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You still had to supply the constraints so the sampling
is not complete for any waveform. This is like supplying $234 to buy that big screen TV when you have to supply $1000 under the table to actualy get it delivered. All the money is not upfront and the $234 is a lie. "Ray Andraka" wrote in message news:2gdtf.58906$4l5.30943@dukeread05... SolarFlare wrote: OK let's go with your analogy example of 1234 being represnted by 234 only. You have no way of decoding 234 into 1234 without passing information of 1000 as your baseband info and therefore the the number 1234 has not been successfuly representedm as being reproduced without further information. Now we could further argue algorythms as part of the information or part of the sample. Likewise, you have no way of discerning 234 is actually 234 and not 1234 with a 3 digit decimal number system. The problem is not unique to sub-sampling, it exists at baseband as well. The only difference is that at baseband the representation looks the same as the signal. In either case, you need to know the fixed constraints of the system to fully comprehend the meaning of the representation. For example, in a 3 decimal digit system, you have no way of knowing that 234 really is 234 and not 1234 or 2234 unless you also know that the inputs are limited to the range 0 to 999. The only way around that is to have an infinite number of "symbols" to represent all the possible data when the set of possible data is infinite. As soon as that set is not infinite, we can take advantage of our knowledge of the system to reduce the set of symbols to a manageable number of elements. I'd argue that any engineering requires a set of implied constraints in order to make the problem solvable. In the case of the subsampling, we know by design what the pass-band of the anti-alias filter is. That is a constant parameter designed into the system, so presumably it is know to designers of all the components of the system. In the example case, then, we set as a system constraint the fact that all inputs are in the range of 1000 to 1234. That constraint is a constant, and is implied by the design. No information is lost by not transmitting the constant that is already known throughout the system. Doing so simply wastes bandwidth on your communications channel. |
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