Question

Find the output of the system to x(n)=(0.5)∧nu[n] using two different methods: a. Find it directly using "filter" function (initial conditions are zero).

Answer 1

To find the output of the system x(n)=(0.5)∧nu[n] using the filter function, create an impulse response signal, h(n), which is given by (0.5)∧n. Then, use the filter function to convolve x(n) with h(n) and apply the initial conditions.

Step-by-step explanation:

To find the output of the system to x(n)=(0.5)∧nu[n] using the filter function, you can follow these steps:

1. Create an impulse response signal, let's call it h(n), which represents the system response to an impulse input. In this case, the impulse response is given by h(n) = (0.5)∧n.
2. Use the filter function to filter the input signal x(n) with the impulse response h(n). This can be done by convolving the two signals, which is equivalent to multiplying their respective Fourier transforms and then inversely Fourier transforming the result.
3. Apply the initial conditions, which are zero in this case.
4. Evaluate the filtered signal at the desired time indices n to obtain the output values.