ABSTRACT
Discrete Fourier Transform (DFT) discrete representation of the Fourier transform
discrete having values at distinct times or locations
discrete Fourier series discrete representation of a Fourier series
dynamic varying in time
dynamic calibration calibration using a time-dependent input
dynamic error error related to the amplitude difference between a system’s input and output
electric field electric force acting on a positive charge divided by the magnitude of the charge
electric potential potential energy per unit charge
electric power electric energy transferred per unit time
electric resistivity material property related to its resistance
emitter electrode in a transistor where electrons originate
ensemble collection of time history records
epistemic caused by a lack of knowledge
ergodic ensemble-averaged values equal the corresponding average values computed over time from an arbitrary, single time history in the ensemble
even function function symmetric about the ordinate
event outcome
exhaustive space spanned by a set and its complement
expectation see expected value
expected value probabilistic average value
experiment act in which one physically intervenes with the process under investigation and records the results
explorational conducted to explore an idea or possible theory
extraneous variable that cannot be controlled
fallibilism process in which experiments are performed to test the validity of a conjecture
Fast Fourier Transform (FFT) method that recursively divides the sample points in one-half down to two-point samples before it performs the Fourier transform
finite bounded or limited in magnitude or in spatial or temporal extent
first central moment mean
first-order replication level level that considers the additional random error resulting from small uncontrolled factors
Fourier analysis procedure that identifies the Fourier amplitudes of a signal
Fourier coefficients coefficients in a Fourier series
Fourier series series represented by sines and cosines of different periods and amplitudes that are added together to form an infinite series
Fourier synthesis procedure that constructs a signal representation from a series of appropriately weighted sines and cosines
Fourier transform mathematical transformation of a signal that gives the signal’s amplitude versus frequency
Science
Fourier transform pairs pair of equations consisting of the Fourier transform and the inverse Fourier transform
fourth central moment see kurtosis
fractional uncertainty uncertainty in a result divided by the value of the result
frequency measure of a signal’s temporal variation
frequency distribution plot of the number of occurrences of a certain value divided by the total number of occurrences versus the value of the occurrence
frequency resolution the range of discrete frequencies divided by the number of discrete frequencies
fundamental dimensions length, mass, time, temperature, electrical current, amount of substance, and luminous intensity
Gaussian distribution see normal distribution
general uncertainty analysis simplified approach to uncertainty analysis that considers each measurand’s overall uncertainty and its propagation into the final result
high-pass filter filter that passes a signal’s amplitude above but not below a specific frequency
histogram literally means picture of cells; plot of the number of occurrences of a certain value versus the value of the occurrence
hysteresis difference in the indicated value obtained when approaching a particular input value in increasing versus decreasing directions
impedance electrical resistance of a circuit containing linear passive components (resistors, capacitors, and inductors)
impulse rapid change of a variable in time
independent not dependent upon another variable
inductivism process arriving at the laws and theories of nature based upon facts gained from experiments
infer estimate statistically
instrument error sum of an instrument’s elemental errors identified through calibration
intersection set of all members common to both sets
intrinsically linear variables variables in a higher-order equation that can be transformed to yield a linear expression
inverse Fourier transform inverse of the Fourier transform that gives the signal’s amplitude versus time
kurtosis fourth central moment normalized by the square of the variance
least significant digit rightmost nonzero digit
level of significance one minus the χ2 probability
linear device device in which the output amplitude is linearly proportional to its input amplitude
lognormal distribution continuous distribution of the logarithm of a normally distributed variable
loop closed path in a circuit going from one node back to itself without passing through any intermediate node more than once
low-pass filter filter that passes a signal’s amplitude below but not above a specific frequency
magnitude extent of dimension; size
magnitude ratio ratio of a dynamic system’s output amplitude to its input amplitude
measure see magnitude
measurand measured variable
measurement error true, unknown difference between measured value and true value
measurement uncertainty estimate of the error in a measurement
mode most frequently occurring value
modulus absolute value of a complex number
most significant digit leftmost nonzero digit
mutually exclusive two sets not sharing any common members
mutually orthogonal set in which each pair of functions is orthogonal
node point in a circuit where two or more elements meet
nondeterministic random
nonstationary not stationary (see stationary)
Science
normal continuous distribution caused by a very large number of small, uncontrollable factors that influence the outcome
normal equations equations resulting from the method of least squares
normalized z-variable a nondimensional variable indicating the number of standard deviations that a specific value deviates from the mean value
notch filter filter that passes a signal’s amplitude over a range of frequencies above and below a specified range
Nth-order replication level level at which more than one random error beyond that in the first-order replication level is considered
null method use of a Wheatstone bridge to determine an unknown resistance by having two of its other four resistances fixed and varying the fourth until the bridge is balanced
null set set of all occurrences in which a desired event is not the outcome
numerical equation equation containing only the measures of physical quantities
octave frequency ratio of 2:1
odd function function symmetric about the origin
order degree in a continuum of size or quantity
orthogonal property of two functions whose inner product is equal to zero over an interval
outcome result of a test
over-damped having a damping ratio greater than unity
overall uncertainty measure of the uncertainty in a variable; the product of the coverage factor and the combined standard uncertainty
parameter variable or function of variables that is fixed during an experiment
passive requiring no external power supply to produce a voltage or current output
pedagogical class of experiment designed to teach the novice or to demonstrate something that is already known
periodic repeating itself in time
permutations number of ways that a set can be arranged respective of its members’ order
phase lag lag of an output signal with respect to an input signal
Poisson distribution a continuous distribution describing rarely occurring events
pooled formed into one set from a set of replicated experiments each involving multiple measurements
population collection of all possible values of a random variable
potential difference difference between two electric potentials
power spectrum plot of a signal’s power versus frequency
precision variation of a variable’s values obtained by repeated measurements
precision error see random error
precision interval interval characterized by the product of a coverage factor and a random uncertainty
probability number of specific occurrences over the total number of occurrences
probability density function (pdf) function when integrated yields the probability
probability distribution function (PDF) integral of the probability density function; also known as the cumulative probability distribution function
ramp method method to perform electronically analog-to-digital conversion by increasing a voltage and comparing it to the analog input signal’s voltage
random having no particular order
random error error related to the scatter in the data obtained under fixed conditions; also known as the precision error
random uncertainty estimate of the random error
random variable variable whose value has no deterministic relation to any of its other values
range lower to upper limits of an instrument or test
reactance influence of a coil of wire upon an alternating current passing through it that impedes the current
readability closeness with which the scale of the instrument is read
Science
reduced-chi square variable χ2 variable normalized by the number of degrees of freedom
regression analysis process identifying the regression coefficients in the method of least squares
regression coefficients coefficients found in the method of least squares
relative accuracy accuracy divided by the true value
relative systematic uncertainty ratio of the reliability of the systematic uncertainty to the systematic uncertainty
reliability estimate of the accuracy of a systematic uncertainty
bf reluctance the ratio of magnetomotive force to magnetic flux
repeatability ability to achieve the same value upon repeated measurement
repetition repeated measurements made during the same test under the same operating conditions
replacement return of members to their set after selection, thereby allowing for their re-occurrence
replicates experiments identical to the original
replication duplication of an experiment under similar operating conditions
resistance defined by Ohm’s law as the ratio of voltage to current
resolution smallest physically indicated division that an instrument displays or is marked
result variable that is a function of one or more measurands
ringing frequency frequency at which a second-order system rings or continually oscillates
rise time time required for a first-order system to respond to 90 % of a step change
root mean square (rms) positive square root of the mean of the squares
round off truncate a number to its desired length
sample subset of the population
sample mean mean of a sample
sample variance variance of a sample
sample-to-sample measurand values are recorded for multiple samples
scattergram discrete representation of an analog signal
scientific method method of investigation involving observation and theory to test scientific hypotheses
second central moment the variance
sensor device that senses a physical stimulus and converts it into an impulse
sequential systematically increased
set group of all occurrences in which a desired event is the outcome
settling time time beyond which a second-order system’s response remains within ±10 % of its steady-state value
signal measurement system’s representation of the temporal variation of a measurand
signal conditioning preparing the signal in its final form to be processed optimally and then recorded
signal processing operating on a signal to obtain desired results
signal sample period time period used to determine the statistical properties of a signal
significant figures number of digits required to express a result
simple RC filter filter comprised of a resistor and a capacitor
skewness third central moment normalized by the cube of the standard deviation
source groups groups that help to categorize sources of error, which are typically grouped as calibration, data acquisition, and data reduction
standard known value usually used as a basis of calibration
standard deviation square root of the variance, which characterizes the width of the probability distribution
standard deviation of the means (SDOM) standard deviation of the mean values obtained from groups of repeated measurements
standard error of the fit error characterizing the differences between data and its curve fit
standardized normal variate nondimensional variable indicating the number of standard deviations that a variable deviates from its mean value
static steady in time
Science
static calibration calibration performed when the system is static
static sensitivity slope of a static calibration curve at a particular input value
stationary each of a signal’s ensemble-averaged statistical properties are time invariant
statistics branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
steady-state response the periodic part of a second-order system’s response
strongly stationary having all ensemble moments invariant with respect to the record’s time
successive approximation method method to perform analog-to-digital conversions electronically by subtracting the analog input signal from a digital-to-analog converter’s output signal
supplementary nondimensional units that do not represent a fundamental dimension
system of units system in which physical quantities can be expressed and related to one another through physical laws
systematic error error related to the difference between a measured and true value; sometimes called the bias error
systematic uncertainty estimate of the systematic error
third central moment see skewness
time history record plot of a signal’s amplitude versus time for a given period of time
time lag delay in time between a signal’s input and output through a device
timewise experiment in which measurand values are recorded sequentially in time
transducer device that changes an impulse into a desired quantity
transient response part of a second-order system’s response that decays in time
transient solutions homogeneous solutions to a differential equation that decay to zero in time
true mean value mean value of the population
true value error-free value of a variable
true variance variance of the population
uncertainty estimate of error in a variable
under-damped having a damping ratio less than unity
union set of all members of two sets that are in only one, only in the other, or in both
unit precisely specified quantity in terms of which the magnitudes of other quantities of the same kind can be stated
unit equation equation in which only units are used or defined
validational experiment conducted to validate a specific hypothesis
variables physical quantities involved in the process that can undergo change and thereby affect the process
variance statistical measure of the spread of values with respect to their mean
variational experiment quantifying the mathematical relationships between experimental variables
voltage divider a circuit consisting of a voltage source and two resistors in series to ground
waveform actual shape of a signal
weakly stationary having the ensemble mean and autocorrelation invariant with respect to the record’s time
Weibull distribution continuous distribution describing the time to failure of a physical system
Wheatstone bridge electrical circuit consisting of four resistors in a specific configuration and a voltage source
windowing mathematical method that reduces the magnitude of a signal’s record at its beginning and end
zeroth central moment integral of the probability density function; equals unity if the probability density function is normalized correctly
zeroth-order replication level level at which only measurement system errors are present
