Question

Consider the signal x[n] = [1 -1 1] and the impulse response of a filter h[n] = [1 2 1]. Compute the output signal.

Answer 1

To compute the output signal, we need to convolve the input signal with the impulse response of the filter. The output signal is a single value of 1.

Step-by-step explanation:

To compute the output signal, we need to convolve the input signal with the impulse response of the filter. Convolution involves shifting the impulse response and multiplying it element-wise with the input signal at each shift. Here's how it's done:

1. Shift the impulse response to the right by 1: [0 1 2 1]
2. Shift the impulse response to the right by 2: [0 0 1 2 1]
3. Multiply the shifted impulse response with the input signal at each shift:
   [1 -1 1] * [1 0 2 1] = [1 0 2 -1 -1]
4. The output signal is the sum of the products at each shift:
   [1 + 0 + 2 + (-1) + (-1)] = 1

The output signal is a single value of 1.