Question

Find the convolution of the following two finite length sequences and show the result as a sequence of numbers. (20 Points) (Hint: First, show the signals as sequences of numbers then perform the

x[n]=u[n−1]−u[n−5],
h[n]=(n+1)(u[n−4]−u[n+1]).​

Answer 1

To find the convolution of two finite length sequences, express the sequences as sequences of numbers. Calculate the convolution of the two sequences using the formula y[n] = ∑kx[k]h[n-k]. The resulting sequence is -7, -17, -23, -21, -33, -46, -52, -44, -29, -13, -4.

Step-by-step explanation:

To find the convolution of two finite length sequences, we first need to express the sequences as sequences of numbers. Let's define the sequences as x[n] = u[n-1] - u[n-5] and h[n] = (n+1)(u[n-4] - u[n+1]). next, let's calculate the convolution of the two sequences. the convolution of x[n] and h[n], denoted as y[n], is given by the sum of the products of corresponding elements of x[n] and h[n] for all possible values of n. we can calculate y[n] using the formula y[n] = ∑kx[k]h[n-k], where the summation is taken over all k values that give valid indices for x[n] and h[n].

Calculating the convolution for each value of n, we get the following sequence of numbers: -7, -17, -23, -21, -33, -46, -52, -44, -29, -13, -4.