Jerry Avins wrote: Curiosus:>> - The sampling period: the sampling process cannot represent >> accurately events shorter than the sampling period. For example >> music CDs are using a sampling frequency of 44,100 Hz.> Shorter than twice the sampling period, assuming real > (not complex) samples.Yes, that is the formula for waves. But I had in mind a discrete pulse: if the duration of the pulse is more than one sampling period, we are sure not to miss it, when we are not sure if it is shorter.>> - The sampling resolution: the sampling process cannot represent >> values smaller than the resolution (for example 1 / 2^16 by using >> 16 bits A/D converters.)> Higher sample rates than specified above can make interpolation > possible under the right circumstances.Yes. One of the applications is to use oversampling processes to build sample/rate converters, or to build anti-aliasing filters.> If you figured all this out independently, your knowledge is deep > and you are very insightful.Thank you. I was a student in physics once a time, but I had to quit after 3 years for financial reasons and eventually I became engineer. But I remain quite interested by physics. I spotted the analogy between signal processing and quantum mechanics when looking at the result of optical interference experiments filmed with ultra-fast cameras: they were displaying the photons one by one. With 5 photons, there are just 5 random points. But as you accumulate photons, they are eventually distributed according to a sinusoidal pattern. It so occurs that I had already a similar experience in the field of digital processing. That is possible to reproduce a similar pattern with the following experiment (I suppose you have already made similar observations.) - Take a D/A converter with a 48 kHz sampling frequency. (A raw converter, without any anti-aliasing filter at the output) - Send a digital sine wave in the converter, with a 20kHz frequency - Connect an oscilloscope to the analog output of the converter - Take only one shot at a time: you see like a staircase on the screen, that has nothing to do with a sine wave. - Then synchronize the oscilloscope with the original analog sine wave: what do you see? A perfect sine wave! So with the accumulation of data, we can observe a sinusoidal wave, when with only a few samples, we have like 'particles'. From that day, the duality wave / particle of photons became quite clear. Currently physics does not fully integrate that duality: according to the context, light is considered as a wave or as made or particles, but seldom both things at a time. Moreover, physics does not consider the waves as really real, but as waves of probability of presence of photons. The situation becomes simple and intuitive, by considering that there is an analog universe, where continuous waves really exist, and that our physical universe is the quantified and discrete representation of this analog universe. For signal processing engineers, that makes sense I suppose. For physicists, that would be solving many a paradox and contradiction (for example the duality wave/particle, the Einstein/Bohr debate). That is just necessary to postulate the existence of an analog and infinite upper universe, our parent universe, so to speak. Best regards, -- Curiosus http://www.geocities.com/curiosus_2008/