Answers
Let f(z) = (4z ² + 2z) / (2z ² - 3z + 1).
First, carry out the division:
f(z) = 2 + (8z - 2) / (2z ² - 3z + 1)
Observe that
2z ² - 3z + 1 = (2z - 1) (z - 1)
so you can separate the rational part of f(z) into partial fractions. We have
(8z - 2) / (2z ² - 3z + 1) = a / (2z - 1) + b / (z - 1)
8z - 2 = a (z - 1) + b (2z - 1)
8z - 2 = (a + 2b) z - (a + b)
so that a + 2b = 8 and a + b = 2, yielding a = -4 and b = 6.
So we have
f(z) = 2 - 4 / (2z - 1) + 6 / (z - 1)
or
f(z) = 2 - (2/z) (1 / (1 - 1/(2z))) + (6/z) (1 / (1 - 1/z))
Recall that for |z| < 1, we have
[tex]\displaystyle\frac1{1-z}=\sum_{n=0}^\infty z^n[/tex]
Replace z with 1/z to get
[tex]\displaystyle\frac1{1-\frac1z}=\sum_{n=0}^\infty z^{-n}[/tex]
so that by substitution, we can write
[tex]\displaystyle f(z) = 2 - \frac2z \sum_{n=0}^\infty (2z)^{-n} + \frac6z \sum_{n=0}^\infty z^{-n}[/tex]
Now condense f(z) into one series:
[tex]\displaystyle f(z) = 2 - \sum_{n=0}^\infty 2^{-n+1} z^{-(n+1)} + 6 \sum_{n=0}^\infty z^{-n-1}[/tex]
[tex]\displaystyle f(z) = 2 - \sum_{n=0}^\infty \left(6+2^{-n+1}\right) z^{-(n+1)}[/tex]
[tex]\displaystyle f(z) = 2 - \sum_{n=1}^\infty \left(6+2^{-(n-1)+1}\right) z^{-n}[/tex]
[tex]\displaystyle f(z) = 2 - \sum_{n=1}^\infty \left(6+2^{2-n}\right) z^{-n}[/tex]
So, the inverse Z transform of f(z) is [tex]\boxed{6+2^{2-n}}[/tex].
Related Questions
yo where are the answer :/
Answers
Answer:
yaa what he said
Explanation:
Coving is a curved edge between a floor and a wall.
O True
O False
Answers
Answer:
True.
Explanation:
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!
Which of the following describe what the material of an object can impact?
achievements and failures
geometric shapes and figures
sustainability and durability
durability and achievement
Answers
Answer:
geometric shapes and figuresAnswer:
Sustainability and durability
Explanation:
Technician A says that the most effective way to diagnose wheel speed sensor circuit faults is to utilize the live data function of your scan tool. Technician B says that once you have identified the affected circuit, the next step is to test at the sensor with a graphing multi-meter or an oscilloscope. Who is correct
Answers
Answer:
Both Technicians A & B are correct
Explanation:
In diagnosing wheel systems, both steps said by technicians A & B are correct because it's the normal procedure to diagnose wheel speed sensor circuit faults.
A method used to control density and overcrowding by restricting setbacks, building height, or ratio of open area is known as _________ zoning.
Answers
Answer:
Bulk zoning.
Explanation:
Zoning is a method used by municipal authorities or government authorities to divide a land area into zones. It is a urban planning method. There are several types of zoning; bulk zoning being one of them.
Bulk zoning can be defined as a set of regulations used to control lot size, ratio of floor area, open space, yards, setbacks, bulding height, etc. These setbacks and restrictions, then, help authorities to determine maximun size of a building on a zoning area, and also the positioning of the building.
Therefore, bulk zoning is the correct answer.
However, motors are designed so that the polarity of the electromagnet constantly flips. That is, the north pole becomes the
south pole, and the south pole becomes the north pole, every time the electromagnet turns 180 degrees
Why is it designed this way?
OA.
OB.
Oc.
OD.
to conserve the energy in the battery
so the magnetic field will get stronger
so the electromagnet will continuously turn
to constantly polarize the field magnet
Answers
Answer:
c
Explanation:
if the poles didn't flip then the motor would not be able to spin
help ill give BRAINLYEST ( if it lets me )
Determine what each letter represents in the Punnett square.
Letters A and B represent the genotypes of the ______
.Letters C, D, E, and F represent the genotypes of the _______
ps theres no pic
.
Answers
Answer:
Letters A and B represent the genotypes of the Parents
Letters C, D, E, and F represent the genotypes of the Offspring.
Explanation:
The Punnet square is a square shaped figure or diagram used to anticipate the genotypes of offspring after a certain parental cross. It helps in determining the genotype as well as phenotype of the offspring if we know the genotype of parents.
Air space used to separate a water supply outlet from any potentially contaminated source is called a(n)
O back-siphoning device
O backflow
O alr gap
O closed water container
Answers
Answer:
air gap
Explanation:
It is also called air doors or fly fans. Air space used to separate a water-supply outlet from any potentially contaminated source. The air space between the floor drain and the drainpipe of a sink is an example. An air gap is the only completely reliable method for preventing backflow.
Answer:
air gap
Explanation:
What is the purpose of the graphic language?
Answers
Answer:
enables the representation, analysis and communication of various aspects of an information system. These aspects correspond to varying and incomplete views of information systems and the processes therein.
The point in an electrical circuit that is connected to the negative side of a power supply is called what?
A. Battery source
B. Ground
C. Loop
OD. Short circuit
Answers
Answer:
ground or B
Explanation:
Which statement is true?
A.Temperature measures the average kinetic energy of particles.
B.Temperature equivalents indicate the same thermal energy.
C.Temperature depends on the density of the substance.
D.Temperature measures the thermal energy of object.
Answers
When temperature increases the motion of particles also increases.
Technician A states that a pressure bleeder may be needed to bleed EBC system hydraulic circuits. Technician B states that once the scan tool indicates that the HCU is bled, it may direct you to bleed the brakes manually to remove any remaining air from the system. Who is correct
Answers
Answer:
Both Technician A and Technician B
Explanation:
ABS modulators such as the Ford EBC310 version which are not equipped with bleeders are to have there valves cycled and their pumps activated to enable the bleeding out areas which are not easily bled by the wheel based bleeding
The brakes can be either pressure bled or bled manually, however, the HCU will require additional processes to completely bleed out the system, such as the use of a scan tool
When would you normally use a pin punch?
Answers
Answer:
the main use of a pin punch is to remove pins from a chain provided the diameter and the length of the shank are compatible with the pin dimensions
Which is the correct way of dual dimensioning using the position method
Answers
Answer:
by placing one of the two measurements below the other or by separating them with a stroke
Explanation:
I had a test on this and it was correct
How many times has the ITU-R revised the CCIR 601 international standard? A. four B. five C. six D. seven
Answers
Answer:
b or c I think it's c
Explanation:
..............
Bridge Reflection:
You’ve just spent a month either designing or designing & constructing a bridge structure. Reflect (think back on) and write a reflection essay about your recent experience with the bridge structure project. Use multiple paragraphs (2-3 sentences per paragraph) to complete your feedback. Minimum words: 500
for the following questions:
• Now that you’ve spent a month designing/making a bridge, how does it feel to be done?
• What specific steps did you enjoy the most in designing/making your bridge?
• What did you like the least (or not like at all)?
• If you could start all over again today, how would you change your method? What
would you do differently?
• What/Who was most helpful during the process of planning, cutting, and assembling
your bridge (for on campus students)?
• How could this project be improved?
• How could conditions in the shop be improved (on campus students)?
• What other thoughts would you like to share on the bridge structure design project?
Answers
Answer:
IT feels proud to be done making a bridge
Explanation:
Compare similarities between the inventions of Thomas Edison and Bill Gated
Answers
Help me with this for brainiest:)
Answers
Explain how Peccerelli's team identifies the bodies they find.
Answers
Answer:
Two methods are;
DNA
Forensic anthropology
Explanation:
Forensic investigators may use DNA samples to classify suspects or evaluate parentage. A DNA profile is just like a fingerprint.
Digital forensics is a particular sub-field of forensic science that incorporates the application of archaeological skeletal research and methods to solve crime crimes.
Answer:
They identified the bodies using DNA and forensic anthropology and DNA.
Explanation:
An example of a good electrical conductor is?
Answers
13. This type of insulation comes in rolls and is commonly a fiberglass type
material. It is applied by hand and is stapled when installed on walls. *
A. batt insulation
B. spray foam insulation
C. cellulose insulation
D. none of the above
Answers
Answer:
i think the answer is C.
Explanation:
Answer:
Can you mix cellulose and fiberglass insulation?
No. Even if you have moisture in your attic, once all bypasses are sealed (and/or your roof repaired by a qualified contractor, if necessary) cellulose is blown directly over the existing insulation. ... Adding new cellulose insulation on top of existing fiberglass insulation is called "capping".
Explanation:
What is the primary responsibility of ABET?
A. certifying engineering technologists and engineering technicians
B. administering examinations
C. accrediting educational programs worldwide
D. creating and amending ethical standards for engineers
E. accrediting high schools and universities
Answers
Answer:
C
Explanation:
The ABET (Accreditation Board for Engineering and Technology) is a non-governmental organization that accredits programs in applied science, computing, engineering, and engineering technology, both in the United States and elsewhere.
Give Brainliest pls
Answer:
Give Brainliest. Answer is C. Accrediting educational programs worldwide
Explanation:
The notes stated,
" The ABET ( Accreditation Board for Engineering and Technology ) is a non-governmental organization that accredits programs in applied science, computing, engineering, and engineering technology."
What is the Energy of moving things?
mechanical
sound
nuclear
Light
Answers
Answer: Kinetic energy
Explanation: If you live in a country other than UK you will probably call it something different
Mechanical energy is the answer
what is 18x2?????????????????
Answers
Answer:
36
Explanation:
because you add 8+8=16
you add a 1 above the other i then 1x2=2+1 =3
then you put the 6 beside the 3 and get
36
) Chain drive ratio is a the ratio between the rotational speeds of the input and output _________ of a roller chain drive system.
Answers
Answer:
Sprockets.
Explanation:
A chain drive is an efficient technique used for the transmission of mechanical power from one point to another. For example, it is used for transmitting power to the wheels of a bicycle, motorcycle, motor vehicle and other machineries such as chain saw etc.
Chain drive ratio is the ratio between the rotational speeds of the input and output sprockets of a roller chain drive system. This ultimately implies that, chain drive ratio is the ratio of the number of teeth on the driving sprocket (T1) divided to the number of teeth on the driven sprocket (T2).
Also, the chain drive ratio can be calculated by dividing the number of teeth on the large sprocket by the number of teeth on the small sprocket.
Additionally, the rotational speed of a sprocket is measured in revolutions per minute (RPM).
One of the issues with the roller chain is that, as the roller chain moves round the sprocket link by link, it affects its speed (surge) due to the change in acceleration and deceleration i.e the rise and fall of its pitch line.
Which of the following is an acronym used in mechanical plans?
Answers
Complete Question:
Which of the following is an acronym used in mechanical plans?
Group of answer choices
A. BTR
B. CAT
C. HVAC
D. TAN
Answer:
C. HVAC.
Explanation:
Mechanical plans can be defined as a construction document which typically comprises of drawings that illustrate, describe or show the placement, size, type and routes of various conduit and surface duct works and components.
An example of an acronym used in mechanical plans is HVAC.
HVAC is simply an acronym for heating, ventilation and air conditioning.
Basically, a HVAC system is a technology designed and developed to provide cooling and heating comfort (features) to vehicular and indoor environments such as submarines, cars, aeroplane, ships, restaurants, hotels, residential facilities or buildings etc.