Q. Consider the signal
h[n] = [( 1/2 )^n−1]{u[n + 3] − u[n − 10]}
Express A and B in terms of n so that the following equation holds:
h[n − k] ={( 1/2 )^(n-k−1), A<k<B
0, elsewhere}
To express A and B in terms of n, we need to determine the values of n where the condition in the equation holds. Let's break it down step by step.
First, let's clarify the given equation:
h[n - k] = (1/2)^(n - k - 1), A < k < B
h[n - k] = 0, elsewhere
Here, u[n] represents the unit step function, which is 1 for n >= 0 and 0 for n < 0.
Now, let's find the values of n where the condition in the equation holds:
1. When h[n - k] = (1/2)^(n - k - 1), we have:
(1/2)^(n - k - 1) = 0
This equation has no solution since (1/2) raised to any power cannot be zero. So, there is no value of n where this condition holds.
2. When h[n - k] = 0, we have:
0 = 0
This equation is always true irrespective of the values of n and k. Hence, for any value of n and k, when h[n - k] is zero, it satisfies the condition.
Therefore, there is no specific range of values for A and B in terms of n that can satisfy the given equation, as the condition (1/2)^(n - k - 1) = 0 has no solution.