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BlackZzzverrR [31]
3 years ago
15

H is a discrete-time LTI system with impulse response h[n] = δ[n] − 2δ[n − 1] + 3δ[n − 2]. Find the output signal y[n] in terms

of the input signal x[n] (use the convolution equation and the properties of convolution with deltas). Hint: since the input signal x[n] is unknown, your answer should express the output signal y[n] as a linear combination of the shifts of x[n].
Mathematics
1 answer:
n200080 [17]3 years ago
4 0

Answer:

The output is given as y(n)=x[n]-2x[n-1]+3x[n-2]

Step-by-step explanation:

As the output is given as y(n) and the input is given as x(n) thus the

equation of the output is given as

y(n)=h(n)*x(n)

Here the impulse response h(n) is given as

h(n)=\delta[n]-2\delta[n-1]+3\delta[n-2]

So the output is given as

y(n)=h(n)*x(n)\\y(n)=(\delta[n]-2\delta[n-1]+3\delta[n-2])*x(n)

By distributive property,(ax1[n] + bx2[n]) * h[n] = ax1[n] * h[n] + bx2[n] * h[n]

y(n)=h(n)*x(n)\\y(n)=\delta[n]*x(n)-2\delta[n-1]*x(n)+3\delta[n-2]*x(n)

Now by the convolution properties with delta \delta[n- k] *x[n] = x[n-k]

so

y(n)=\delta[n]*x(n)-2\delta[n-1]*x(n)+3\delta[n-2]*x(n)\\y(n)=\delta[n-0]*x(n)-2\delta[n-1]*x(n)+3\delta[n-2]*x(n)\\y(n)=x[n]-2x[n-1]+3x[n-2]

So the output is given as y(n)=x[n]-2x[n-1]+3x[n-2]

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swat32

Answer:

45

Step-by-step explanation:

KL- because triangle is a isosceles

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8 0
2 years ago
9) A bookstore sold 15 books in 5 days. At
Alla [95]
1. Find the unit rate

15 books divided by 5 days = 3 books sold per day.

Since we are looking for how many days it would take the store to sell 21 bucks, we could do 21 (amount of books) divided by 3 (how much books is sold in a day).

Therefore, it will take a week / 7 days to sell 21 books.
8 0
2 years ago
The distribution of weekly salaries at a large company is right skewed with a mean of $1000 and a standard deviation of $350. Wh
Shtirlitz [24]

Answer:

68.76% probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 1000, \sigma = 350, n = 50, s = \frac{350}{\sqrt{50}} = 49.5

What is the probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50

This is the pvalue of Z when X = 1000+50 = 1050 subtracted by the pvalue of Z when X = 1000-50 = 950. So

X = 1050

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{1050-1000}{49.5}

Z = 1.01

Z = 1.01 has a pvalue of 0.8438

X = 950

Z = \frac{X - \mu}{s}

Z = \frac{950-1000}{49.5}

Z = -1.01

Z = -1.01 has a pvalue of 0.1562

0.8438 - 0.1562 = 0.6876

68.76% probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50

4 0
2 years ago
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Answer:

a). -6x³ - 12x²    b). -12     c). 12

Step-by-step explanation:

a). (g x f)(x) can also equal f(g(x))

= f (2x +4)

= -3x² (2x+4)

= -6x³ - 12x²

b). f(g(-1))

g(-1) = 2(-1) + 4

= -2 + 4

= 2

f(2) = -3x²

= -3(2)²

= -12

c). g(h(3))

h(3) = 3x-1/2

= 3(3) - 1 / 2

= 4

g(4) = 2x + 4

= 2(4) + 4

= 12

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3 years ago
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Sveta_85 [38]

Answer:

497.563

Step-by-step explanation:

(4x 100) + (9 x 10) + (7 x 1) + [5x(1/10)] + [6x (1/100))+ [3x (1/1000)]

<u>Place value chart</u> :

\begin{matrix}\text{hundreds} &\text{tens} &\text{ones} &&\text{tenths} &\text{hundredths} &\text{thousandths} \\ 4&9&7&.&5&6&3\end{matrix}

8 0
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