Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > Consider a discrete time signal:X [n] = 0.2x...
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Consider a discrete time signal:
X [n] = 0.2xt [n − n0] − 2
A discrete transformed signal of x[n] is given by xt [n] = 5x [n + n0] + K.
The value of constant K is (Answer up to the nearest integer)
Correct answer is '10'. Can you explain this answer?
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Consider a discrete time signal:X [n] = 0.2xt [n − n0] − 2A discrete ...
Given:
Discrete time signal: X[n] = 0.2xt[n − n0] − 2
Discrete transformed signal: xt[n] = 5x[n + n0] K
To find:
Value of constant K
Explanation:
We are given a discrete time signal X[n] and its transformed signal xt[n]. We need to find the value of the constant K.
Step 1: Expressing X[n] in terms of xt[n]:
From the given information, we know that X[n] = 0.2xt[n − n0] − 2
Step 2: Expressing xt[n] in terms of X[n]:
We are also given that xt[n] = 5x[n + n0] K
We can substitute the value of X[n] in the expression for xt[n]:
xt[n] = 5(0.2xt[n − n0] − 2 + n0) K
Simplifying the expression:
xt[n] = xt[n − n0] + 5n0 K
Step 3: Comparing the two expressions for xt[n]:
By comparing the two expressions for xt[n], we can equate the corresponding terms:
xt[n] = xt[n − n0]
5n0 K = 0
For the equation to hold true, the coefficient of n0 should be zero. Therefore:
5n0 = 0
This implies that n0 = 0, as any non-zero value multiplied by zero will result in zero.
Step 4: Finding the value of K:
Substituting n0 = 0 in the expression for xt[n], we get:
xt[n] = xt[n] + 5(0) K
This simplifies to:
xt[n] = xt[n] K
To satisfy the equation, the constant K must be equal to 1.
Step 5: Rounding off the answer:
As per the question, we need to round off the answer to the nearest integer. Since K is equal to 1, the nearest integer is 1.
Conclusion:
The value of the constant K is 1 (rounded off to the nearest integer).
Discrete time signal: X[n] = 0.2xt[n − n0] − 2
Discrete transformed signal: xt[n] = 5x[n + n0] K
To find:
Value of constant K
Explanation:
We are given a discrete time signal X[n] and its transformed signal xt[n]. We need to find the value of the constant K.
Step 1: Expressing X[n] in terms of xt[n]:
From the given information, we know that X[n] = 0.2xt[n − n0] − 2
Step 2: Expressing xt[n] in terms of X[n]:
We are also given that xt[n] = 5x[n + n0] K
We can substitute the value of X[n] in the expression for xt[n]:
xt[n] = 5(0.2xt[n − n0] − 2 + n0) K
Simplifying the expression:
xt[n] = xt[n − n0] + 5n0 K
Step 3: Comparing the two expressions for xt[n]:
By comparing the two expressions for xt[n], we can equate the corresponding terms:
xt[n] = xt[n − n0]
5n0 K = 0
For the equation to hold true, the coefficient of n0 should be zero. Therefore:
5n0 = 0
This implies that n0 = 0, as any non-zero value multiplied by zero will result in zero.
Step 4: Finding the value of K:
Substituting n0 = 0 in the expression for xt[n], we get:
xt[n] = xt[n] + 5(0) K
This simplifies to:
xt[n] = xt[n] K
To satisfy the equation, the constant K must be equal to 1.
Step 5: Rounding off the answer:
As per the question, we need to round off the answer to the nearest integer. Since K is equal to 1, the nearest integer is 1.
Conclusion:
The value of the constant K is 1 (rounded off to the nearest integer).
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Consider a discrete time signal:X [n] = 0.2xt [n − n0] − 2A discrete transformed signal of x[n] is given by xt [n] = 5x [n + n0] + K.The value of constant K is (Answer up to the nearest integer)Correct answer is '10'. Can you explain this answer?
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