Final answer:
To compute the convolution y[n] = x[n] * h[n] for the given sequences x[n] = {1, 2, -1, 0.3} and h[n] = {-1, -2, 2, 1}, you can follow these steps:
Step-by-step explanation:
To compute the convolution y[n] = x[n] * h[n] for the given sequences x[n] = {1, 2, -1, 0.3} and h[n] = {-1, -2, 2, 1}, we can perform the following steps:
- Reverse the sequence h[n] to get h[-n] = {1, 2, -2, -1}.
- Compute the partial sums of x[n] and h[-n] as follows:
- x[-2] = 0, x[-1] = 1, x[0] = 3, x[1] = 2.3, x[2] = 1.3, x[3] = 0.3, and x[4] = 0.
- h[2] = -1, h[1] = 1, h[0] = 1, h[-1] = -1, h[-2] = -2, h[-3] = 2, and h[-4] = 1.
- Compute the convolution by multiplying the corresponding elements and summing them up:
- y[0] = x[-2] * h[0] + x[-1] * h[1] + x[0] * h[2] = 0 + 1 + 3 = 4.
- y[1] = x[-2] * h[-1] + x[-1] * h[0] + x[0] * h[1] + x[1] * h[2] = 0 + 2 - 1 + 6.3 = 7.3.
- y[2] = x[-2] * h[-2] + x[-1] * h[-1] + x[0] * h[0] + x[1] * h[1] + x[2] * h[2] = 0 + 1 - 1 + 2.3 - 2.6 + 2.6 = 4.3.
- y[3] = x[-1] * h[-2] + x[0] * h[-1] + x[1] * h[0] + x[2] * h[1] + x[3] * h[2] = 1 - 1 + 1.3 - 0.6 + 0.3 = 1.
- y[4] = x[0] * h[-2] + x[1] * h[-1] + x[2] * h[0] + x[3] * h[1] + x[4] * h[2] = 3 - 2 + 1.3 + 0.6 + 0 = 2.9.
Therefore, the convolution y[n] = {4, 7.3, 4.3, 1, 2.9}.