There are three possible ROC's:
1. Outside all poles (a, b, c)
2. Between innermost and outermost pole
3. Inside all poles
So the possible ROC's are:
1. Outside circle through a, b, c
2. Annular region between a, c
3. Inside circle through a, b, c
a b c Re
The z-Transform
Important z-Transform Pairs
Important z-Transform Pairs
1. Unit Impulse: δ(n)
1, if n = 0
δ(n) = 0, otherwise
1
X(z) =
2.
EXPERT SYSTEMS AND SOLUTIONS
Project Center For Research in Power Electronics and Power Systems
IEEE 2010 , IEEE 2011 BASED PROJECTS FOR FINAL YEAR STUDENTS OF B.E
Email: expertsyssol@gmail.com,
Cell: +919952749533, +918608603634
www.researchprojects.info
OMR, CHENNAI
IEEE based Projects For
Final year students of B.E in
EEE, ECE, EIE,CSE
M.E (Power Systems)
M.E (Applied Electronics)
M.E (Power Electronics)
Ph.D Electrical and Electronics.
Training
Students can assemble their hardware in our Research labs. Experts will be guiding the projects.
EXPERT GUIDANCE IN POWER SYSTEMS POWER ELECTRONICS
We provide guidance and codes for the for the following power systems areas.
1. Deregulated Systems,
2. Wind power Generation and Grid connection
3. Unit commitment
4. Economic Dispatch using AI methods
5. Voltage stability
6. FLC Control
7. Transformer Fault Identifications
8. SCADA - Power system Automation
we provide guidance and codes for the for the following power Electronics areas.
1. Three phase inverter and converters
2. Buck Boost Converter
3. Matrix Converter
4. Inverter and converter topologies
5. Fuzzy based control of Electric Drives.
6. Optimal design of Electrical Machines
7. BLDC and SR motor Drives
A crash coarse in stochastic Lyapunov theory for Markov processes (emphasis is on continuous time)
See also the survey for models in discrete time,
https://netfiles.uiuc.edu/meyn/www/spm_files/MarkovTutorial/MarkovTutorialUCSB2010.html
Optimal multi-configuration approximation of an N-fermion wave functionjiang-min zhang
We propose a simple iterative algorithm to construct the optimal multi-configuration approximation of an N-fermion wave function. That is, M≥N single-particle orbitals are sought iteratively so that the projection of the given wave function in the CNM-dimensional configuration subspace is maximized. The algorithm has a monotonic convergence property and can be easily parallelized. The significance of the algorithm on the study of entanglement in a multi-fermion system and its implication on the multi-configuration time-dependent Hartree-Fock (MCTDHF) are discussed. The ground state and real-time dynamics of spinless fermions with nearest-neighbor interactions are studied using this algorithm, discussing several subtleties.
This was the first public representation of a proposal for an Essential Health Care Patent Pool. The venue was the XIV International AIDS Conference, July 2002 in Barcelona, Spain
EXPERT SYSTEMS AND SOLUTIONS
Project Center For Research in Power Electronics and Power Systems
IEEE 2010 , IEEE 2011 BASED PROJECTS FOR FINAL YEAR STUDENTS OF B.E
Email: expertsyssol@gmail.com,
Cell: +919952749533, +918608603634
www.researchprojects.info
OMR, CHENNAI
IEEE based Projects For
Final year students of B.E in
EEE, ECE, EIE,CSE
M.E (Power Systems)
M.E (Applied Electronics)
M.E (Power Electronics)
Ph.D Electrical and Electronics.
Training
Students can assemble their hardware in our Research labs. Experts will be guiding the projects.
EXPERT GUIDANCE IN POWER SYSTEMS POWER ELECTRONICS
We provide guidance and codes for the for the following power systems areas.
1. Deregulated Systems,
2. Wind power Generation and Grid connection
3. Unit commitment
4. Economic Dispatch using AI methods
5. Voltage stability
6. FLC Control
7. Transformer Fault Identifications
8. SCADA - Power system Automation
we provide guidance and codes for the for the following power Electronics areas.
1. Three phase inverter and converters
2. Buck Boost Converter
3. Matrix Converter
4. Inverter and converter topologies
5. Fuzzy based control of Electric Drives.
6. Optimal design of Electrical Machines
7. BLDC and SR motor Drives
A crash coarse in stochastic Lyapunov theory for Markov processes (emphasis is on continuous time)
See also the survey for models in discrete time,
https://netfiles.uiuc.edu/meyn/www/spm_files/MarkovTutorial/MarkovTutorialUCSB2010.html
Optimal multi-configuration approximation of an N-fermion wave functionjiang-min zhang
We propose a simple iterative algorithm to construct the optimal multi-configuration approximation of an N-fermion wave function. That is, M≥N single-particle orbitals are sought iteratively so that the projection of the given wave function in the CNM-dimensional configuration subspace is maximized. The algorithm has a monotonic convergence property and can be easily parallelized. The significance of the algorithm on the study of entanglement in a multi-fermion system and its implication on the multi-configuration time-dependent Hartree-Fock (MCTDHF) are discussed. The ground state and real-time dynamics of spinless fermions with nearest-neighbor interactions are studied using this algorithm, discussing several subtleties.
This was the first public representation of a proposal for an Essential Health Care Patent Pool. The venue was the XIV International AIDS Conference, July 2002 in Barcelona, Spain
Z Transform And Inverse Z Transform - Signal And SystemsMr. RahüL YøGi
The z-transform is the most general concept for the transformation of discrete-time series.
The Laplace transform is the more general concept for the transformation of continuous time processes.
For example, the Laplace transform allows you to transform a differential equation, and its corresponding initial and boundary value problems, into a space in which the equation can be solved by ordinary algebra.
The switching of spaces to transform calculus problems into algebraic operations on transforms is called operational calculus. The Laplace and z transforms are the most important methods for this purpose.
z-Transform is for the analysis and synthesis of discrete-time control systems.The z transform in discrete-time systems play a similar role as the Laplace transform in continuous-time systems
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
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Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
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This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
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LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
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PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
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- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
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- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
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Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
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And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
2. Content
Introduction
z-Transform
Zeros and Poles
Region of Convergence
Important z-Transform Pairs
Inverse z-Transform
z-Transform Theorems and Properties
System Function
4. Why z-Transform?
A generalization of Fourier transform
Why generalize it?
– FT does not converge on all sequence
– Notation good for analysis
– Bring the power of complex variable theory deal with
the discrete-time signals and systems
6. Definition
The z-transform of sequence x(n) is defined by
∞
X ( z) = ∑ x ( n) z
n = −∞
−n
Fourier
Transform
Let z = e−jω.
∞
X (e ) = jω
∑ x ( n )e
n =−∞
− jω n
7. z-Plane
∞
∑ x ( n) z −n Im
X ( z) =
n = −∞
z = e−jω
ω
∞ Re
jω
X (e ) = ∑ x ( n )e
n =−∞
− jω n
Fourier Transform is to evaluate z-transform
on a unit circle.
11. Definition
Give a sequence, the set of values of z for which the
z-transform converges, i.e., |X(z)|<∞, is called the
region of convergence.
∞ ∞
| X ( z ) |= ∑ x ( n) z − n =
n = −∞
∑ | x(n) || z |− n < ∞
n = −∞
ROC is centered on origin and
consists of a set of rings.
12. Example: Region of Convergence
∞ ∞
| X ( z ) |= ∑ x ( n) z − n =
n = −∞
∑ | x(n) || z |− n < ∞
n = −∞
Im ROC is an annual ring centered
on the origin.
r
Re Rx − <| z |< Rx +
jω
ROC = {z = re | Rx − < r < Rx + }
13. Stable Systems
A stable system requires that its Fourier transform is
uniformly convergent.
Im Fact: Fourier transform is to
evaluate z-transform on a unit
circle.
1
A stable system requires the
Re ROC of z-transform to include
the unit circle.
14. Example: A right sided Sequence
x ( n) = a n u ( n)
x(n)
... n
-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
15. Example: A right sided Sequence
For convergence of X(z), we
x ( n) = a u ( n)
n
require that
∞
∑
∞
| az −1 | < ∞ | az −1 |< 1
X ( z) = ∑ a u (n)z
n = −∞
n −n
n =0
∞ | z |>| a |
= ∑ a n z −n ∞
1 z
n =0 X ( z ) = ∑ (az ) =
−1 n
−1
=
∞ n =0 1 − az z−a
= ∑ (az −1 ) n
| z |>| a |
n =0
16. Example: A right sided Sequence
ROC for x(n)=anu(n)
z
X ( z) =
z−a
, | z |>| a | Which one is stable?
Im Im
1 1
−a a −a a
Re Re
17. Example: A left sided Sequence
x(n) = −a nu (−n − 1)
-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
... n
x(n)
18. Example: A left sided Sequence
For convergence of X(z), we
x(n) = −a u (−n − 1)n
require that
∞ ∞
X ( z ) = − ∑ a u (− n − 1)z
∑ | a −1 z | < ∞
−n
| a −1 z |< 1
n
n = −∞
−1
n =0
= − ∑ a n z −n
n = −∞
| z |<| a |
∞
= −∑ a − n z n ∞
1 z
n =1 X ( z ) = 1 − ∑ (a z ) = 1 −
−1 n
−1
=
∞ n=0 1− a z z − a
= 1 − ∑ a −n z n
n =0 | z |<| a |
19. Example: A left sided Sequence
ROC for x(n)=−anu(− n−1)
z
X ( z) =
z−a
, | z |<| a | Which one is stable?
Im Im
1 1
−a a −a a
Re Re
21. Represent z-transform as a
Rational Function
P( z ) where P(z) and Q(z) are
X ( z) = polynomials in z.
Q( z )
Zeros: The values of z’s such that X(z) = 0
Poles: The values of z’s such that X(z) = ∞
22. Example: A right sided Sequence
z
x ( n) = a n u ( n) X ( z) = , | z |>| a |
z−a
Im
ROC is bounded by the
pole and is the exterior
a
Re of a circle.
23. Example: A left sided Sequence
z
x(n) = −a nu (−n − 1) X ( z) = , | z |<| a |
z−a
Im
ROC is bounded by the
pole and is the interior
a
Re of a circle.
24. Example: Sum of Two Right Sided Sequences
x ( n) = ( 1 ) n u ( n) + ( − 1 ) n u ( n)
2 3
z z 2 z ( z − 12 )
1
X ( z) = + =
z−2 z+3
1 1
( z − 1 )( z + 1 )
2 3
Im
ROC is bounded by poles
and is the exterior of a circle.
1/12
−1/3 1/2 Re
ROC does not include any pole.
25. Example: A Two Sided Sequence
x(n) = (− 1 ) n u (n) − ( 1 ) n u (−n − 1)
3 2
z z 2 z ( z − 12 )
1
X ( z) = + =
z+3 z−2
1 1
( z + 1 )( z − 1 )
3 2
Im
ROC is bounded by poles
and is a ring.
1/12
−1/3 1/2 Re
ROC does not include any pole.
26. Properties of ROC
A ring or disk in the z-plane centered at the origin.
The Fourier Transform of x(n) is converge absolutely iff the ROC
includes the unit circle.
The ROC cannot include any poles
Finite Duration Sequences: The ROC is the entire z-plane except
possibly z=0 or z=∞.
Right sided sequences: The ROC extends outward from the outermost
finite pole in X(z) to z=∞.
Left sided sequences: The ROC extends inward from the innermost
nonzero pole in X(z) to z=0.
27. More on Rational z-Transform
Consider the rational z-transform
with the pole pattern:
Im
Find the possible a b c
ROC’s Re
28. More on Rational z-Transform
Consider the rational z-transform
with the pole pattern:
Im
Case 1: A right sided Sequence.
a b c
Re
29. More on Rational z-Transform
Consider the rational z-transform
with the pole pattern:
Im
Case 2: A left sided Sequence.
a b c
Re
30. More on Rational z-Transform
Consider the rational z-transform
with the pole pattern:
Im
Case 3: A two sided Sequence.
a b c
Re
31. More on Rational z-Transform
Consider the rational z-transform
with the pole pattern:
Im
Case 4: Another two sided Sequence.
a b c
Re
33. Z-Transform Pairs
Sequence z-Transform ROC
δ(n) 1 All z
All z except 0 (if m>0)
δ( n − m ) z −m
or ∞ (if m<0)
1
u (n) | z |> 1
1 − z −1
1
− u (−n − 1) | z |< 1
1 − z −1
1
n
a u (n) | z |>| a |
1 − az −1
1
− a nu (−n − 1) | z |<| a |
1 − az −1
34. Z-Transform Pairs
Sequence z-Transform ROC
1 − [cos ω0 ] z −1
[cos ω0 n]u (n) | z |> 1
1 − [ 2 cos ω0 ]z −1 + z −2
[sin ω0 ]z −1
[sin ω0 n]u (n) | z |> 1
1 − [2 cos ω0 ]z −1 + z −2
1 − [ r cos ω0 ]z −1
[r n cos ω0 n]u (n) | z |> r
1 − [ 2r cos ω0 ]z −1 + r 2 z − 2
[r sin ω0 ] z −1
[r n sin ω0 n]u (n) | z |> r
1 − [ 2r cos ω0 ]z −1 + r 2 z − 2
a n 0 ≤ n ≤ N −1 1− aN z−N
| z |> 0
0 otherwise 1 − az −1
37. Linearity
Z [ x(n)] = X ( z ), z ∈ Rx
Z [ y (n)] = Y ( z ), z ∈ Ry
Z [ax(n) + by (n)] = aX ( z ) + bY ( z ), z ∈ Rx ∩ R y
Overlay of
the above two
ROC’s
38. Shift
Z [ x(n)] = X ( z ), z ∈ Rx
Z [ x(n + n0 )] = z X ( z )
n0
z ∈ Rx
39. Multiplication by an Exponential Sequence
Z [ x(n)] = X ( z ), Rx- <| z |< Rx +
−1
Z [a x(n)] = X (a z )
n
z ∈| a | ⋅Rx
45. Convolution of Sequences
Z [ x(n)] = X ( z ), z ∈ Rx
Z [ y (n)] = Y ( z ), z ∈ Ry
Z [ x(n) * y (n)] = X ( z )Y ( z ) z ∈ Rx ∩ R y
46. Convolution of Sequences
∞
x ( n) * y ( n) = ∑ x(k ) y (n − k )
k = −∞
∞
∞
−n
Z [ x(n) * y (n)] = ∑ ∑ x(k ) y (n − k ) z
n = −∞ k = −∞
∞ ∞ ∞ ∞
= ∑ x(k ) ∑ y(n − k )z −n
= ∑
k = −∞
x(k ) z − k ∑ y (n)z − n
n = −∞
k = −∞ n = −∞
= X ( z )Y ( z )
50. Nth-Order Difference Equation
N M
∑a
k =0
k y (n − k ) = ∑ br x(n − r )
r =0
N M
Y ( z )∑ ak z − k = X ( z )∑ br z − r
k =0 r =0
M N
−r −k
H ( z ) = ∑ br z ∑ ak z
r =0 k =0
51. Representation in Factored Form
Contributes poles at 0 and zeros at cr
M
A∏ (1 − cr z −1 )
H ( z) = N
r =1
∏ (1 − d r z −1 )
k =1
Contributes zeros at 0 and poles at dr
52. Stable and Causal Systems
Causal Systems : ROC extends outward from the outermost pole.
Im
M
A∏ (1 − cr z −1 )
H ( z) = N
r =1
Re
∏ (1 − d r z −1 )
k =1
53. Stable and Causal Systems
Stable Systems : ROC includes the unit circle.
Im
M
A∏ (1 − cr z −1 ) 1
H ( z) = N
r =1
Re
∏ (1 − d r z −1 )
k =1
54. Example
Consider the causal system characterized by
y (n) = ay (n − 1) + x(n) Im
1 1
H ( z) =
1 − az −1 a Re
h( n) = a n u ( n)
55. Determination of Frequency Response
from pole-zero pattern
A LTI system is completely characterized by its
pole-zero pattern.
Im
Example: p1
z − z1 e j ω0
H ( z) =
( z − p1 )( z − p2 ) z1
Re
e jω0 − z1 p2
H (e jω0 ) =
(e jω0 − p1 )(e jω0 − p2 )
56. Determination of Frequency Response
from pole-zero pattern
A LTIjω
|H(e )|=?
pole-zero pattern.
jω
∠H(e )=?
system is completely characterized by its
Im
Example: p1
z − z1 e j ω0
H ( z) =
( z − p1 )( z − p2 ) z1
Re
e jω0 − z1 p2
H (e jω0 ) =
(e jω0 − p1 )(e jω0 − p2 )
57. Determination of Frequency Response
from pole-zero pattern
A LTIjω
|H(e )|=?
pole-zero pattern. ∠H(e )=?
system is completely characterized by its
jω
Im
Example: p1
| | φ2
jω
|H(e )| = e j ω0
| || | z1
φ1 φ3 Re
∠H(ejω) = φ1−(φ2+ φ3 ) p2
58. Example
1 20
H ( z) = −1
1 − az 10
dB
0
Im
-1 0
0 2 4 6 8
2
1
a Re 0
-1
-2
0 2 4 6 8