Re: integration of a continuous function



illywhacker wrote:

On Feb 24, 11:24 pm, jim <".sjedgingN0sp"@m...@xxxxxxx> wrote:
illywhacker wrote:

On Feb 24, 8:11 pm, "Alex_001" <a.bast...@xxxxxxxx> wrote:
What could be simpler then a moving average filter?

it's not what we need..our acquisitions are on a 5 ms windows at
different time instants (when particoular events occur)

Extra knowledge is harmful to the idiots.

not everybody can spend all his time reading posts and insulting
people..someone has also to work.

"Matlab does all thinking for us" (TM)

what I need is EXACTLY a cookbook solution...I am not a geniuos like you.
(and I cited Matlab just as an example).

what's the problem with you man?
Chill out!

Don't worry Alex. Genius is a long way from what Vladimir is.

On the other hand, Jim's suggestion is relevant. The reconstruction
theorem as stated only applies if sampling is really by delta
functions which it never is. Presumably what you really want is the
integral of the force itself, isn't it? You could get much better
results if you knew more details about the sensor, the filtering, and
the sampling.

That was not really my point. He doesn't want the integral of force. Force is
just an abstract concept here so is integration. Movement in space is what
produces a voltage.

Is he not using a piezoelectric sensor, i.e. one that generates a
voltage when deformed? This deformation can be produced by a number of
effects depending on how the sensor is set up, acceleration being one,
applied pressure being another. Since the OP mentions 'force', I
assume it is the latter rather than the former. Did I miss something?

No you didn't miss that. I was thinking he said acceleration but you are correct
he said force.

But the concept of force and acceleration are just abstract concepts (they
exist in your head but not in reality). In order for a voltage to be produced
their needs to be motion. Without motion there is no voltage. Obviously since
the device is rigid and fixed and going nowhere that motion needs to be
oscillating. As long as that oscillating motion stays with in certain frequency
range then he can call the output "force" because the sensor device filters the
signal that motion produces in a way that very closely matches that concept of
force you have stuck in your head.
Numerical integration is also just an abstraction. What it is really is a
filter that has a frequency response similar to the frequency response of
integration of a continuous function. The important part of the frequency
response of summing the samples (moving average filter) is actually 1/sin(f) not
1/f, but since sin(f)=f when f is near zero this isn't a problem when the signal
is sufficiently oversampled.




The amount of voltage output for a given displacement
depends on the frequency at which that dispacement occurs.
The sensor is essentially a filter with a certain frequency response. That
means you move the sensor in space at certain frequencies and it attenuates
those frequencies in a predictable way. It just acts as a linear filter. The
frequency response of this filter just happens to be very close to proportional
to the square of the frequency. But it isn't exact. For example, just loosening
or tightening the mounting bolt(s) on this type of sensor can change the
frequency response curve.
If the sensor is mounted in the manner the manufacturer designed it to be and
and the movement in space driving it is at frequencies within a certain band you
can do simple double numerical integration and get an output that follows the
input movement simply because you are applying a filter to the data that happens
to be very close to the exact inverse of the sensor's frequency response and
thus the output is close to a flat response to the input. But in a real
situation it often won't work so nicely because the mounting is not ideal or the
input motion is not strictly limited to those frequencies at which the sensor
has a simple response curve.

Thanks for the lesson, Jim, but these are trivialities. But if he
wants the applied pressure then there is no need to do doubly
integrate. What produces this applied pressure, and why he might want
to integrate that I have no idea.

The reason he wants to integrate seems obvious -> he wants to recover the
original signal. I.E. he wants to recover the original continuous signal that
was producing the voltage. What isn't obvious are what the circumstances are
that are causing him to believe he isn't getting an accurate output that closely
matches the input motion.

-jim



illywhacker;
.

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