Re: Doubts in Sampling


"Jerry Avins" <jya@xxxxxxxx> wrote in message
news:ZeIxm.15008$ma7.12687@xxxxxxxxxxxxxxx
Nikhil A D wrote:
(...)
Let us assume that we have an ideal function generator. An ideal
function
generator is the one which has zero loss on energy inside it and the
energy
at the output is the same as the input.

With such a function generator if I reproduce 'sin(wt)' and connect a
100
Ohm resistor across the two output terminals, then the power dissipated
in
the resistor has to be same as the power drawn from the AC supply on
which
the function generator is running.

Let's take about digital signals.

From a digital signal representing the sequence [1.2, 2.7, 5.6, 4.1],
if I
create a voltage signal with the same sample values (using a dumb
digital-to-analog converter that does not have an interpolator), then
the
energy of the voltage signal is the same as the that of discrete
samples
taken before converting the samples in a sequence of bits (using an
ADC)
and storing them in a memory.
How does that relate to the energy of the sampled signal? My pocket
radio's battery is nominally 9 volts. My old car battery was 6.3 volts.
Which do you suppose was more powerful?

jerry
--
Engineering is the art of making what you want from things you can get.


If the exact definition of energy or power is not available, we talk
about
normalized energy or normalized power. Normalized power is the power
dissipated in a 1 ohm resistor.

So at the output of DAC if we have samples [1.2, 2.7, 5.6, 4.1], then
their (normalized) energy is (1.2)^2 + (2.7)^2 + (5.6)^2 + (4.1)^2 = 56.9
.

In the case of your batteries, 9 volts and 6 volts, which one is more
powerful will depend on the actual current ratings on the batteries. But
if
we accept the definition of normalized power, then 9 volt battery is more
powerful.

Try to crank a car with it!

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

To some extent. you are both ignoring the fact that energy is not power and
are using the terms interchangably. Clearly a charged 6-volt car battery
(can it still hold a charge after so many years?) holds much nore energy
than a 9-volt transistor radio battery. However if you put 1 ohm resistors
across both, the one attached to the 9-volt battery will get warmer, at
least for a short while.

That said, the voltage (or power into into a resistor) of a D/A converter
depends on the D/A converter. A sequence of numbers chosen at random, say
[1,2,3,4,5], could output [1,2,3,4,5] volts (with some agreed upon sampling
rate) or {.001,.002,.003,.004,.005] volts. Of course, the output of a D/A
converter doesn't have to be voltage. It could be amps of current, PSI of
gas, GPM of water.....

Saying that a sequence of numbers has a certain power ignores the implicit
scaling factors,


.

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