Download Recording temperature – analogue signals

analogue signal
A signal that can take any value in a continuous range.
An example of an analogue signal is the temperature indicated by the height of the
mercury column of a standard thermometer. The height of the column can increase or
decrease by infinitesimal amounts. In principle the thermometer can indicate any
temperature within its operating range. The practical difficulty of reading small changes
does not affect the fact that the temperature indication is continuous within the
thermometer’s range.
It is useful to distinguish between analogue signals and digital signals, and between
continuous-time and discrete-time signals.
Recording temperature – analogue signals
(a) and (b) show different ways of recording the variation in temperature over a period of
a few hours. Each is an analogue representation.
In (a) the temperature variation is recorded as a continuous line; in this analogue
representation, both the recorded temperature and time vary continuously. The graph
could represent the voltage output from a temperature sensor – in this case, it would be
an ‘electrical analogue’ of the temperature.
Graph (b) is a ‘sampled’ or ‘discrete-time’ version of (a). The temperature is measured
only at discrete time intervals, known as the sampling instants (every hour in the
example shown). It is still an analogue signal, however, since the samples are (in
principle) exact analogues of the temperature at the sampling instants.
Digital versions of (a) and (b) are shown by (c) and (d) respectively.
Recording temperature – digital signals
In (c) the temperature value is continuously quantized (rounded up or down) to the
nearest degree. The display of a digital room thermometer can be thought of as this type
of signal, since in effect the display changes whenever the temperature changes
sufficiently.
The representation in (d) is both digital and discrete-time; the temperature is sampled
hourly and rounded to the nearest degree. In practice, a sampled, digital value is usually
held constant until the next sampling instant. This is represented by the dashed line in
(d) above. Because of this, there are two common ways of representing this type of
signal – as a sequence of samples, or as a ‘staircase’ waveform.
In most practical situations, analogue signals are continuous-time signals such as in (a),
and digital signals are discrete-time signals such as (d).
The key features of such an analogue signal are:
1.
2.
it can take any value within a range, and
it can change continuously with time.
The key features of such a digital signal are:
1.
2.
it is restricted to a finite set of values within a range, and
it is allowed to change only at fixed, regular intervals.
The distinction between analogue and digital signals is important for signal transmission.
The example of recording temperature given above might be transmitted in either
analogue or digital form. The record of (a) might be transmitted as an electrical voltage
directly proportional to the measured temperature – that is, as an analogue voltage.
Alternatively, a sampled, digital version like that shown in (d) might be transmitted as a
sequence of numerical values. To do this, the sample values might typically be encoded
in binary form and then transmitted as electrical voltage pulses along a cable, or as light
pulses in an optical fibre.
Whether the digital values of (d) are coded as binary values depends on the transmission
system in use. Although binary is often used, it is not the only possibility for representing
digital signals.
Activity
Car speeds are usually indicated on a speedometer by the position of a pivoted needle.
On older cars, the needle actually indicates the size of an electric current generated by
the dynamo effect. The faster the wheels turn, the larger the current. Which of the
following describes such a method of indicating speed? Think how you would justify your
answer.
(a) Analogue, continuous in time.
(b) Sampled analogue, discrete time.
(c) Digital, continuous in time.
(d) Sampled digital, discrete time.
Answer
The speedometer is analogue, because the needle can lie anywhere within a continuous
range of possible positions. Therefore the speed it indicates lies anywhere within a
continuous range of possible speeds.
The speedometer is continuous in time. That is, there is never a moment when the
needle is not indicating the car’s current speed.
Hence the answer is (a), analogue, continuous in time.
Activity
A car speedometer has a calibrated dial behind the needle, marked with speeds 0, 5, 10,
15, etc. If the passenger chooses to interpret the number nearest to the needle-tip as the
current speed, what sort of device is the speedometer effectively? How would you justify
your answer?
(a) Analogue, continuous in time.
(b) Sampled analogue, discrete time.
(c) Digital, continuous in time.
(d) Sampled digital, discrete time.
Answer
Because the passenger chooses to interpret the number nearest to the needle-tip as the
current speed, the speedometer is effectively digital. That is, the speedometer effectively
indicates speeds from a discontinuous range of possibilities: 0, 5, 10, 15, etc.
However, the speedometer is still continuous in time. That is, there is never a moment
when the needle is not indicating the current speed.
Hence the answer is (c), digital, continuous in time.
Activity
Imagine that owing to an electrical fault, the car speedometer works only intermittently
and momentarily. The needle climbs to its correct position, and then immediately drops
back. It does this repeatedly.
During the moments when the speedometer works, the driver takes the needle’s position
just before it drops back to be the speed. The passenger, however, takes the nearest
number on the dial to be the speed.
For each person (driver and passenger), say whether the device is:
(a) Analogue, continuous in time.
(b) Sampled analogue, discrete time.
(c) Digital, continuous in time.
(d) Sampled digital, discrete time.
Answer
Owing to the intermittent fault, the speedometer does not continuously indicate speed.
Hence it is not continuous in time. The speedometer is a discrete-time device. That is, the
speed indication is a succession of samples. So options (a) and (c), which are both
continuous-time options, are eliminated.
For the driver, the position of the needle indicates the speed, and may be anywhere
within a continuous range of possibilities. So the indication of speed is analogue, and
hence (b) is the answer: sampled analogue, discrete time.
For the passenger, the speed has a value taken from a discontinuous range of
possibilities: 0, 5, 10, 15, etc. So the indication of speed is effectively digital, and
sampled digital owing to the intermittent (or discrete time) functioning of the meter.
Hence (d) is the answer: sampled digital, discrete time.
digital signal
A signal that can only take values which are in a set of discrete values, and which cannot
take an intermediate value.
An example of the use of digital signals is the tone dialling used on modern telephones. A
small set of discrete tones is used in this system. The tones are used to signal the digits
have been dialled to the exchange. Each button pressed on the telephone can be
identified at the exchange by its characteristic tone.
As this example shows, the value of a digital signal is not necessarily restricted to just
two, binary values. Digital signals therefore are not necessarily binary signals, although
the values of a digital signal may be coded by strings of binary digits.
sound digitization
The process of digital representation of sound, conventionally in terms of binary codes for
storage and processing by computer, or for transmission over computer networks.
In order to digitize sound, sampling is used. This consists of breaking the sound into
equal-duration segments and assigning some numerical characteristic to each segment.
sound: sampling, resolution and quantization
The figure below shows an electrical analogue waveform corresponding to the words
‘flowers, trees and weeds’.
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Waveform of 'flowers, trees and weeds'
The waveform of the word ‘trees’ is shown in greater detail below.
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Waveform of 'trees'
The ‘ee’ part is clearly an almost regular waveform. The ‘tr’ and ‘s’ sounds are less
recognizably wave-like because they contain a lot of high frequency sound. But at
sufficiently high magnification these too would be discernibly wave-like.
To digitize this sound, the analogue waveform is sampled – that is, it is measured at
successive instants in time. This is equivalent to reading the height of the waveform at
successive instants, as shown in below (where the timescale is much expanded).
Digitization of a waveform by sampling the amplitude at successive instants in
time
The graph above shows that the sample sizes are converted to, in this case, 8-bit two’s
complement numbers. (Two’s complement is a way of using binary numbers to represent
positive and negative values.)
The use of eight bits in this case determines the number of different sample sizes that
can be represented in binary form. There are 28 of them, or 256, to cover the range from
the largest sample size to the smallest (that is, the most negative). In a case like this, we
speak of the digital conversion as having a resolution of 8 bits.
In practice, a voltage range of 256 volts for an analogue signal is unrealistically wide. A
more realistic range might be, say, 10 volts, from +5 volts to –5 volts. In an analogueto-digital conversion using a resolution of 8 bits, the value +5 volts would be allocated
the largest 8-bit number, and –5 volts to the smallest. All intermediate values would be
scaled appropriately, giving 256 numbers to cover the range from +5 volts to –5 volts.
The more numbers, or levels, used to cover a given voltage range, the more closely
packed the levels become, and so the smaller the interval between adjacent levels. The
quantization interval is the size of the interval between adjacent levels. It can be defined
as the input range divided by the number of levels available.
Activity
What is the quantization interval of an 8-bit converter covering the range from +5 volts
to –5 volts?
Answer
The range is 10 volts, and the number of levels is 256, so the quantization interval is
10/256 volts, or 0.039 volts.
Activity
A converter with 4-bit resolution is used to cover an input range from +2.5 volts to –2.5
volts. What is the quantization interval? Hence find the peak quantization noise.
Answer
A resolution of 4 bits means 24 levels, or 16. The input range is 5 volts. The quantization
interval is therefore 5/16 volts, or 0.3125 volts.
The peak quantization noise is half of this, or approximately 0.16 volts.