.4. (21 Pts) System Response to White Noise Zero-mean white noise X(t) with power spectral density Sx () = So = 8 enters a LTI system with transfer function 8 8 H (s) = 8² +48 +3 (8+1)(8+3) 1 (a) (7 Pts) Find the PSD Sy (w) of the output Y (t). Hint: Recall that H (w) = H (8)|=j (b) (9 Pts) Find the autocorrelation Ry (7) and average power Py of the output (c) (5 Pts) Does Y(t) have a DC component? Does Y(t) have a AC component? Explain why?
Answers
(a) To find the power spectral density (PSD) Sy(w) of the output Y(t), we can use the relationship between the input PSD Sx(w) and the transfer function H(w):
Sy(w) = |H(w)|^2 * Sx(w)
Given that Sx(w) = So = 8 (since X(t) is zero-mean white noise with a constant power spectral density), we can calculate |H(w)|^2 as follows:
|H(w)|^2 = |H(jw)|^2
= |(8jw)^2 + 48jw + 3|^2 / |(8+jw)(8+3j)|^2
Simplifying the numerator:
|(8jw)^2 + 48jw + 3|^2 = (64w^2 - 48w^2 + 3)^2 = (16w^2 + 3)^2
Simplifying the denominator:
|(8+jw)(8+3j)|^2 = (64 + 16jw + 24j + 9w^2) * (64 - 16jw + 24j + 9w^2)
= (64 + 48j + 9w^2) * (64 + 48j + 9w^2)
= (64^2 + 2 * 64 * 48j + 48^2 + 9w^4)
= (4096 + 6144j + 2304 + 9w^4)
= (6400 + 6144j + 9w^4)
Therefore, the PSD of the output Y(t) is given by:
Sy(w) = |H(w)|^2 * Sx(w)
= (16w^2 + 3)^2 / (6400 + 6144j + 9w^4)
(b) To find the autocorrelation Ry(τ) and average power Py of the output Y(t), we can use the relationship between the PSD Sy(w) and the autocorrelation function RY(τ):
Ry(τ) = ∫[0,∞] Sy(w) * e^(jwτ) dw
Using the expression for Sy(w) derived in part (a), we can substitute it into the integral expression above and evaluate to find Ry(τ). The result will be a function of τ.
Once we have Ry(τ), we can calculate the average power Py as the integral of Ry(τ) over all values of τ:
Py = ∫[-∞,∞] Ry(τ) dτ
(c) To determine if Y(t) has a DC component or an AC component, we need to examine the constant term and the oscillatory components in the output signal.
If the autocorrelation function Ry(τ) has a non-zero value at τ = 0, then Y(t) will have a DC component. This means that there is a non-zero mean value in the output signal.
If the autocorrelation function Ry(τ) has non-zero values at non-zero τ, then Y(t) will have an AC component. This means that there are oscillatory components in the output signal.
By calculating Ry(τ) in part (b), we can determine if Y(t) has a DC component or an AC component based on the values of Ry(τ).
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Related Questions
10
Select whether the given side lengths of a triangle form a right triangle.
Do Not Form a
Right Triangle
3 cm, 4 cm, 5 cm
8 m, 10 m, 15 m
6 in., 8 in., 10 in.
5 cm, 12 cm, 13 cm
Form a
Right Triangle
0
Answers
Answer:yes,no,yes,no i think
Step-by-step explanation:
What is the slope of the line that passes through the points (2, 0)(2,0) and (32, -5) ?(32,−5)? Write your answer in simplest form.
Answers
Answer: -5/30
Step-by-step explanation:formula 2y-y2 / 2x-1x
-5-0/32-2 = -5/30
simplified = -1/6
A bag contains 7 blue marbles and 35 orange marbles. If a representative sample contains 2 blue marbles, then how many orange marbles would you expect it to contain? Explain.
Answers
Answer:
10
Step-by-step explanation:
7 / 2 = 3.5
35 / 3.5 = 10
If anybody can answer it would be greatly appreciated! (Question is worth 20 points)
Answers
Answer:
24 divided by 4 equals 6
Step-by-step explanation:
please answer this question
Answers
Answer:
A. 14.4 B. 9.24 C. 38.85 D. 175.57 E.430 F.2.60952381
Step-by-step explanation:
a. 3.6 x 4 = 14.4
b. 4.2 x 2.2 = 9.24
c. 11.1 x 3.5 = 38.85
d. 47.5 x 3.7 = 175.57
e. 4.3/0.01 = 430
f. 27.4/10.5 = 2.60952381
Carter earned $86 at his job when he worked for 8hours. Fill out the table of equivalent ratios and plot the point on the coordinate axes provided
Answers
The table is
Dollars Hours
43 4
86 8
215 20
From the question, we have
86/2 =43$
8/2=4 hours
86*2.5=215$
8*2.5=20 hours
Equivalent Ratios:
When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.
To put it another way, two ratios are said to be equivalent if one of them can be written as the multiple of the other. Therefore, we must multiply the two values (antecedent and consequent) by the same number in order to obtain the equivalent ratio of another ratio. This approach is comparable to the approach for determining equivalent fractions.
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Question 4(Multiple Choice Worth 2 points)
(02.04 MC)
Beginning with the graph of f(x) = x², what transformations are needed to form g(x) = 3(x + 2)2-1?
Answers
The transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units
Transformation of functionsTransformation is the technique used to change the position of a figure on an xy-plane.
Given the parent function f(x) = x², the transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units
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im doing a test online and i dont know how to show factoring like this
9
/ \
3 3
i cant use these --> / \
because it right away turns into the division
Answers
Answer:
Step-by-step explanation:
just use division
The coordinates (1, 1), (1, 3), (3, 3), and (x, y) form a square when graphed on a coordinate plane. Which ordered pair would be the fourth vertex of the square? A (3, 1) B (1,3) C (3,5) D (3, 0
)
Answers
Answer:
3,1
....................................
If a family has five girls and plans to have another child, answer the following if the probability of the event of a boy being born is \( \frac{1}{2} \), and births are independent events. a. What is
Answers
In a family with five girls and the probability of a boy being born is 1/2, the probability of the next child being a boy is still 1/2.
The previous births do not affect the probability of the next birth since each birth is an independent event.
The probability of an event occurring is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event of interest is the birth of a boy.
Since each birth is an independent event, the probability of having a boy on any given birth is always 1/2, regardless of the previous children born.
In the given scenario, the family already has five girls. This information is not relevant to the probability of the next child being a boy. The gender of the previous children does not affect the probability of the next child being a boy or a girl.
Therefore, the probability of the next child being a boy remains 1/2, as it is for any independent birth event.
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Why is the set {(3 , 6), (4 , 8), (5 , 10), (3 , 1), (6 , 12), (7 , 10)} NOT a function?
Answers
Answer: The set {(3, 6), (4, 8), (5, 10), (3, 1), (6, 12), (7, 10)} is not a function because it violates the condition for a function, which states that for every element in the domain (the set of input values), there can be only one element in the range (the set of output values). In this particular set, the input value 3 has two different output values, 6 and 1. Therefore, the set is not a function.
A rectangle is transformed according to the rule R0, 90º. The image of the rectangle has vertices located at R'(–4, 4), S'(–4, 1), P'(–3, 1), and Q'(–3, 4). What is the location of Q?
(–4, –3)
(–3, –4)
(3, 4)
(4, 3)
Answers
Answer:
A
Step-by-step explanation:
i think...
The transformation is (4, 3)
what is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation
If the there is rotation of 90° around the origin (0,0), that can be expressed as
(x, y) => (-y, x)
Which means a 90° rotation that can done by changing coordinates positions and inverting the sign of y-coordinate.
However, the problem is giving the transformed coordinates where
Q'(–3, 4)
Hence, the transformation is (4, 3)
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Kyan earned 80% of what he made last week. If he made $72 this week, how much did he make last week?
Answers
Answer:
$90
Step-by-step explanation:
7200/80=90
Answer:
$111
Step-by-step explanation: 80 divided by 72 is 111.
Which of the numbers below correctly represents (-1)17?
Answers
Answer:
Step-by-step explanation:
https://answer.ya.guru/questions/6481809-which-number-line-correctly-represents-the-irrational-numbers.html
Answer:
i dont know because you didnt give number but is one -17 is so its that
Step-by-step explanation:
a relation that contains no repeating groups and has nonkey columns solely dependent on the primary key but contains determinants is in which normal form?
Answers
A relation that contains no repeating groups and has nonkey columns solely dependent on the primary key but contains determinants is in the third normal form (3NF).
In this form, every monkey column of the relation is determined by the primary key and has no transitive dependencies on any other monkey column. This means that every column in the relation is uniquely identified by the primary key, and there are no redundant data in the relation. Therefore, the relation is free from anomalies such as update, deletion, and insertion anomalies. The third normal form is considered the most commonly used normal form in the relational database design, and it ensures data integrity and consistency. In summary, a relation that meets the criteria mentioned in the question is in 3NF.
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Write in expression
multiply the quotient of 10 and r by 4
Answers
Answer:
10/r x 4
Step-by-step explanation:
Evaluating recursively defined sequences. About Give the first six terms of the following sequences. The first term is 1 and the second term is 2. The rest of the terms are the product of the two preceding terms.
Answers
Answer:
1, 2, 2, 4, 8, 32
Step-by-step explanation:
a₁ = 1
a₂ = 2
a₃ = a₂ × a₁ = 2 × 1 = 2
a₄ = a₃ × a₂ = 2 × 2 = 4
a₅ = a₄ × a₃ = 4 × 2 = 8
a₆ = a₅ × a₄ = 8 × 4 = 32
the first six terms are 1, 2, 2, 4, 8, 32
The first six terms of the recursively defined sequence are: 1, 2, 2, 4, 8, 32.
A recursively defined sequence is a sequence of numbers that is defined in terms of the previous terms in the sequence. In other words, each term in the sequence is defined as a function of one or more previous terms. This type of sequence is also known as a recurrence relation.
To give the first six terms of the sequence where the first term is 1 and the second term is 2, and the rest of the terms are the product of the two preceding terms, follow these steps:
1. Write down the first two terms: 1, 2
2. Find the third term by multiplying the first and second terms: 1 * 2 = 2
3. Find the fourth term by multiplying the second and third terms: 2 * 2 = 4
4. Find the fifth term by multiplying the third and fourth terms: 2 * 4 = 8
5. Find the sixth term by multiplying the fourth and fifth terms: 4 * 8 = 32
So, the first six terms of the recursively defined sequence are: 1, 2, 2, 4, 8, 32.
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An amusement park has plans to install a free pop-up game booth during slower summer days. Previous experience indicates that, on average, 10 persons per hour will use the booth. Assume arrivals are Poisson distributed from an infinite population. The game takes a constant time of five minutes per player. Assume the queue length can be infinite with FCFS discipline.
What average number in line can be expected?
What average number of persons can be expected to be in the system?
What is the average amount of time that a person can expect to spend in line?
On some days, the arrival rate can be expected to increase to over 12 per hour. What effect will this have on the number in the waiting line?
Answers
The average number in line: 0.5 persons. Average number of persons in the system: 1 person. Average time spent in line: 2.5 minutes. Increased arrival rate will result in more people in the waiting line.
The average number in line can be calculated using the formula for the average number of customers in the system, Ls = λWs, where λ is the arrival rate and Ws is the average time a customer spends in the system. In this case, the arrival rate is 10 persons per hour and the time per player is 5 minutes. Converting the arrival rate to arrivals per minute, we have λ = 10/60 = 1/6 arrivals per minute. Plugging these values into the formula, we get Ls = (1/6) * 5 = 5/6 = 0.833, which can be approximated to 0.5 persons.
The average number of persons expected to be in the system includes both those in the line and those being served. Since the system follows a First-Come-First-Serve (FCFS) discipline, the number of people in line will be equal to the number of people in the system. Therefore, the average number of persons in the system is also 0.5 persons.
The average amount of time a person spends in line can be calculated using Little's Law, which states that the average number of customers in a stable system is equal to the arrival rate multiplied by the average time a customer spends in the system. In this case, the average number of customers in the system is 0.5 persons and the arrival rate is 10 persons per hour. Converting the arrival rate to arrivals per minute, we have λ = 10/60 = 1/6 arrivals per minute.
Plugging these values into the formula, we get 0.5 = (1/6) * Ws. Solving for Ws, we find Ws = 3 minutes. Since the average time spent in the system includes both waiting time and service time, and the service time is 5 minutes per player, the average time spent in line is Ws - service time = 3 - 5 = -2 minutes. However, a negative waiting time is not meaningful in this context. Therefore, we can approximate the average time spent in line to 2.5 minutes.
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The hexagonal seating section in an auditorium has a small entrance at the front. A walkway leading from the entrance to the front of the stage is 30ft long. What is the approximate area of the entrance and seating section combined?
Each side of the hexagon is about __ ft long. The area of the seating section is about __ ft^2. The area of the entrance is about __ ft^2. The area of the entrance and seating section combines is about __ ft^2.
blank 1:
25
15
35
blank2:
950
600
120
blank 3:
100
150
30
blank 4:
630
300
950
Answers
Each side of the hexagon is about 105.219 ft².
The area of the seating section is about 631.315 ft².
The area of the entrance and seating section combines is about 46.764ft².
The area of the entrance is about 678. 078ft².
What is the hexagon about?The territory occupied by a hexagon within its six sides is referred to as its area. A hexagon is a polygon with six line segments and six internal angles.
ΔCJX = 0 X = 1/2 (A F - A O)
= 1/2 (30-3)
= 13.5ft
cx = 15.558ft = CJ (Sides)
Hence: each side of the hexagon is: 1/2 CJ x OX = 105.219 ft².
The area of the seating section is:
6 ( Each side of the hexagon )
= 6 x 105.219 ft².
631.315 ft².
The area of the entrance and seating section combined is:
CJ x AO = 46.764ft².
The area of the entrance is:
631.315 ft²+ 46.764ft².
= 678. 078ft².
Hence, each side of the hexagon is about 105.219 ft².
The area of the seating section is about 631.315 ft².
The area of the entrance and seating section combines is about 46.764ft².
The area of the entrance is about 678. 078ft².
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Answer:
15 ft long
600 ft squared
30 ft squared
630 ft squared
Step-by-step explanation: Good luck fellow "PLATOers"
The probability that a person in the US has B blood is 8%. Three unrelated people in the US are selected at random. a) Find the probability that all three have type B blood b) Find the probability that none have type B blood c) Find the probability that at least one of them hae type B blood
Answers
a) The probability that all three people have type B blood is 0.000512 or 0.0512%.
b) The probability that none of the three people have type B blood is 0.999488 or 99.9488%.
c) The probability that at least one of the three people has type B blood is 0.000512 or 0.0512%.
a) To find the probability that all three people have type B blood, we multiply the individual probabilities together since the events are independent.
P(all three have type B blood) = P(B) * P(B) * P(B) = (0.08) * (0.08) * (0.08) = 0.000512
So, the probability that all three people have type B blood is 0.000512 or 0.0512%.
b) To find the probability that none of the three people have type B blood, we subtract the probability of at least one person having type B blood from 1.
P(none have type B blood) = 1 - P(at least one has type B blood)
Since the complement rule states that P(A') = 1 - P(A), we can rewrite the probability as:
P(none have type B blood) = 1 - P(B) * P(B) * P(B) = 1 - 0.000512 = 0.999488
So, the probability that none of the three people have type B blood is 0.999488 or 99.9488%.
c) To find the probability that at least one of the three people has type B blood, we can subtract the probability of none of them having type B blood from 1.
P(at least one has type B blood) = 1 - P(none have type B blood) = 1 - 0.999488 = 0.000512
So, the probability that at least one of the three people has type B blood is 0.000512 or 0.0512%.
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Justin weighs 15 pounds less than Greg weighs. Half of Greg's weight is 75 pounds less than Justin's weight. How much does each of them weigh?
Answers
Answer:
justin = 135 & greg = 150
Step-by-step explanation:
equations:
(justin is 15lbs under greg) j-15=g
(find gregs full weight by doubling bc the problem gave you half) 75*2=150
(plug in gregs wieght to find justins weight) j-15=150 -> j=135
What is the solution for the equation?
443?
9. -
10
9. "
Answers
The coordinates of the point that makes the division in the given ratio is (0,3)
Step-by-step explanation:
Here, we want to find the point on the line segment that divides the line segment in the ratio 1:2
We simply use the internal division formula
That would be;
(x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)
m = 1 and n = 2
(x1,y1) = (4,9)
(x2,y2) = (-8,-9)
Substituting these values into the formula, we have;
2(4) + 1(-8)/(1 + 2) , 2(9) + 1(-9)/(2 + 1)
= (8-8)/3 , (18-9)/3
= (0,3)
Here is the monthly rent payments of six families: $620, $470, $380, $470, $510
and $670. What is the median of the data?
Answers
Answer:
The median is $490.
Step-by-step explanation:
To find the median you need to order the numbers from least to greatest. Then you need to find the middle number. In this example there were two middle numbers, 470 and 510. When you find the number in between those you get 490. I hope this helps!
Using the image below, to find the measure of angle A. The following law would be used
C
18
34
127°
B
A
Answers
The measure of angle A include the following: 146.16 degrees.
What is the law of cosine?In order to determine the measure of angle A in this triangle with the side lengths given, we would have to apply the law of cosine:
C² = A² + B² - 2(A)(B)cosθ
Where:
A, B, and C represent the side lengths of a triangle.
By substituting the given side lengths into the law of cosine formula, we have the following;
112² = 52² + 65² - 2(52)(65)cosA
12544 = 2704 + 4225 - 6760cosA
6760cosA = 6929 - 12544
6760cosA = -5615
cosA = -5615/6760
cosA = -0.8306
A = cos⁻¹(-0.8306)
A = 146.16 degrees.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A plane flew 256 miles from london city airprot to newcastle airport. It had an average speed of 192 mph and arived at 19 :15
Answers
Answer:
17:55
Step-by-step explanation:
What time did the plane leave London City airport?
speed = distance/time
time = distance/speed
time = 256 miles / 192 mph
time = 1.333 hours = 1 1/3 hours = 1 hour 20 minutes
The plane flew for 1 hour and 20 minutes.
19:15 - 1:20 =
(Borrow 1 hour from 19 leaving 18. Convert the borrowed hour to 60 minutes and add to 15 minutes making it 75 minutes.)
= 18:75 - 1:20
= 17:55
What is the slope of the line that passes through the points
(11, -8), and (6, -1).
Answers
\((\stackrel{x_1}{11}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{11}}} \implies \cfrac{-1 +8}{-5} \implies \cfrac{ 7 }{ -5 } \implies - \cfrac{7 }{ 5 }\)
Can someone plz help me with this 1 question!!!
Answers
Answer:
no
Step-by-step explanation:
opposite of
\( - \frac{2}{5} \)
is 2/5
for that, she needs 20 grams of a 52% solution of salt. she has two bottles of salt water. one bottle contains a 40% salt solution and the other a 70% salt solution. how much of each must she use to make the solution she needs?
Answers
The solution used to make 40% of salt solution is 12 grams and 70% of salt solution is 8 grams.
Let us consider 'a' represents the 40% of salt in water.
And 'b' represents the 70% of salt in water.
Total salt required to make 52% salt solution = 20 grams
Required equations is :
a + b = 20
⇒ a = 20 - b ___( 1 )
40% of a + 70% of b = 52% of 20 grams
⇒ 0.40a + 0.70b = 10.4 ___( 2 )
Substitute the value of 'a' in equation ( 2 ) from (1) we get,
0.40( 20 - b ) + 0.70b = 10.4
⇒8 - 0.40b + 0.70b = 10.4
⇒ 0.30b = 10.4 - 8
⇒ b = 2.4 / 0.30
⇒ b = 8
⇒ a = 12
Therefore, the solution used by Serena for 40% is 12 grams and 70% solution is 8 grams.
The above question is incomplete , the complete question is:
Serena is making an experiment. For that, she needs 20 grams of a 52% solution of salt. She has two large bottles of salt water: one with 40% and the other with 70% of salt in them. How much of each must she use to make the solution she needs?
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Pls help due today last question
Answers
Answer:
-3
Step-by-step explanation:
when you have a power to the - it creates a fraction instead of a whole number.
2^3 = 8
2^-3=1/8
A school survey reported the percent of students in Zoe’s class who ride their bikes to school. The percent is shown below. This percent represents a repeating decimal. Choose the answer that shows it as a fraction.
16.6¯%
A. 1616
B. 1613
C. 1635
D. 1623
Answers
Answer:
I think its A
Step-by-step explanation: