EC-8.5 Sampling, Data Acquisition and the Digital Record

What this is and why it exists

Sampling was proved in the signals and systems module as a result about functions. Here it is a chain of physical parts, each of which can spoil the record.

The ordering of those parts is the thing most often got wrong, and it is the one mistake that cannot be undone afterwards. Once a record has been taken with the filter in the wrong place, no amount of later processing recovers what was lost.

This topic is therefore about the chain, not about the theorem. The theorem tells you what rate you need. The chain tells you what to build.

The vocabulary

• Signal conditioning — amplification, attenuation and filtering applied before conversion.
• Anti-alias filter — a low-pass filter placed before the converter to remove content above half the sample rate.
• Sample and hold — a circuit that freezes the input while the converter works on it.
• Sample rate — how many samples are taken per second.
• Record length — how many samples are kept in one capture.
• Least significant bit — the smallest step a converter can represent, equal to the range divided by the number of steps.
• Pre-trigger — samples kept from before the trigger condition occurred.

The mental model

The chain runs sensor, conditioning, anti-alias filter, sample and hold, converter, storage. Each stage limits what the next one can do, so the weakest stage sets the quality of the whole record. A twenty-four-bit converter behind a noisy amplifier records noise to twenty-four bits.

The anti-alias filter is the part with the ordering rule attached. Anything present above half the sample rate does not disappear when you sample. It reappears in the record disguised as a lower frequency, and once it is there it is indistinguishable from real signal.

The filter must be in front of the converter, because after the converter the damage is already recorded. This is the single most important sentence in the topic. A filter applied to the stored data removes the band you told it to remove, including whatever real signal was there. The disguised content is left untouched.

Rate and length answer two different questions and people confuse them. The rate sets the highest frequency you can see. The total length of the record sets the finest frequency difference you can distinguish. Wanting to see high frequencies and to separate two close ones at the same time is what makes acquisition files enormous.

A useful habit is to write the requirement as two sentences before choosing anything. The highest frequency of interest is this, so the rate must be at least twice that and in practice several times more. The two features to be separated differ by this much, so the record must last at least the reciprocal of that difference.

Resolution and range work together. A converter divides its input range into steps. Twelve bits over a ten-volt range gives about two and a half millivolts per step. If your signal only ever spans half a volt, you are using a twentieth of the available steps and throwing away more than four bits.

Amplifying the signal to fill the range is the fix, and it is what the conditioning stage is for. The limit is clipping: fill the range so completely that a transient runs off the end and the record is worthless.

Triggering is what lets you capture something that happens once. The instrument is armed, it waits for a condition, and it records. Pre-trigger storage keeps the samples from before the condition occurred, which is almost always where the cause is visible. A capture that starts at the fault shows you the fault and not the reason for it.

Storage is the part everyone treats as an afterthought and later regrets. A column of numbers with no sample rate, no units, no range setting and no date is unusable a month later. That includes the person who took it.

The metadata is part of the measurement. Writing the instrument, the settings, the conditions and the date beside the data costs a minute and is far cheaper than repeating the experiment. This is also the point where the experimental method topic and this one meet.

What you should now be able to explain or do

• Lay out the acquisition chain in order and say what each stage limits.
• Explain why the anti-alias filter must precede the converter, and what happens if it does not.
• Choose a sample rate from the highest frequency and a record length from the resolution you need.
• Match a converter's range to a signal, and say what is lost by leaving most of the range unused.
• Use pre-trigger capture to record a one-off event together with its cause.
• List the metadata that has to be stored beside a record for it to remain usable.

Check yourself