Introduction to Measurements

Measurement is the science of extracting meaningful information about the real world. A physical quantity related to something in our real world is translated to data that can be seen, heard or in some other way communicated to a human being or to a machine, such as a computer.

Measurement is often followed by the translation (or mapping) of aspects of the real world to a few, simple numbers or concepts that are easy to relate to. The elephant is "big", the jet engine is "noisy", I am "tall". Each of these measurement terms carry with them a certain conciseness of data. In one word, we give a meaningful communication of the most relevant data. Now these words are not quantitative, and therefore actually represent an interpretation of the measurement results: i.e. the data of the size of the elephant is turned into the interpretation of "big". The noise level of 152 dB of the jet engine is "noisy", and the 196 cm height is considered "tall".

These simple examples illustrate some very important principles of measurement: That we start by the acquisition of quantitative data, perform data transformation and/or data reduction, and turn the data into results, which is interpretation. Data reduction is important in most measurements because the world is so complex, that we need to find models of it that are simple to understand and still useful. It is interesting to see that although we start with quantitative data, the interpretation often is quite subjective.

Together with the science of extracting the information, is the art of choosing which information to extract, how to extract it, and how to interpret it. We use the word "art" to imply that there is no fixed procedure for doing something, there is no predefined formula for getting the job done. Art implies experience, skill, judgment, creativity and intuition. And the quality of these judgments can have a tremendous impact on the quality of the measurement. For example, it does little good to use a 16 bit analog to digital converter in an environment with a high hum level unless the inputs are balanced to get rid of the hum. Yes, this is a fairly precise rule, but because there are thousands of such "rules" necessary to make good measurements, we often call it art.

Likewise the art of choosing which interpretation method to use is vital. If we are looking for periodic or repeated phenomena, we may use the Fourier Transform (or spectrum analysis) since it is a technique which looks for harmonics of sines and cosines. For transients or short bursts of data, we may choose wavelets, which perform "pattern matching" for these types of signals. Although the frequency spectrum of a very short transient may be mathematically correct, accurately calibrated and measured, it may not be meaningful for our needs because it represents the data in a domain (frequency) where the height and duration of the transient are not at all obvious.

Part of every measurement is identifying how "good" the measurement is. This is a complex combination of a number of factors:

• The quality of the transducer used to pick up the measurement.
• The connection of that transducer to the object being tested.
• The quality of the data acquisition/conversion devices
• The quality of measurement algorithm
• The statistical characteristics of the sampling methods used.

Fundamental to all measurements is a proper understanding of statistics. By definition, every measurement consists of sampling of data. Aspects such as the observation window, sampling rate, and averaging techniques, play an important role in the overall quality of the measurement.

The accuracy of the measurement is related to the accuracy of the entire measurement chain. It is important to be able to calibrate the entire measurement chain, as well as its individual components. This calibration results in specification of the accuracy of the measurements, which can be broken into two categories: 1. bias errors which are a deviation of the result in one particular direction compared to the true value, and 2. random errors, which is a uniform scattering of the values around the actual value being measured.

It is vital to remember that although the measurement chain may have a very high accuracy, it may not be possible to measure the statistical properties of the signal with the same accuracy. For example, assume that you want to measure the RMS voltage of a random noise signal. You may then take 1000 samples, each with 0.01% accuracy. However, the statistical rules state that for 1000 samples of a random signal, you will only have a confidence interval of about 3%. Another example of this, can be the sampling of people's voting choices for a political poll. 1000 people may be asked, and each may answer with 100% accuracy that they will vote for candidate A or B. However, since this is a limited sample of a larger class, its statistics will dictate relatively poor accuracy. There is nothing wrong in itself with the 1000 samples, but since they are a subset (i.e. based on a limited observation window), the statistical accuracy will be limited.

Finallly, before performing a measurement it is important to identify what are the characteristics of the signal that you want to measure, or if you measure a system response function, what are its fundamental characteristics. Signals, for example, may be stationary and noise free, or they be non-stationary and also have a fair amount of noise in them. Different technques must be applied for different signal types. Likewise, systems can have stable, stationary transfer characteristics, they may be linear or non-linear, and they may also have varying degrees of noise. Again this has significant impacts on the choice of measurement techniques.

The many different considerations that must be taken into account in making quality measurements can seem overwhelming. Interestingly, whether you think of these aspects or not, they are present in every measurement. Experience and common sense will help in shaping your experience, so you know which of these aspects have the largest influence related to the overall objectives of the measurement you are trying to perform.

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