Applied Science - Engineering Systems

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

"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 /

‘System’ Definition
Can we describe exactly what we mean ?
“This singularly simple question directs us to an
ongoing (endless) philosophical debate that is
less than helpful for engineers and scientists”
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

“A group of interacting, interrelated, or interdependent
elements forming a complex whole”
The most concise de
fi
nition I can
fi
nd but not entirely satisfactory
for any engineering purposes…
literature
Thousands of publications
* The whole may be simple, complicated or complex, and there
may or may not be any interdependence !

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

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:

‘Systems take energy, matter, information, and transforms their
nature’
* Ergo: All Systems are Entropic
Not Published
My tight/sufficient (?) definition

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

S O L U T I O N
Select specialist teams

Taking an interest in every system known to mankind pays dividends in
providing us with insights and challenging concepts and occasionally , really
useful results...
…we 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 …that 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

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

• 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 don’t make the complex simpler
• There are no simple solutions to complex problems
• There is a huge di
ff
erence between complicated and complex systems

• 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!

Mother Natures propensity for Simple Systems resulting in Complex Outcomes
WHAT WE generally observe
A natural & designed world complexity - simplicity inversion

Humans propensity for Complex Systems resulting in Simple Outcomes
WHAT WE generally observe
A natural & designed world complexity - simplicity inversion

Dominant
System
Trend
WHAT WE KNOW FOR SURE
We cannot manage 21C societies with 17C thinking/systems

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

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 *****

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

Generalities
All systems share similar models
mathematical/analysis frameworks
Electrical, Electronic, Mechanical, Civil Engineering & Physics share the same
or very similar equations sets…’know one and you know the other’

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

‘SIMPLEst’ 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

S I M P L E S Y S T E M S
Within the span of ‘a’ 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
Mathematics works
Linear behaviour
Predictable

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
Maths ‘mostly’ works(ish)
Unnatural materials required
Computer modelling a necessity
Complicated SYSTEMS
A deep understanding beyond the grasp of ‘a’ human

Complicated
Sea skimming missile detection
Time of flight ~ 10 - 20s

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

Complex SYSTEMS
Global Air Traffic - highly unpredictable
exhibits continual adaptation aka life!

Complex SYSTEMS
Global Shipping - highly unpredictable

Complex SYSTEMS
Global Internet Traffic - beyond prediction

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
“Established wisdoms do not apply
Mathematics non-contributor
Emergent behaviours/rule
No general laws”
“NOTE: These are ‘generalised comments
and there are always opportunities for
exceptions”

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
‘Always’ non-linear
Only modest compute power
Good network connectivity
Maths nears irrelevancy
Now ‘breeding’ malware

Stability
Two extremes/bounds
Conditionally Stable
Conditionally Unstable
Only becomes unstable when
there is some system failure
Under any and all conditions

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

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

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
…evolved
designoid
solutions

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
“Economics & market forces are failing
Ignorance and bigotry on the rise
Politics & democracy is in peril“

LEMMING LIKE
Doing what they thing is right

Fourier + Laplace - time and frequency
g(t)
f(t)❋g(t)
f(t)
F(ω)
G(ω)
F(ω).G(ω)
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

Time
Domain
Frequency
Domain
Real
Mathematical Abstraction
Reality CHECK

Temporal
Function
Frequency
Function
Frequency
Function
Temporal
Function
TRANSFORMATIONS
Difficult problems rendered easy(ier)
Fourier: time frequency domain
=
Laplace: time frequency
domain transient signals

Temporal
Function
Frequency
Function
Frequency
Function
Temporal
Function
Applicable to time and
s p a c e , h e a t
fl
o w ,
mechanical systems,
probability theory +++
TRANSFORMATIONS
Difficult problems rendered easy(ier)
Fourier: time frequency domain
=
Laplace: time frequency
domain transient signals

TRANSFORMATIONS
Analogue and Digital/Discrete) formulations

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
+++

What’s 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

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)

FEEDBACK & FEEDBACK ?
s(t) h(t) o(t)
FB o(t)
FF s(t)
Noise reduction loop
-ve FeedBack induces stability
+ve FeedBack induces instability
Mathematical tractability reduced by the # loops
Stability and response
shaping loop

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)

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

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

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)

Simple System - Key Features II
s(t) h(t) o(t)
Sometimes we cannot satisfy this wish list 100%

known, or well de
fi
ned,
Complicated/Complex - Features I
s(t) = Stimulus
h(t) = Operator
o(t) = Output }
environment
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)

known, or well de
fi
ned,
s(t) = Stimulus
h(t) = Operator
o(t) = Output }
environment
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
X

known, or well de
fi
ned,
s(t) = Stimulus
h(t) = Operator
o(t) = Output }
environment
s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
X X

known, or well de
fi
ned,
s(t) = Stimulus
h(t) = Operator
o(t) = Output }
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

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
Complicated/Complex - Features II

s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
true
Almost by de
fi
nition we cannot satisfy this wish list 100%

s1(t)
s2(t)
s3(t)
si(t)
o1(t)
ok(t)
o3(t)
o2(t)
hi(t)
true
Almost by de
fi
nition we cannot satisfy this wish list 100%
X

Man and Mother Nature…
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

Mother Nature…proviso
Only evolves systems
Only builds bottom up and never top down
Only goes for ‘good enough’ 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...

Hundreds of diverse inputs and outputs: cannot be
fully
fl
ood, or combinatorially tested…
Hundreds/thousands of feedback & feedforward
loops along with memory and adaptation…
REALITY BYTES !
Complexity in all things becoming the norm

“Perfection is the enemy of Good Enough”
De
fi
ning ‘good enough’ is not always trivial
and is generally the biggest challenge !
~80% of the need satis
fi
ed by ~20% of the
effort….and then often destroyed/devalued
by speci
fi
cation creep….
APEING Nature
We are building evolved systems
AI, AL, IoT, Internet, Security are now evolutionary

“Perfection is the enemy of Good Enough”
De
fi
ning ‘good enough’ is not always trivial
and is generally the biggest challenge !
~80% of the need satis
fi
ed by ~20% of the
effort….and then often destroyed/devalued
by speci
fi
cation creep….
APEING Nature
We are building evolved systems
AI, AL, IoT, Internet, Security are now evolutionary
This future will be full of surprises -
‘emergent behaviours’ - 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

U N R E A L
Not realistic/impossible

T R A D E O F F S
You can’t have it all - not forever anyway

Size
Scale
Complexity
Connectivity
Sophistication
Connectivity
MTBF
Speed
Agility
Reliability
Testability
Predicability
Responsivity
Common/General system traits

Size
Scale
Complexity
Connectivity
Sophistication
Connectivity
MTBF
Speed
Agility
Reliability
Testability
Predicability
Responsivity
Often difficult
to define
with
any great
precision

Size
Scale
Complexity
Connectivity
Sophistication
Connectivity
MTBF
Speed
Agility
Reliability
Testability
Predicability
Responsivity
Cost MTTR Latency
Power Heat Resources
Often difficult
to define
with
any great
precision

A long storage life and very
short operational activity
HUH ??

Short storage life and very
long operational activity
HUH ?
?

Brittleness ALWAYS rules
Reliability/resilience and optimisation are mutually exclusive
Highly optimised components result
in mission critical failures

η
€ € €
Ef
fi
ciency
𝓷
Efficiency is ‘easy’
People overlook the cost of failure!

η
Failure free
operating cost
with ef
fi
ciency f1(
𝓷
)
Failure cost with
ef
fi
ciency f2(
𝓷
)
€ € €
Ef
fi
ciency
𝓷

η
𝓷
Failure free
operating cost
with ef
fi
ciency f1(
𝓷
)
Failure cost with
ef
fi
ciency f2(
𝓷
)
€ € €
Ef
fi
ciency
𝓷
f1’(
𝓷
) + f2’(
𝓷
) = 0
For the speci
fi
c exponential
case:
C = Aexp(-a.
𝓷
) + Bexp(b.
𝓷
)
𝓷
o =
b - a
__
1 loge Aa
Bb
_
The optimum operating
ef
fi
ciency is found to be:

Bathtub Reliability Curve
Failure Rate
End of life
wear out
failures
Normal/useful life
low level failures
Time
Infant mortality
- early failures
Failure
Rate

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

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
MTBF = 11.4 years
1 second

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

MTBF = Mean Time Between Failures
MTTR = Mean Time To Repair
Mean = Average - and Averages don’t 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 ‘average’ level

Resilience = The capacity to recover
Failure modes: Graceful/Phased
Predominant in the world of analogue system - precursors evident

Resilience = The capacity to recover
Failure modes: catastrophic/instant
Predominant in the world of digital systems - precursors often hidden

Some still ‘to do’s’
Specifically for the digital domain
Failure precursor detection
Integrates graceful fail mode
Pre-emptive failure switchover
Golden ‘brick’ 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 ‘post mortem’ facility
Species comparators ++++

Sniper Locating
M u l t i p l e a c o u s t i c s e n s o r s

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
Today’s Performance
~200m

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

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

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

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

Filter Characteristic
A wide range of selectivity configurations is
possible
Naked Microphone Insert
Filter 1
Filter 2

E a c h f i lt e r/m i c
a s s e m b l y i s
m e c h a n i c a l l y
isolated by foam -
n o a c o u s t i c
linkage assembly to
assembly
Detail

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

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

Sniper rifle buried in
machine gun signal

Sniper Ri
fl
e
+
Machine Gun
Autocorrelation
Sniper Detected
Pre mic acoustic
fi
ltered signal
Processing Delay

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
“The march of science and technology does not
imply growing intellectual complexity in the lives
of most people. It often means the opposite”
Thomas Sowell

Applied Science - Engineering Systems

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