This document discusses systems and complexity from multiple perspectives. It begins by exploring definitions of systems and noting their complexity can range from simple to complicated to complex. Complex systems are characterized as having emergent behaviors that are unpredictable and non-linear. The document then examines trends toward greater complexity in both natural and designed systems. It emphasizes that simple solutions are inadequate for complex problems and notes the biggest challenge is many do not comprehend the shift from a linear to non-linear world.
1. A p p l i e d S c i e n c e
E n g i n e e r i n g S o l u t i o n s N o M a t t e r W h a t !
S Y S T E M S
P r o f P e t e r C o c h r a n e O B E D S c
w w w. p e t e r c o c h r a n e . c o m
2. "Simple can be harder than complex. You have to work
hard to get your thinking clean to make it simple"
Steve Jobs
"Global terrorism is extreme both in its lack of realistic
goals and in its cynical exploitation of the vulnerability
of complex systems"
Jurgen Habermas
"Today the network of relationships linking our species
to the biosphere is so complex that all aspects a
ff
ect all
others to an extraordinary degree. We should be
studying the whole system, because no gluing together
of partial studies of a complex nonlinear system can
give a good idea of the behaviour of the whole"
Murray Gell-Mann
COMPLEXITY
O u r b i g g e s t c h a l l e n g e
C l o s e 2 N D
M u l t i d i s c i p l i n a r y
P r o b l e m s S t o c h a s t i c /
3. "Simple can be harder than complex. You have to work
hard to get your thinking clean to make it simple"
Steve Jobs
"Global terrorism is extreme both in its lack of realistic
goals and in its cynical exploitation of the vulnerability
of complex systems"
Jurgen Habermas
"Today the network of relationships linking our species
to the biosphere is so complex that all aspects a
ff
ect all
others to an extraordinary degree. We should be
studying the whole system, because no gluing together
of partial studies of a complex nonlinear system can
give a good idea of the behaviour of the whole"
Murray Gell-Mann
COMPLEXITY
O u r b i g g e s t c h a l l e n g e
C l o s e 2 N D
M u l t i d i s c i p l i n a r y
P r o b l e m s S t o c h a s t i c /
4. âSystemâ Definition
Can we describe exactly what we mean ?
âThis singularly simple question directs us to an
ongoing (endless) philosophical debate that is
less than helpful for engineers and scientistsâ
We need something both meaningful and
concise that affords us sufficient licence
to assist our understanding in designing
and building machines and networks
that invoke positive advantage and
progress at minimal risk employing
progressively less energy & material
5. âA group of interacting, interrelated, or interdependent
elements forming a complex wholeâ
The most concise de
fi
nition I can
fi
nd but not entirely satisfactory
for any engineering purposesâŚ
literature
Thousands of publications
* The whole may be simple, complicated or complex, and there
may or may not be any interdependence !
6. Functionally related groups of elements, especially:
- Human body regarded as a functional physiological unit
- Organisms as a whole, especially with regard to vital processes/functions
- Groups of physiologically or anatomically complementary organs or parts
- Interacting mechanical or electrical components dispersed or local
- Networks and channels, for communication, travel, or distribution
- Interrelated computer software, hardware, and data transmission devices
Correct(ish) but inconcise, incomplete, and also unsuitable:
literature
Thousands of discourses
7. An organised set of interrelated ideas or principles
- Social, economic, or political organisational forms
- Naturally occurring groups of objects or phenomena: the solar system.
- Objects or phenomena grouped together for classi
fi
cation or analysis
- Condition of harmonious, orderly interaction
- Organised and coordinated method; ie procedures
literature
Thousands of discourses
Correct(ish) but inconcise, incomplete, and also unsuitable:
8. âSystems take energy, matter, information, and transforms their
natureâ
* Ergo: All Systems are Entropic
Not Published
My tight/sufficient (?) definition
9. A W I D E R L E N S
Only art, science, and engineering
Divisions: Mathematics, Physics Chemistry, Biology, Art are all artificial silos,
and so are Electrical, Mechanical, Software, Chemical, Civil Engineering et al
introduced sometime after the reformation; and whilst they accelerated our
progress & understanding they now sees widespread limited thinking and a
lack of mutual understanding that is often disadvantageous
Galileo
Galilei
Michael
Angelo
Leonardo
da Vinci
11. Taking an interest in every system known to mankind pays dividends in
providing us with insights and challenging concepts and occasionally , really
useful results...
âŚwe no longer design, deploy and operate our systems in isolation...we live
in a world of the natural and unnatural, the evolved, designed, and
designoid âŚthat in general are connected to interact
...the way they connect coexist and interact is important especially when life
dependency and mission critical issues are at stake !
An essential PRACTICE
For completeness of enquiry we need a better radar
12. Systems are never stronger than their weakest element
Systems are never simpler than their most complex element
Systems are always more complex than their most complex elements
G E N E R A L A X I O M S
For individual & connected/networked systems
13. ⢠Complex systems never get easier to characterise
⢠Complex systems always make the simple more complex
⢠Complex systems are never rendered simpler - without incurring costs !
⢠Simple systems tend toward being rendered more complex !
⢠Simple systems tend to get more di
ffi
cult to characterise
⢠Simple systems donât make the complex simpler
⢠There are no simple solutions to complex problems
⢠There is a huge di
ff
erence between complicated and complex systems
G E N E R A L A X I O M S
For individual & connected/networked systems
14. ⢠Simple systems tend to migrate toward complication
⢠Complicated systems tend to migrate toward complexity
⢠Complex systems can comprise simple and/or complicated elements
⢠Entropy always follows the direction (1, 2, 3) and never the reverse
⢠The converse of the construct (1, 2, 3) seldom occurs - if ever !
⢠Cluster of simple/complicated systems can become complex a whole
Our lack of understanding never deterred us from exploiting anything, but
we have often witnessed some pretty big mistakes/fails in the process!
G E N E R A L A X I O M S
For individual & connected/networked systems
15. Mother Natures propensity for Simple Systems resulting in Complex Outcomes
WHAT WE generally observe
A natural & designed world complexity - simplicity inversion
16. Humans propensity for Complex Systems resulting in Simple Outcomes
WHAT WE generally observe
A natural & designed world complexity - simplicity inversion
18. V I S I B L E T R E N D S
Irreversible progression to complexity
DESIGNED EVOLVED
Well behaved Out of control
Well Understood Knowledge Gap
TOOLS MODELS
Physical Laws Emulation
Low Combinatorics
Certainty the Norm
High Predictability
High Combinatorics
Uncertainty the Norm
Emergent Behaviour
Mathematics Simulations
Plasma
Biology
Physics
Weather
Universe
Genetics
Ecologies
Chemistry
Proteomics
Combustion
Earthquakes
Global Warming
Immune Systems
Quantum Mechanics
National Security
Search Engines
Globalisation
Management
Mobile Nets
Leadership
Intelligence
Economics
Nano-Tech
Bio-Tech
Con
fl
ict
M&A
COMPLEX
Telephone
Car Engine
Jet Turbine
MRI Scanner
Rocket Motor
Air Conditioner
Server Farm
Computer
Lap-top
Tablet
Radio
TV
COMPLICATED
Long Bow
Catapult
Pulley
Canal
Mill
SIMPLE
Drill
Lathe
Bicycle
Ratchet
19. g e n e r a l i t i e s
Sureties, actualities, challenges
Digital
Analogue
Hybrid Analogue//Digital
Our knowledge base
Our understanding
Made by mankind
Made by machine
Our species survival
Our planets survival
Machine intelligence
Symbiosis necessary
Challenges to be addressed
dominant
remains a vital core
ubiquitous & growing
advancing and accelerating
limited by our technologies
insu
ffi
cient for our populous survival
vital to our survival and prosperity
depends upon good systems *****
depends upon good stewardship/tech
overtaking us in many areas
man-machine partnership underway *****
formidable but interesting and vital *****
20. BEWARE
Not so obvious exceptions
Quantum Computing is essentially analogue
AI is migrating toward a mix of analogue and digital
Modern radio systems are a mix of analogue and digital
Optical
fi
bre systems are a mix of analogue and digital
Robots are a mix of analogue and digital
Sensors are a mix of analogue and digital
VR and AR a mix of analogue and digital
21. Generalities
All systems share similar models
mathematical/analysis frameworks
Electrical, Electronic, Mechanical, Civil Engineering & Physics share the same
or very similar equations setsâŚâknow one and you know the otherâ
22. Differences: Chemistry, Biology, Sociology,
Information/Computing Networks Systems
tend to be observed through a different
lens but still share many similarities
Generalities
All systems share similar models
mathematical/analysis frameworks
23. âSIMPLEstâ SYSTEMS
Lie within the grasp of one human mind & hands Designed top down
Always predictable
Easy to specify
Easy to design
Easy to model
Easy to realise
Easy to control
Easy to operate
Do not evolve
Do not adapt
Unchanging
Stable/well behaved
Essentially Linear
Laws of physics apply
Mathematics works
Linear behaviour
Predictable
Conceived, designed and produced by one human
24. S I M P L E S Y S T E M S
Within the span of âaâ human mind or team Designed top down
Always predictable
Easy to specify
Easy to design
Easy to model
Easy to realise
Easy to control
Easy to operate
Do not evolve
Do not adapt
Unchanging
Stable/well behaved
Essentially Linear
Laws of physics apply
Mathematics works
Linear behaviour
Predictable
25. Di
ffi
cult to understand
Designed top down
Di
ffi
cult to specify
Di
ffi
cult to design
Hard to model
Hard to realise
Hard to control
Hard to operate
Seldom non-linear
Generally predictable
Do not evolve - stable
Stable/well behaved
Essentially Linear
Laws of physics apply
Maths âmostlyâ works(ish)
Unnatural materials required
Computer modelling a necessity
Complicated SYSTEMS
A deep understanding beyond the grasp of âaâ human
28. C O M P L E x
The concatenation of large numbers
of simple and/or complicated sub-
systems can lead to unpredicted
non-linearities and thus surprises -
unexpected emergent behaviours
due to the whole becoming complex
32. Initial/intuitive top down design
Evolution rapidly dominates
Modelling a major challenge
Accurate speci
fi
cation hard
Fundamentally stochastic
Design; a tough challenge
Realisation is easy/hard
Operation is easy/hard
Control is easy/hard
Non-linear/chaotic
Complex SYSTEMS
Beyond human wisdoms & mental abilities
Dominated by many non-linear elements
âEstablished wisdoms do not apply
Mathematics non-contributor
Emergent behaviours/rule
No general lawsâ
âNOTE: These are âgeneralised comments
and there are always opportunities for
exceptionsâ
33. Machine DESIGNED
We have entered a realm where we have no clue!
AI + AL derived AL evolution
Impossible (?) to understand
Seeded from the bottom up
Accurate spec impossible
Outcome unpredictable
Beyond (?) modelling
Very easy to realise
No human control
Autonomous code
âAlwaysâ non-linear
Only modest compute power
Good network connectivity
Maths nears irrelevancy
Now âbreedingâ malware
35. Output
Input
Linear : NON-LINEAR
Confusing and often confused
These are all non-linear
responses as they give
wildly di
ff
erent outputs
for the same input every
time
These are all linear
responses in that an
input gives the same
output every time
Established wisdoms do not apply
Mathematics non-contributor
Emergent behaviours rule
No general laws
36. THESE DAYS HAVE Long GONE
We a r e n o w m o s t d e f i n i t e l y i n a m a c h i n e a g e
a n d e r a d i c a t i n g p e o p l e f r o m t h e c o n t r o l l o o p
i s a n u r g e n t n e c e s s i t y
37. In a simple
disconnected
world... ...we can
address
problems
in isolation
...and simple
solutions
mostly work
In a complex
connected
world...
...we have
to consider
the whole
...simple
solutions
never work
AI
...modelling,
simulation,
decision
support
...BIG
DATA
...everything
online, and
networked
...a living
organism...
R E A L I T Y
Simple is now a rarity
AL
âŚevolved
designoid
solutions
38. BIGGEST WORRY
The majority do not comprehend
Simple linear and
a well behaved arena:
intuition, experience, &
wisdoms mostly worked
well and were adequate
across the most societies
A universe characterised by a
limited range of relationships,
concepts and equations that
were readily understood
Non-linear, complex and
highly unpredictable arena:
intuition, experience, wisdoms
are mostly unreliable at best &
highly dangerous at worse
A universe characterised by
a wide range of immature and
developing concepts/computer
models not readily understood
by lay people, politicians, +++
PAST TO DAY
FUTURE
âEconomics & market forces are failing
Ignorance and bigotry on the rise
Politics & democracy is in perilâ
41. Fourier + Laplace - time and frequency
g(t)
f(t)âg(t)
f(t)
F(Ď)
G(Ď)
F(Ď).G(Ď)
Simple Multiplication
Complicated Convolution
Laplace forces integrals to converge - best used on transients signals
Fourier can see integrals to diverge - best used on repetitive signals
BASIC SYSTEM
Nomenclature - Methodology
Frequency
Domain
Descriptor
Time
Domain
Descriptor
This is the original analogue version we
have now rendered discrete and digital -
Digital Fourier/Laplace Transform
46. ENVIRONMENT?
s(t) h(t) o(t)
Other systems of the same or differing type may be sharing the same
space or some part of it, and therefore there can be many obvious and
hidden opportunities for aliasing....
Air
Water
Earth
Machines
Lifeforms
Fluids
Solids
Chemicals
Radiation
Information
Chemical
Physical
Information/Data Processing
Mathematical
Natural
Unnatural
Biological
Electrical
Electronic
Mechanical
Computational
Optical
Acoustic
Organic
Inorganic
Life forms
+++
47. Whatâs in THE BOX ?
What are the limits to what we describe and de
fi
ne
s(t) h(t) o(t)
What can we describe and de
fi
ne
Optical
Acoustic
+++
+++
Life forms
o(t) = h[s(t)] = h(s) for ease of notation
o = a + bt + ct2 + dt3 et4 + ft5 is the largest polynomial we
can solve for very limited and
narrow range of cases
In the absence of a closed form solution we often reduced to using polynomial or some
other form of approximate descriptor
48. AND the output ?
s(t) h(t) o(t)
In the general case it impacts/changes the
environment and the input and is often a
grossly non-linear series of loops
e(t)
f(t)
51. General SYSTEM traits
s(t) h(t) o(t)
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
Simple
Singular
Linear
Complicated
/Complex
Multi - I/O
Linear
Non-Linear
In general can be
fully tested and
characterised
In general cannot
be fully tested
and characterised
52. All known, understood, well described and
characterised, bounded, and well behaved
with causality preserved
Contained/bounded in/by some
known, or well de
fi
ned,
environment/conditions
Simple System - Key Features 1
s(t) h(t) o(t)
s(t) = Stimulus
h(t) = Operator
o(t) = Output }
s(t) and o(t) originate
and terminate within the
environment
53. Response matches need
Symbiotic with the environment
Predictable, reliable, with a fast recovery time
Upgrades and changes not traumatic or risky
Shocks are not terminal or unduly debilitating
Reproducible, easy to deploy and maintain/repair/replace
Simple System - Key Features II
s(t) h(t) o(t)
54. Response matches need
Symbiotic with the environment
Predictable, reliable, with a fast recovery time
Upgrades and changes not traumatic or risky
Shocks are not terminal or unduly debilitating
Reproducible, easy to deploy and maintain/repair/replace
Simple System - Key Features II
s(t) h(t) o(t)
Sometimes we cannot satisfy this wish list 100%
55. All known, understood, well described and
characterised, bounded, and well behaved
with causality preserved
Contained/bounded in/by some
known, or well de
fi
ned,
environment/conditions
Complicated/Complex - Features I
s(t) = Stimulus
h(t) = Operator
o(t) = Output }
s(t) and o(t) originate
and terminate within the
environment
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
56. All known, understood, well described and
characterised, bounded, and well behaved
with causality preserved
Contained/bounded in/by some
known, or well de
fi
ned,
environment/conditions
Complicated/Complex - Features I
s(t) = Stimulus
h(t) = Operator
o(t) = Output }
s(t) and o(t) originate
and terminate within the
environment
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
X
57. All known, understood, well described and
characterised, bounded, and well behaved
with causality preserved
Contained/bounded in/by some
known, or well de
fi
ned,
environment/conditions
Complicated/Complex - Features I
s(t) = Stimulus
h(t) = Operator
o(t) = Output }
s(t) and o(t) originate
and terminate within the
environment
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
X X
58. All known, understood, well described and
characterised, bounded, and well behaved
with causality preserved
Contained/bounded in/by some
known, or well de
fi
ned,
environment/conditions
Complicated/Complex - Features I
s(t) = Stimulus
h(t) = Operator
o(t) = Output }
s(t) and o(t) originate
and terminate within the
environment
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
X
Any one or more
or all of these
conditions may no
longer true
X X
59. s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
One or more of these
conditions no longer holds
true
Response matches need
Symbiotic with the environment
Predictable, reliable, with a fast recovery time
Upgrades and changes not traumatic or risky
Shocks are not terminal or unduly debilitating
Reproducible, easy to deploy and maintain/repair/replace
Complicated/Complex - Features II
60. s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
One or more of these
conditions no longer holds
true
Response matches need
Symbiotic with the environment
Predictable, reliable, with a fast recovery time
Upgrades and changes not traumatic or risky
Shocks are not terminal or unduly debilitating
Reproducible, easy to deploy and maintain/repair/replace
Almost by de
fi
nition we cannot satisfy this wish list 100%
Complicated/Complex - Features II
61. s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
One or more of these
conditions no longer holds
true
Response matches need
Symbiotic with the environment
Predictable, reliable, with a fast recovery time
Upgrades and changes not traumatic or risky
Shocks are not terminal or unduly debilitating
Reproducible, easy to deploy and maintain/repair/replace
Almost by de
fi
nition we cannot satisfy this wish list 100%
X
Complicated/Complex - Features II
62. Man and Mother NatureâŚ
Design, understanding, desire, intent v evolution and chance
Only we design
Only we optimise
Only we do centralised control
Only we comprehend and assume responsibility
Design v evolution
Top down v bottom up
Optimisation v good enough
63. Mother NatureâŚproviso
Only evolves systems
Only builds bottom up and never top down
Only goes for âgood enoughâ and optimises nothing
Extremely
complex cells
and reasonably
simple constructs
with distributed control
She conceals her underlying
complexity at every level
of her constructs
and activity...
64. Hundreds of diverse inputs and outputs: cannot be
fully
fl
ood, or combinatorially testedâŚ
Hundreds/thousands of feedback & feedforward
loops along with memory and adaptationâŚ
REALITY BYTES !
Complexity in all things becoming the norm
65. âPerfection is the enemy of Good Enoughâ
De
fi
ning âgood enoughâ is not always trivial
and is generally the biggest challenge !
~80% of the need satis
fi
ed by ~20% of the
effortâŚ.and then often destroyed/devalued
by speci
fi
cation creepâŚ.
APEING Nature
We are building evolved systems
AI, AL, IoT, Internet, Security are now evolutionary
66. âPerfection is the enemy of Good Enoughâ
De
fi
ning âgood enoughâ is not always trivial
and is generally the biggest challenge !
~80% of the need satis
fi
ed by ~20% of the
effortâŚ.and then often destroyed/devalued
by speci
fi
cation creepâŚ.
APEING Nature
We are building evolved systems
AI, AL, IoT, Internet, Security are now evolutionary
This future will be full of surprises -
âemergent behavioursâ - and we are
having to abandon the idea of 100%
testability and characterisation - and
we will surely lose control too!
New mind sets and new system
thinking is going to be essential
77. Ρ
Failure free
operating cost
with ef
fi
ciency f1(
đˇ
)
Failure cost with
ef
fi
ciency f2(
đˇ
)
⏠⏠âŹ
Ef
fi
ciency
đˇ
Efficiency is âeasyâ
People overlook the cost of failure!
78. Ρ
đˇ
Failure free
operating cost
with ef
fi
ciency f1(
đˇ
)
Failure cost with
ef
fi
ciency f2(
đˇ
)
⏠⏠âŹ
Ef
fi
ciency
đˇ
f1â(
đˇ
) + f2â(
đˇ
) = 0
For the speci
fi
c exponential
case:
C = Aexp(-a.
đˇ
) + Bexp(b.
đˇ
)
đˇ
o =
b - a
__
1 loge Aa
Bb
_
The optimum operating
ef
fi
ciency is found to be:
Efficiency is âeasyâ
People overlook the cost of failure!
79. Bathtub Reliability Curve
Failure Rate
End of life
wear out
failures
Normal/useful life
low level failures
Time
Infant mortality
- early failures
Failure
Rate
80. 0.001
0.01
0.1
1
10
100
1,000
10,000
100,000
1,000,000
1 10 100 1,000 10,000 100,000 1,000,000
MTBF - hours
Mean Time Between Failures
MTTR - seconds
Mean Time To Repair
99.999%
99.99%
99.9%
99%
90%
0.1
1 year 10 years
1 month
1 week
1 day
1 minute
1 hour
1 day
Availability
Offsetting inevitable failures
1 second
81. 0.001
0.01
0.1
1
10
100
1,000
10,000
100,000
1,000,000
1 10 100 1,000 10,000 100,000 1,000,000
MTBF - hours
Mean Time Between Failures
MTTR - seconds
Mean Time To Repair
99.999%
99.99%
99.9%
99%
90%
0.1
1 year 10 years
1 month
1 week
1 day
1 minute
1 hour
1 day
Availability
Offsetting inevitable failures
MTBF = 11.4 years
1 second
82. System 1
System 2
System N
?
Not co-located
Not the same power feed
Not the same software
Not the same network connections
No centralised control
Switch
Or Sum
Voting
A =1- (1 - Av)N
Av
Av
Av
A = Availability
Hot standby
Offsetting inevitable failures
83. MTBF = Mean Time Between Failures
MTTR = Mean Time To Repair
Mean = Average - and Averages donât tell us much!
Distribution is key !
Availability = Av = MTBF/(MTBF + MTTR)
Unavailability = Uv = 1 - Av = 1 - MTBF/(MTBF + MTTR)
= MTTR/(MTBF + MTTR)
Relationships
At the most basic âaverageâ level
84. Resilience = The capacity to recover
Failure modes: Graceful/Phased
Predominant in the world of analogue system - precursors evident
85. Resilience = The capacity to recover
Failure modes: catastrophic/instant
Predominant in the world of digital systems - precursors often hidden
86. Some still âto doâsâ
Specifically for the digital domain
Failure precursor detection
Integrates graceful fail mode
Pre-emptive failure switchover
Golden âbrickâ reference models
Comprehensive test methodologies
Brittleness threshold/onset detection
Abnormal system operation identification
No-GO realm/region/mode recognition
Autonomous failure recover modes
Penetration/illegal act detection
Full outcomes characterisations
Decision âpost mortemâ facility
Species comparators ++++
89. Sniper Locating
with acoustic sensors
Acoustic Cone of
U n c e r t a i n t y
3 - 5o
Sensor
Unit
War Zone
Ambient
Noise
Dynamic
R a n g e
Limited
Todayâs Performance
~200m
90. Acoustic Cone
of
U n c e r t a i n t
y
3 - 5o
Sensor
Unit Dynamic
R a n g e
Limited
~200m
In Combat Multi-Mic Array
MODERN SYSTEM
91. Filtering
Post Microphone analogue/digital filtering/
processing
~
~
~
DSP
~
~
~
Noise Filtering
Directivity - Focus
Voice Characteristics
Anticipated Subject
Matter
Correlated sniper
shot signal - a
matched filter by
any other name
Dynamic range limiting
background noise
T i m e
waveform
and spectrum
o f s i n g l e
sniper shot
92. Primary dynamic range limiter - the
diaphragm
Diaphragm driven to
mechanical saturation by
noise and thereby limiting
dynamic range for the
wanted/weak signal
T i m e
waveform
and spectrum
o f s i n g l e
sniper shot
Pre-Filter
93. Noise Filtering
Directivity - Focus
Voice Characteristics
Multiple analogue resonant cavity
filtering
Pre-Diaphragm acoustic filter
reduces noise input to improves
dynamic range and directivity
T i m e
waveform
and spectrum
o f s i n g l e
sniper shot
Filter Config
94. Filter Characteristic
A wide range of selectivity configurations is
possible
Naked Microphone Insert
Filter 1
Filter 2
101. Ambient Battle
fi
eld Noise
Sniper Ri
fl
e Spectrum
Containment > 95% of Sniper Spectral Energy
Filter Rejection Zone
This region is not generally critical to
detection but can contain energy vital
to identification
Peak
to
Peak
highly
distance
dependent
2 10 100 1k 5kHz
102. Ambient Battle
fi
eld Noise
Sniper Ri
fl
e Spectrum
Containment > 95% of Sniper Spectral Energy
Filter Rejection Zone
Peak
to
Peak
highly
distance
dependent
2 10 100 1k 5kHz
Relative and non specific energy levels
for the purpose of illustration - all
location and situation defined
Prototype Filter Response
106. w w w. p e t e r c o c h r a n e . c o m
T h a n k Y o u
âThe march of science and technology does not
imply growing intellectual complexity in the lives
of most people. It often means the oppositeâ
Thomas Sowell