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What is the objective of any measurement?
To answer a question to the level of detail required
Which device is more appropriate to measure a child’s temperature?
A thermometer
A typical measurement system is composed of:
A sensor stage, calibration, transducer stage, and output stage
What does a transducer do?
Converts sensed information (from a sensor) into a digital signal.
What are the three parts of a complete experimental test plan?
1. ) Parameter design plan, 2.) System and tolerance design plan, 3.) Data reduction design plan
Extraneous variables are those that:
Manifest in noise/interference, noise causes scatter and interference cause unwanted changes.
Randomizing the test matrix order:
Randomizes the extraneous variable and cuts the # of tests in half.
Repetitions:
Repeated measurements made during any single test run.
Replications:
An independent duplication of measurements using similar operating conditions but on a different day.
What is calibration?
Calibration applies a known input value to a measurement system to observe the system’s response.
Why are sinusoidal inputs typically used for dynamic calibrations?
They are easy to repeat
The measurement resolution defines:
The smallest increment in the measured value that can be detected
The accuracy of a measurement refers to:
Deviation of the reading from a known input
The following image describes what type of errors:
High systematic, low random
Uncertainty in a measurement is:
A numerical estimate of the possible range of the error in the measurement.
Hysteresis describes:
When an instrument exhibits a difference in readings based on if approached above/below
T/F: Concomitant methods produce two or more estimates for different results using different methods that can be used to check the accuracy of both methods.
True
T/F: A proper calibration uses a control process with an accuracy at least as good as the instrument being calibrated.
False
T/F: systematic error adds unknown, precision error causing scatter in test results.
False
T/F: four significant digits should be used in calculations.
True
What information do we need to reconstruct an original dynamic signal?
Amplitude, frequency, general waveform
Which of the following order model equations represent a 1st order system?
The first and last equations
Why are zero-order systems not the best model choice for most measurement systems?
Most real-world examples model time-dependent responses to dynamic input signals
What type of model is necessary to account for inertial characteristics of a system?
Second order system model
The rise time is the time required for a system to reach ______ of the response to a step input.
90%
Why is it better to record a system’s response from t = 0 to steady state in order to determine the time constant?
1.) Real systems deviate from first order, and the semilog plot shows the deviations
2.) Regression minimizes random error
Frequency response describes how:
The amplitude response and phase shift of the output signal varies with respect to the signal’s input frequency.
Frequency bandwidth is the band over which the magnitude ratio is:
-3dB ≤ M(w) ≤ 3dB
29. A second-order system’s output may oscillate at a ringing frequency for what condition:
If the system is underdamped
A second-order system’s time constant is defined as:
1/damping ratio*natural frequency
The time required for a system’s oscillations to resolve within 10% is its:
Settling time
A good compromise between too much output ringing and an acceptable settling time includes:
A damping ratio near 0.7
Distortion occurs when:
Some frequencies receive different amplitude and phase shifts than others
T/F: in zero-order systems, the output responds instantly to the input
True
T/F: A system’s time constant is the time required for the system to reach 90% response to a step input.
False
T/F: Both frequency response and phase shift for a first order system are frequency dependent
True
T/F: phase shift describes the attenuation of the amplitude as a function of frequency.
False
T/F: A second order system’s steady response is a function of the input frequency.
False
A waveform:
Is a graphical representation of how a signal varies with time.
A signal:
A physical quantity/variable that carries informatoon.
Discrete time signals:
Only contain information at discrete points in time, usually by sampling.
Quantization refers to:
Assigning a single number to represent a range of measurements (ex. clock displaying hours and minutes)
The process which produces a digital signal from an analog one is called:
Analog to digital conversion
Which type of signal contains only one frequency?
Simple periodic waveform
Which type of signal is nondeterministic?
Signals with no recognizable pattern
The method to determine the appropriate sines and cosines to represent a signal is called:
Fourier analysis
Musical pitch is represented by which frequency present in the audio signal?
Fundamental frequency
A harmonic is:
An integer multiple of fundamental frequency.
Fourier coefficients specify the ______________ of the sine and cosine components of a signal.
Amplitudes
The units of a power spectrum are:
The original signal’s units squared divided by frequency.
Frequency resolution of a Fourier transform is related to:
The total sample period
Resolution of an A/D converter specified in bits is:
Sometimes stated in SNR (signal to noise ratio) which relates the signal’s power through Ohm’s Law to power resolved through quantization.
How well discrete data represents the original analog signal depends on:
1.) Frequency content of analog signal
2.) Time between sampled points
3.) Total sample period
The sampling theorem states “to reconstruct the frequency content of a measured signal
accurately, the sample rate must be ___________ the highest frequency contained in the
measured signal.”
More than twice
If the sample rate is lower than the sampling theorem requires, higher frequency content can
show up as:
Alias frequency
To avoid alias frequency content, why shouldn’t we sample as fast as we can?
Sampling at a high rate increases the amount of data that needs to be processed.
In terms of sampling and digital Fourier transforms, what conditions are necessary to minimize spectral leakage?
Varying the sample period or spectral resolution
A 10bit A/D converter has how many different binary values as its resolution?
1024
When an analog input voltage falls between two adjacent levels of bit resolution, we incur what
type of error?
Quantization error
T/F: the mean value of an analog signal is called the AC offset
False
T/F: the rms value of an alternating signal typically has a bigger magnitude than its
average value
True
T/F: all signals can be approximated by a series of sine and cosine functions
True
T/F: a function g(t) is labeled even if g(t) = g(-t)
True
T/F: signal-to-noise ratio improves with lower resolution A/D converters
False
What information do we need to quantify a given set of data?
1.) A single variable that best characterizes the average
2.) A representative value that provides a measure of the variation of the set.
When assessing the quality of data, why do we typically focus on random errors and not
systematic errors?
Random error is present in every measurement, and all measured variables behave like random variables.
What items are necessary to produce a complete measurement statement for a true value?
x̄ - most probable estimate of x based on measured data
ux̄ - uncertainty interval of the estimate at some probability or confidence level (P%)
What condition allows a histogram to be interpreted as a probability density function?
As N (sample size) → ∞
Two standard deviations away from a mean value should cover how much of a normal
distribution?
95.45%
When working with finite data sets, we use what to quantify the uncertainty in prediction of a
next data point?
Confidence intervals and prediction intervals
Skew and kurtosis give us a way to understand when:
Something is affecting the measurand other than random errors.
Pooled statistics are helpful when:
Dealing with two or more populations with similar variances
The chi-squared distribution helps us:
Know how well the sample variance (s²ₓ) predicts the population variance (σ²)
_____________ establishes the functional relationships between inputs and outputs.
Regression
A correlation coefficient:
Measures how one variable changes in respect to another.
How can we determine if a data point is an outlier?
By Chauvenet’s criterion or the three sigma test
T/F: the idea of central tendency of a random variable represents the tending of a
measured probability distribution to a normal distribution
False
T/F: the standard normal variate distribution helps us determine a reliable estimate of the sample’s uncertainty.
True
