# Effect of increasing Detector Range in Power Usage

I have two separate systems. System 1 can measure well biochemical events in the frequency [1,180] Hz. System 2 is designed to measure low frequency electromechanical processes in the frequency [0.001,1] Hz. However, separate systems are not enough. Electromechanical processes also come to the biochemical events' frequency bands sometimes such that measuring unsteadily there and there is not possible. I need to measure both systems at the same time.

However, I have no idea about how the accuracy of the measurements can change if you decide to measure 10^3 bigger segment. I think it should not change, but the power should instead change.

## Proposal for the measurement system

• Sampling rate: 360 Hz
• Resolution up to 180 Hz and down to 0.001 Hz.

Problem. I cannot understand how it is possible keep sampling rate fixed when increasing resolution from (down to 1 Hz) to (down to 0.001 Hz). How does the sampling rate changes when increasing resolution from 1 Hz to 0.001 HZ?

• I am not sure how the situation would differ if we would change the range from 180 Hz to 180 x 10e3 Hz. I think nothing. When going down or up, the situation is the same for the power. Is this a right assumption?

## Power and Safety

I am not sure how accuracy changes when measuring so big scale. I think uncertainties mostly come from the system but nothing else.

I think the wider range should be possible in theory by just increasing power, as described in the thread increasing metal detector range. However, the problem in my application is that I cannot increase the power too much. A cheap transformer is used 220 V in the chip ADuM4400 which withstands 5000 V for 60 seconds. There is no risk when 380 V peak (<< 5000) which is well within safety margins, currently with separate systems. Power usage is as a function of CPU usage. Power measurement error is normally distributed.

Unknown is the relation between Detector Range and Power

$$l \propto_{?} P$$ where l is the size of the range in the detector, and P is the system power.

How can you estimate the effect of 10e3 x range in the power usage of the system?

1. The sampling rate needs to be at least 2x the highest frequency, in theory. the lowest frequency has no bearing on the minimum required sample rate.

In any real system, you're going to need to sample more than 2x the highest frequency. You care about data up to 180 Hz, so the system needs to pass that reasonably unmolested.

You also have to deal with higher frequencies, even if you don't care about them. If you sample at 360 Hz, then anything higher than 180 Hz in the signal will alias and look like valid signal.

You probably want some analog low pass filtering that rolls off a bit above 180 Hz, so as to not affect 180 Hz much. This filter needs some room to attenuate the noise to the don't-care level. Let's say you put two poles of R-C filtering at 360 Hz. Two octaves above that, at 1.44 kHz, noise will be attenuated by about 15. Only you can say if that's good enough.

If it is good enough, then you need to sample at least 2x that, or 2.9 kHz. Now you can apply a tighter filter digitally that, let's say, goes from pass to stop within one octave. That octave would be from 180-360 Hz, so using this filter you can decimate the 2.9 kHz stream down to 720 Hz. This is doable with a low end DSP.

2. Talking about resolution as a function of frequency makes no sense, unless you are trying to measure frequency content, but you haven't said that. The resolution you get is a function of the number of good bits of your A/D. For example, 10 bits gives you about 1 part in 1000 resolution.

• Yes, I actually I am using some distributions in converting the signal into time-frequency plane. So I am measuring the frequency content. I want as little filtering as possible before getting those planes because I may be capable of doing the filtering also postprocessively. I just do not want to lose any actual data points. I am still mostly worried about the range [0.001, 1] Hz. You suggest me that that sampling rate 360 is enoug to include so low frequencies too. It would be nice to understand which bands are too low for the detection. You can assume that time range is sufficiently long. – Léo Léopold Hertz 준영 Jan 18 '16 at 12:27