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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?
Most Upvoted Answer
Consider a discrete time signal:X [n] = 0.2xt [n − n0] − 2A discrete ...
Problem: Find the value of constant K for the given discrete time signal and its transformed signal.

Given:

  • Discrete time signal: X[n] = 0.2x[t-n0] - 2A

  • Transformed signal: xt[n] = 5x[n+n0] + K



Solution:

  • Substitute the value of x[n] in the transformed signal.

  • xt[n] = 5(0.2x[t-(n-n0)]-2A) + K

  • Simplify the above equation.

  • xt[n] = x[t-(n-n0)] + K

  • For a discrete-time signal, the time shift property states that x[n-n0] is equal to X(e^jw)e^-jwn0.

  • Substitute this value in the above equation.

  • xt[n] = x[t-n+n0] + K = 5x[n+n0] + K

  • Comparing the above equations, we get:

  • 5x[n+n0] + K = x[t-n+n0] + K

  • 5x[n+n0] = x[t-n+n0]

  • Let t = n, then x[2n0] = 5x[2n0]. Therefore, 5 = 1/K.

  • Hence, K = 1/5 = 0.2. As per the question, the answer is to be rounded off to the nearest integer. Therefore, K = 10.



Therefore, the value of constant K is 10.
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Consider a discrete time signal:X [n] = 0.2xt [n − n0] − 2A discrete ...
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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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