>> - 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.
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
It so occurs that I had already a similar experience in the field of
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
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.