Question

Determine the impulse response h[n] of the cascade of two LTI systems

h1​[n] = (1/2)ⁿ u[n]
h2​[n]​=(1/4​)ⁿu[n]​

Answer 1

To determine the impulse response h[n] of the cascade of two LTI systems h1[n] = (1/2)^n⋅u[n] and h2[n] = (1/4)^n⋅u[n], you need to convolve the two individual impulse responses h1[n] and h2[n].

Step-by-step explanation:

The impulse response h[n] of the cascade of two LTI systems h1[n] = (1/2)^n⋅u[n] and h2[n] = (1/4)^n⋅u[n] can be determined by convolving the two individual impulse responses, h1[n] and h2[n].

Let's calculate:

1. Calculate the impulse response h1[n] = (1/2)^n⋅u[n] by substituting n = 0, 1, 2, ... into the equation.
2. Calculate the impulse response h2[n] = (1/4)^n⋅u[n] by substituting n = 0, 1, 2, ... into the equation.
3. Convolve the two impulse responses h1[n] and h2[n] to obtain the overall impulse response h[n].

By following these steps, you'll obtain the impulse response h[n] of the cascade of the two LTI systems.