How do I compute impulse response?

import numpy as np import matplotlib.pyplot as plt

1. Define the system equation y[n] = -5*X[n] + 2*X[n-1] - 5*X[n-2] + 2*X[n-3]

1. Define the length of the signal (let's take a range from n=0 to n=10) n = np.arange(0, 11)

1. Create the impulse response using numpy's delta function delta = np.zeros_like(n, dtype=float) delta[n == 0] = 1 # Impulse signal at n=0

1. Initialize the output y[n] for the impulse response h = np.zeros_like(n, dtype=float)

1. Compute the impulse response for i in range(len(n)): h[i] = -5 * delta[i] + 2 * delta[i-1] - 5 * delta[i-2] + 2 * delta[i-3]

1. Print the impulse response print("Impulse Response h[n]:") for i in range(len(n)): print(f"h[{n[i]}] = {h[i]}")

1. Plot the impulse response plt.stem(n, h, use_line_collection=True) plt.title('Impulse Response h[n]') plt.xlabel('n') plt.ylabel('h[n]') plt.grid(True) plt.show()