# Sampling motion through travel

I have an object with an accelerometer on it that is going to travel rapidly for 14ms. My coworker says, "the bandwidth of this transient is 25Hz" .. "So we can sample at 100Hz to sufficiently capture this event."
Something in me questions this. He received the 25Hz number from using 0.35/.014, which is used when you have a rise time. In this case, it's not exactly rise time, its the entire length of travel.

But, when I think on this, 100Hz is a sample every 10ms. So wouldn't we only capture a single data point during the 14ms travel time?

Thanks for any clarity, and welcome to some suggestions on capturing this travel event.

• What "event" ? The fact of "traveling"? Then a single sample is sufficient (assuming it is noiseless). Nov 19, 2021 at 15:25
• Yes, I want to capture the accelerometer data during the 14ms travel event. Nov 19, 2021 at 15:27
• BTW, accelerometers usually have an "interrupt" pin, which is triggered when acceleration above a certain level. You can use it instead of continuous sampling. Nov 19, 2021 at 15:28
• Ignore 25Hz, not worth to argue. Your criteria is "how many samples you need in 14mS as the resolution (in time domain) in the system requirement, it is only accelerating, ramp up, no band-width stuff.
– jay
Nov 19, 2021 at 15:41
• What is not clear from the question, is what you need to know about the motion. The fact that it's moving? 100Hz is good enough. The acceleration and deceleration profile, within 1%? It obviously isn't. You'll need to clarify the question to get a useful answer.
– user16324
Nov 19, 2021 at 17:50

But, when I think on this, 100Hz is a sample every 10ms. So wouldn't we only capture a single data point during the 14ms travel time?

One or two (e.g. one at 5ms, or one each at 0 and 10 ms).

So, yeah, your coworker's argument doesn't hold.

The systems bandwidth needs to be much larger if it comes from rest to full velocity to rest within 14 ms.

A better signal / physical model might lead you to find an appropriate sampling rate.

Something in me questions this. He received the 25Hz number from using 0.35/.014, which is used when you have a rise time. In this case, it's not exactly rise time, its the entire length of travel.

It makes no sense to me.

Where the 0.35 factor comes from is in a simple 1st-order filtered system where: -

$$t_R\text{ (or rise time)} = \dfrac{0.35}{F_C}$$

Where $$\F_C\$$ is the cut-off frequency of the simple 1st-order filter. However, there is nothing in your information that can lead anyone to argue that the rise time (or fall time) doesn't occur in 1 ns or 1 μs.

This leads me to believe one of two things: -

• You are not providing the same information in your question that your colleague has or,
• He is bastardizing a fairly irrelevant formula without thinking about the consequences.

Either way, sample as fast as your can (probably in excess of 1 kHz rate) and collect as much data as you can. Under-sampling sounds to me like something you might regret doing.

If the waveform you are trying to capture is well-bounded within the constraints of what a first order filter might impose on it, you still don't know what the cut-off frequency is of that 1st-order filter.

• You ought to also mention rise time is not the asymptotic 63% Voltage but rather the 80% step response from 10 to 90%. Nov 19, 2021 at 17:02

The sampling rate must be a product of dynamic range and the -3dB BW which is the step-response slew-interval from 10% to 90%.

So consider a 10 bit ADC with 60 dB range and accuracy limited by this product of dynamic range BW x 2.

However, the spectral density and dynamic range accuracy must be defined before a solution can be considered.

Common problems in g-sensing are that the mounting frame always has some resonance and so the response may be under-damped. There may be multiple resonances such as from a loose package on a skid in a truck.

The requirements need to be known, with respect to fragility and useful information with time stamps and data storage limits. Light objects may be sensitive to high g with short-time intervals and heavy objects sensitive to low g and long time or velocity-sensitive from inertia 1/2mv^2.

A FRAGILITY curve is the damage boundary signature of the vector plot of g and v which defines the limits to damage for any object.

e.g a small cartridge might withstand 100g for 1ms but a human might only survive to 10g for 1 second with a gaussian curve. Thus jerk rates or the derivative of g are just as important as velocity and g.

## other

There are other methods that compress the BW of the ADC storage process of SDC type ADC's with high speed and BW using digital filtering.

If you know the event signatures, data compression can be realized by capturing the peak and hold value with the PW50 decay time ( or interval when average rectified AC drops below 50% . You can also have a variable threshold to trigger captures and measure resonant frequency with a different signal conditioner.