Suppose we have a system defined by the function y(t) = x(t) + ax(-t) where x(t) = beʼu(t). The Laplace Transform of the output is determined to be: Y(s) = , ROC:-1 σ<1 Find the values of a and b. Input your answer as the numeric value for 106+a. Answer: When the input to a certain DT LTI system at rest is 21 n] = {1, 1}, the output is y1[n] = {1,3,1, –1}. What would be the output to the same system when the input is changed to P2 [n] = {1,1,2}? ОА. У2(п] — {2, 5, 1, 1, —1} о в. у2 п] — {1, 3, 3, 3, —2} ос. уз m] — {1,3, 3, 3, —2} O D. Y2[n] = {2, 5, 1, 1, – 1} We are given the following five facts about a real signal a(t) with Laplace transform X(s): • X(s) has exactly two poles. X(s) has no zeros in the finite s-plane X(s) has a pole at s = -1+j e4x(t) is not absolutely integrable. X(0) = 8 Determine X(s). Ο Α. X( s) 32 s2–4s+4 о В. X(:) — 16 s2+2s+2 O C. X(s) = 32 s2+4s+4 O D. X(s) = 16 s2-2s+2
Transfer function
A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.
Convolution Integral
Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is modified with the help of the other one. The process of computing it and the result function is known as convolution. After one is reversed and shifted, it is defined as the integral of the product of two functions. After producing the convolution function, the integral is evaluated for all the values of shift. The convolution integral has some similar features with the cross-correlation. The continuous or discrete variables for real-valued functions differ from cross-correlation (f * g) only by either of the two f(x) or g(x) is reflected about the y-axis or not. Therefore, it is a cross-correlation of f(x) and g(-x) or f(-x) and g(x), the cross-correlation operator is the adjoint of the operator of the convolution for complex-valued piecewise functions.
![Suppose we have a system defined by the function y(t) = x(t) + ax(-t) where x(t) = beʼu(t). The
Laplace Transform of the output is determined to be:
Y(s) =
, ROC:-1 σ<1
Find the values of a and b. Input your answer as the numeric value for 106+a.
Answer:
When the input to a certain DT LTI system at rest is 21 n] = {1, 1}, the output is y1[n] = {1,3,1, –1}. What
would be the output to the same system when the input is changed to P2 [n] = {1,1,2}?
ОА. У2(п] — {2, 5, 1, 1, —1}
о в. у2 п] — {1, 3, 3, 3, —2}
ос. уз m] — {1,3, 3, 3, —2}
O D. Y2[n] = {2, 5, 1, 1, – 1}
We are given the following five facts about a real signal a(t) with Laplace transform X(s):
• X(s) has exactly two poles.
X(s) has no zeros in the finite s-plane
X(s) has a pole at s = -1+j
e4x(t) is not absolutely integrable.
X(0) = 8
Determine X(s).
Ο Α. X( s)
32
s2–4s+4
о В. X(:) —
16
s2+2s+2
O C. X(s) =
32
s2+4s+4
O D. X(s) =
16
s2-2s+2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9cc24caa-5fae-49cf-aedc-95c8e74c6693%2F9d24a4bb-0f7e-438f-9402-1f15d91113b9%2Ftt3nqdb_processed.png&w=3840&q=75)
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