Question

Y(n)=(-1,3)(0)(1,2)

x(n)=(4,5,3,-2)
please use convolutıon
please calculate xn and y convolutions

Answer 1

To perform the convolution between the sequences x(n) and y(n), we reverse the sequence y(n), shift it by k units to the right, multiply each element with x(n), and sum the results. The convolution of x(n) = (4, 5, 3, -2) and y(n) = (-1, 3, 0, 1, 2) is 7.

Step-by-step explanation:

To perform the convolution between the sequences x(n) and y(n), we can follow these steps:

1. Reverse the sequence y(n) to obtain y(-n).
2. Shift the reversed sequence y(-n) by k units to the right to obtain y(-n-k).
3. Multiply each element of x(n) by the corresponding element of y(-n-k) and sum the results to get the convolution sequence.

In this case, x(n) = (4, 5, 3, -2) and y(n) = (-1, 3, 0, 1, 2). Reverse y(n) to obtain y(-n) = (2, 1, 0, 3, -1). Shift y(-n) by k = 0 units to the right to get y(-n-k) = (2, 1, 0, 3, -1). Multiply each element of x(n) with the corresponding element of y(-n-k) and sum the results:

x(n) * y(-n-k) = (4 * 2) + (5 * 1) + (3 * 0) + (-2 * 3) = 8 + 5 + 0 - 6 = 7.

Therefore, the convolution of x(n) and y(n) is 7.