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Z-Transform of a signal x[n] is given as
X(z) = 4/z2-25,|z|<5 the="" z-transform="" of="" y[n]="nx[n]" is="" given="">
(Az2)/(z2-25)B then find the value of 'A+B'.
- a)8
- b)10
- c)12
- d)14
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Z-Transform of a signal x[n] is given asX(z) = 4/z2-25,|z|(Az2)/(z2-2...
We have from properties of Z-Transform,
If, y[n] = n.x[n]
⇒Y(z)
= 8z2/(z2 - 25)2
Thus, A = 8,B = 2
A + B = 10
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Z-Transform of a signal x[n] is given asX(z) = 4/z2-25,|z|(Az2)/(z2-2...
Given:
Z-Transform of the signal x[n] is X(z) = 4/(z^2-25)
The Z-transform of the given signal is given as X(z) = (Az^2)/(z^2-25)B
To find the values of A and B, we can equate the two expressions for X(z) and compare the coefficients of the powers of z.
Comparing the coefficients of the powers of z on both sides, we get:
4 = A
z^2 - 25 = B(z^2 - 25)
Simplifying the equation, we have:
z^2 - 25 = Bz^2 - 25B
Rearranging the equation, we get:
(B - 1)z^2 = -25B
For the equation to hold true for all values of z, the coefficients of the powers of z on both sides must be equal. Therefore, (B - 1) must be equal to 0, and -25B must also be equal to 0.
(B - 1) = 0
B = 1
-25B = 0
B = 0
Since the two equations for B result in different values, we have a contradiction.
Hence, there is no value of B that satisfies the equation.
Therefore, the correct answer is option 'B' which states that the value of B is 0.
Z-Transform of the signal x[n] is X(z) = 4/(z^2-25)
The Z-transform of the given signal is given as X(z) = (Az^2)/(z^2-25)B
To find the values of A and B, we can equate the two expressions for X(z) and compare the coefficients of the powers of z.
Comparing the coefficients of the powers of z on both sides, we get:
4 = A
z^2 - 25 = B(z^2 - 25)
Simplifying the equation, we have:
z^2 - 25 = Bz^2 - 25B
Rearranging the equation, we get:
(B - 1)z^2 = -25B
For the equation to hold true for all values of z, the coefficients of the powers of z on both sides must be equal. Therefore, (B - 1) must be equal to 0, and -25B must also be equal to 0.
(B - 1) = 0
B = 1
-25B = 0
B = 0
Since the two equations for B result in different values, we have a contradiction.
Hence, there is no value of B that satisfies the equation.
Therefore, the correct answer is option 'B' which states that the value of B is 0.
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Z-Transform of a signal x[n] is given asX(z) = 4/z2-25,|z|(Az2)/(z2-25)B then find the value of 'A+B'.a)8b)10c)12d)14Correct answer is option 'B'. Can you explain this answer?
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