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Advancing Physics AS
Chapter 3.1 Signalling
Student Notes
August 2008
John Mascall
The King’s School, Ely
The entry below is taken from the 2008 OCR specification which combines the topics to be
taught in Chapters 1 and 3. References to imaging should be ignored at this stage.
PA 1.1: Imaging and signalling
In the context of the digital revolution in communication, this section introduces elementary ideas
about image formation and digital imaging, and about the storage and transmission of digital
information.
The material can be taught using up-to-date contexts such as mobile telephones, use of internet,
email, and medical scanning and scientific imaging including remote sensing. There are
opportunities to address human and social concerns, for example, the consequences of the growth
of worldwide digital communications.
Assessable learning outcomes
Candidates should demonstrate evidence of:
1. knowledge and understanding of phenomena, concepts and relationships by describing and
explaining:
(i) the formation of a real image by a thin converging lens, understood as the lens changing the
curvature of the incident wave-front;
(ii) the storage of images in a computer as an array of numbers that may be manipulated to enhance
the image (vary brightness and contrast, reduce noise, detect edges and use of false colour);
(candidates are not expected to carry out numerical manipulations in the examination; an
understanding of the nature of the processes will be sufficient);
(iii) digitising a signal (which may contain noise); advantages and disadvantages of digital signals;
(iv) the presence of a range of frequencies in a signal (its spectrum);
(v) evidence of the polarisation of electromagnetic waves;
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2. scientific communication and comprehension of the language and representations of physics, by
making appropriate use of the terms:
(i) pixel, bit, byte, focal length and power, magnification, resolution, sampling, spectrum, signal,
bandwidth, noise, polarisation, refractive index (understood as the ratio of speed of light in
vacuum to the speed of light in material of lens);
and by sketching and interpreting:
(ii) diagrams of the passage of light through a converging lens;
(iii) diagrams of wave-forms, and their spectra;
3. quantitative and mathematical skills, knowledge and understanding by making calculations and
estimates involving:
(i) the amount of information in an image = no. of pixels × bits per pixel;
(ii) power of a converging lens P = 1/f, as change of curvature of wave-fronts produced by the lens;
(iii) use of
1 = 1 + 1
v
u
f
(Cartesian convention; linear magnification
m = image height = v
object height u
restricted to thin converging lenses and real images.
(iv) ν = fλ
I
(v) amount of information, I, provides N = 2 alternatives; I = log N;
2
(vi) minimum rate of sampling ≥ 2 × maximum frequency of signal;
(vii) rate of transmission of digital information = samples per second × bits per sample;
(viii) maximum bits per sample, b, limited by the ratio of total voltage variation to noise voltage
variation: b = log2(Vtotal/Vnoise);
and by showing graphically:
(xi) digitisation of an analogue signal for a given number of levels of resolution.
A Revision Checklist for Chapter 3 can be found on the Advancing Physics
CD-ROM.
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Section 3.1 Digital revolution and the death of distance: digital signals; sampling;
digitising; bits
Learning outcomes
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The world has seen an explosive growth of signalling capacity.
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A signal channel has a capacity; a maximum rate at which it can transmit
information.
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Digital signals have the advantage that:
●
they can be regenerated easily, reducing the effects of noise
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they can readily be switched
●
they can be processed and encoded
●
they can represent different kinds of signal in a uniform way.
●
Analogue signals are made digital by sampling. The sampling must be done fast
enough to reproduce the highest important frequencies in the signal.
●
Samples can be digitised with different resolutions (e.g. 8 bit, 16 bit): N bits gives 2N
different levels of measured values.
●
Suitable coding can make digital transmission essentially error free.
The death of distance
Activity 10S Software based 'Data on the telecommunications explosion'
The worksheet on the Advancing Physics CD-ROM provides sets of data about increases
in telecommunications 1870–2000 to be used in data analysis exercises, presenting
appropriate graphs and conclusions. There is space in the Activities pack for notes you
may wish to write. Remember to store your own data and to print out your graphs.
Sampling and digitising
We start by showing what a digital signal looks like, using a hand-held television or video
controller to generate infrared pulses which are detected with a phototransistor.
Activity 20D Demonstration 'What do digital signals look like?'
We can show data (analogue in this case) being sent over an optical fibre link.
Activity 30D Demonstration 'Data transfer on an optical fibre'
If there is time it is worth looking at analogue to digital conversion and vice-versa.
Activity 80E Experiment 'Looking at signal conversion'
The diagram on the next page shows how ‘noise’ can be removed from digital signals
giving them a distinct advantage over analogue signals. If there is time it is worth looking
at Activity 60D Demonstration ‘Mains interference as noise’. Mains interference introduces
a low-intensity 50 Hz oscillation into many signals. This experiment uses a data logger and
a fast light meter to measure the light intensity from either a mains strip light or a filament
lamp running from an a.c. transformer.
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Digital signals have the advantage over analogue signals when noise is considered.
Display Material 50O
OHT 'Effect of noise on analogue and digital signals'
Signals and noise
analogue signal without noise
analogue signal plus noise
signal recovered from noise loses detail
Analogue signals are spoilt by noise
digital signal without noise
digital signal plus noise
signal accurately regenerated from noise
Digital signals resist effects of noise
To introduce the idea of sampling, a stroboscope is used to visually 'sample' the
movement of a vibrating string.
Activity 40D Demonstration 'Sampling vibrations on a string'
This is a convenient stage to discuss the presence of higher harmonics and the idea of a
frequency spectrum which can be sketched below.
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Display Material 10O
OHT 'Seeing sampling'
The top diagram shows a
sinusoidal oscillation.
The second diagram shows
comb-like gaps between
opaque strips. Imagine what
you would see if this were
to be overlaid on the
oscillation above.
Do the samples peeping
through the gaps suggest
the correct frequency for the
oscillation?
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Display Material 20O
OHT 'Signal sampling'
Sampling a signal
original signal
sampling pulses
0 or 1 from clock
sampled waveform
original waveform
reconstructed
from samples
The original signal can be exactly reconstructed if the sampling
is frequent enough
Some problems with sampling by drawing arbitrary waveforms, taking samples at agreed
intervals, and exchanging the sampled waveform with a partner, to see if the original can
be guessed or not.
Activity 50E Experiment 'Guess a waveform from a sample'
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Display Material 30O
OHT 'Problems with digital sampling'
Problems with sampling
Sampling too slowly misses high frequency detail in the original signal
Problems with sampling
Sampling too slowly creates spurious low frequencies (aliases)
Original signal
Original signal
Samples taken from
signal
Samples taken
from signal
Samples alone
Samples alone
Signal ‘reconstructed’
from samples
Signal ‘reconstructed’
from samples
Aliasing at the movies
Sampling too slowly misses high
frequency detail in the original signal
and can create spurious low
frequencies. The latter effect is known
as aliasing.
When a spinning arrow is illuminated
with a strobe light flashing with a
frequency that is just too low for a
stationary pattern to be obtained, the
arrow seems to rotate forwards slowly.
This is aliasing in that a low frequency
rotation is seen that is not really there!
Wheel turns not quite 1 circle per frame. Wheel seems to rotate slowly backwards
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For effective sampling:
sampling frequency > 2  maximum frequency present
This is known as Nyquist’s theorem. See p 61 of the student text.
High frequency detail in the original signal is missed if the sampling frequency is too low.
'Aliasing' (the production of spurious low frequency components) occurs by sampling a
high frequency too slowly. This is crucial to avoid in sound reproduction on CD.
Display Material 40O
OHT 'Digitising samples'
Digitising a signal
3-bit coding: an example
7 =111
nearest digital
value chosen
quantisation
error
6 =110
The greater the number of bits
the better the resolution.
sample
Note that CDs use 16-bit
coding so that there are 65536
levels.
5 =101
4 =100
3 =011
original
signal
2 =010
On music CDs it is necessary
to sample up to 20 kHz. Why
is this?
1 =001
0 =000
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binary values
001
100
101
110
111
110
100
011
CD uses
16-bit
coding
100
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digital stream of bits
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number of bits N
3
8
number of levels
8
256
2 =8
2 = 256
2N
3
8
16
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65536
16
2
= 65536
The greater the number of bits the better the resolution
Why is 44.1 kHz the standard sampling frequency used for CDs?
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Exercise
(a) Calculate the time interval between each sample used for a CD.
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(b) Calculate the rate of sending bits if each sample requires 16 bits.
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Now try some experiment to explore the effect of sampling less often:
Activity 70S Software based 'Looking less often'
You will need to run Activity 70S on the Advancing Physics CD-ROM. The notes for this
experiment are reproduced in the Activities pack.
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The student text compares the sending of a photo with the sending of an email. The rate of
transmission of bits per second is important when it comes to calculating how low each will
take to send.
Display Material 60O
OHT 'Sending a photo'
Sending a photo
01111000011110
Photo made of about
5 million pixels.
Convert pixels to stream
of bits.
Time to send a photo:
1 photo = 5 million pixels
1 pixel = 24 bit
broadband capacity = 10 million bits per second
5 million pixels × 24 bits per pixel
time to send a photo =
10 million bits per second
= 12 s
Run length compression:
Recode signal as runs of 1 or 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 11 1 1 11 0 0
2
of 1s
13
of 0s
8
of 1s
2
of 0s
Send these numbers instead.
Typical compression 9 : 1
A digital photo is made of millions of pixels, each coded for colour
and intensity by a num be r
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Display Material 70O
OHT 'Sending e-mail'
Sending an e-m ail
De ar s tud e nts ,
Thank you
I h o p e tha t yo u fi nd thi s te xt b oo k a s i n te re sti ng to re ad a s
I ha ve fou n d i l lu stra tin g it . A l o t o f tho u gh t an d de d ic ati o n
h as go n e i nto pro d u ci ng thi s , s o we al l ho p e a t IO P th a t
e ac h a n d e ve ryo n e o f yo u p a ss y o u Al ev el s . G oo d l u ck to
yo u al l .
84 104 97 110 107 32 121 114 117
T ha n k y ou
117 = 01110101
Computer and e-mail
package encode letters as
numbers using ASCII code.
Code numbers stored as
binary digits. One byte (8
bits) per character.
Time to send one page:
1 page = 500 words = 3000 characters approx.
= 3000 byte
= 24000 bit
broadband capacity = 10 million bits per second
24000 bits per page
10 million bits per second
= 0.0024 s
time to send one page =
More coding:
E-mail also sends data which check and correct errors.
Messages are often divided into small packets, each sent
by the best route available at the moment.
Packets have to be re-assembled into messages at the
receiving end.
An e-mail is a set of numbers coding for characters, and sent
as a series of 0s and 1s
The ASCII code uses bytes to represent 256 different symbols including the numerals 0 to
9 and the letters of the alphabet.
Why can 256 different symbols be represented by 1 byte?
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The CD system is discussed in the student text on page 60. More detail about the optical
system is given in Reading 40T ‘Text to read Optics of a CD player’. This assumes a
knowledge of wave superposition ideas that are met formally in Chapter 6. Sampling of
stereo sound is discussed on page 63.
Error-correction codes are used to ensure that the information is free of errors. Each part
of the information may be read more than once and the ‘copies’ checked for agreement.
It can be shown that a CD plays even with a hole drilled in it; this shows the advantages of
the error correction which is possible with digital systems.
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