to control using statistical time-multiplexing tricks as described in [1]. Since conversion between the two formats is rather straightforward in clocked logic, it seems that sticking with SD is best. Then FM can be used when it is convenient, i.e. when interfacing to an unclocked or asynchronously clocked circuit. [1] entry://20090609-111303 [2] http://en.wikipedia.org/wiki/Demodulation#FM_radio

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