Data Acquisition Flashcards
Data acquisition
refers to the gathering of data relating to signals, processes or experiments which provide info on real-world physical events.
Usually implied that this data can be manipulated by computers to obtain some key information about the
events.
data conversion
refers to the conversion of data from continuous analogue form to discrete digital form or vice-versa.
usually an intrinsic part of the Data Acquisition process + results in data being stored in binary coded form in some medium.
analogue signal
a signal which is a continuous function of some variable.
Very often the independent variable is time so signal is observed as a function of time.
essential feature is that signal may have any of an infinite number of values within its range + in theory has
infinite resolution.
digital signal
a signal which is quantised + can only have a limited
number of values within a given range.
- normally thought of as being in numerical format + often in binary coded form.
- essential feature is that the signal may have only one of a finite number of values within a range.
noise
a random signal, the value of which cannot be
predicted with absolute certainty at any point in time and which does not normally contain useful information.
-an intrinsic part of nature + normally appears superimposed on useful signals which we want to
measure to get info.
characterising noise
-can only be characterised in statistical terms of probability.
time on a digital clock
Time can only have a value that is an exact number of minutes. Values in between are not accounted for. This
means that the time is only exactly correct at 1,440 instants in the day.
atomic energy levels
Electrons in atoms such as Silicon can
only have energies at specific values,
i.e. their energy levels are quantised.
height on a ladder
The occupant can only stand at heights where there are rungs on the ladder.
Height is quantised.
digital signals as functions of time
The signal may take on one of the finite number of quantised values, which may change with time in an irregular or regular manner
binary digital signals
a signal which may only have one of two values or states.
In modern digital systems the states are normally represented as HI and LO in logic terms, as 0 Volts and E Volts in electrical terms or as ‘0’ or ‘1’ values in binary arithmetic
no noise present
if no noise is present, the value of the signal at any time can be ascertained and stipulated to any degree of precision required.
error
overall degree of incorrectness in establishing or
measuring value of a signal, process or event.
accuracy
measure of the extremes of the overall error associated with a measurement.
-an indication of limits of confidence we can have in measurements we make.
resolution
measure of the smallest interval with which the event or signal of interest is specified.
In a digital or numerical readout this corresponds to the least significant digit (LSD) + specified in the units in which measurement is made.
resolution and accuracy of measurement
normally resolution is equal to or less than accuracy of the measurement
where measurement errors arise
- electrical interference
- electronic semiconductor noise
- non-linearity of transducers
- manufacturing tolerances
- inaccuracies of instrumentation.
there is also human error but this not what is being
considered here.
positional number system properties
radix
digits
positional weighting
radix
- base/foundation of system
- number of individual numerical symbols/characters present in the system
digits
-Digits of a number system are the individual numerical symbols or characters which make up the system
what does latix mean
Latin meaning ‘root’
binary and decimal system radix
- ten symbols in decimal system, so radix of 10
- 2 symbols on binary system so radix of 2
what does digit mean
Latin meaning ‘finger’
what Bit stands for
‘Binary Digit’
positional weighting
-Positional Number System: several digits combined to form a number which has a value. Each digit in the complete set may be utilised in each position.
-a different weight applies to each position
+ therefore value of the same digit in a diff position is diff
positional weighting in decimal and binary number systems (positioning)
weight is assigned positionally from right to left, in ascending order of exponent powers of the radix.
-significance of the digit increases from
right to left as an increasing power of the radix.
-digits also have an assigned order of increment, with the increments between successive digits being of equal value.
what each weighted position is referred to
referred to as a Decade
Least Significant Digit LSD
the digit in the right hand most position
Most Significant Digit MSD
that in the left hand most position
the Bit
-used to refer to either the digits ‘0’ and ‘1’ as the characters of the Binary number system or to the weighted positions or Binates of a Binary number
counting decimal with binary
When the highest digit is reached in this position, it returns to the lowest digit and the digit in the next position to the left is incremented. This repeated cycling can continue indefinitely,
numerical value - converting decimal to decimal?
- determined by adding up weighted values of all digits in the number
- done by multiplying the digit at each position by the value of the radix raised to the power of the exponent of the radix at the position in question, then summing values of all digits
decimal value –> binary power
for 1, 2, 4, 8, 16
1: 2⁰
2: 2¹
4: 2²
8: 2³
16: 2⁴
binary to decimal conversion
-same procedure except positional weightings applie with be those of a radix 2 system
decimal to binary conversion
- decimal number is converted to binary form by continuously dividing it by the Binary radix 2 and saving the remainder
- identifies powers of the radix which are contained in the number
- remainder of each division operation determines values of the bit in one weighted position at a time
- process continued until nothing remains to be divided into
- process yields value of digits of number in Binary form but in reverse order, so result of process must be read backwards to get the exact Binary number
-check pdf 2 to see graph of how to do it
purpose of data conversion
to convery data acquired in a measurement/recording from analogue form into digital form to exploit the benefits of Binary coding
benefits of data conversion
-noise immunity
coded values can then be either
-stored for future retrieval
or
-subjected to further digital processing or transmitted to another location for use there
how to overcome effects of noise
-if instead of transmitting the analogue signal, you transmit digital pulses
2 ways to encode
1: take samples of analogue signal at regular intervals + convert into Binary form (most common form of analogue-to-digital data conversion)
2: encode each of the digits in Decimal number system into its equivalent Binary form, known as Binary Coded Decimal)
Binary Coded Decimal
- each digit of a decimal value can be coded as a 4-bit binary number
- Decimal value can be transmitted as a sequence of digital pulses
identifying decimal points for encoding
a convention can be used to identify the decimal point
effects of noise
- when nose superimposed on a signal of interest it introduces degree of uncertainty into the value of the signal at any point in time
- accuracy + therefore resolution with which we can measure the signal are limited in the first place
quantisation process
- process is one of imposing a finite degree of resolution on the range of a signal
- range is divided into a number of defined levels equally spaced throughout range covered by the signal
- actual values in between quanta are rounded to nearest quantum value
quantisation graphs
check pdf 3 for better visual understanding of quantisation
quantisation and error
-process introduces an error into the resulting quantised signal when compared with the original input signal
what this quantisation error depends on
depends directly on number of quantisation levels used
quantisation levels and degree of resolution
-no point in having a number of quantisation levels in the process which provides higher degree of resolution than the noise which is present allows
quantisation error
-difference between quantised staircase-like waveform and original sine wave
peak amplitude of quantisation error
dependent on number of quantisation levels used
the smaller the quantisation level
the lower will be the quantisation error
however, the lower the quantisation level, the greater will be the no. of levels needed to quantise a given full-scale voltage range
full scale, fractional error, ± part in
eg.
± % of full scale: 10%
fractional error ± Δ FS: 0.1
± part in (1/Δ): 10
± 1 part in (1/Δ): 1x10¹
Fourier’s Series (theory)
states that any periodic signal can be represented as a summation of sinusoidal components at the fundamental frequency of repetition of the signal and multiples or harmonics of this frequency
baseband spectrum
spectrum shown as a continuous shaded spectrum, up to the maximum frequency of interest
bandlimiting
-in ADC conversion the highest freq present in baseband spectrum is deliberately limited to a maximum value, fₘ
why bandlimiting
-so highest freq present can be guaranteed not to exceed a specified max limit
Sampling Theorem
all of the info present in a bandlimited, time-varying signal is contained within samples of the signal taken at regular intervals in time at a rate which is greater than or equal to twice the highest frequency component contained within the spectrum of the signal
aliasing distortion
If signal sampled at a rate less than Nyquist rate (fs<2fm), results in overlap of image spectra. This results in distortio of the recovered signal so that time profile of recovered signal is different from the original input signal which was digitised
the more the Nyquist sampling rate is infringed
the speech in a voice sample gets more distorted
operations in ADC conversion
- input analogue signal must be bandlimited
- then it must be sampled
- samples must be quantised
- encoded into Binary form
what sampling operation is normally carried out by
a Sample-and-Hold amplifier
Modes of sample and hold amplifier
sample
hold
hold mode
output of sample-and-hold amplifier stays fixed at the previous sample value
data conversion rate
speed with which input analogue signal can be continuously sampled and converted into digital form
(specified in Samples Per Second or Hz)
Kirchhoff’s Current Law
sum of currents at a node is zero
node
any point in a circuit at the same potential which can therefore include several connections to the same electrical point but at different physical locations
if b = 0
switch is OPEN, no current flows in that branch
if b = 1
switch is CLOSED, a current equal to value of the associated current source flows in that branch
