The output of two LTI (Linear Time-Invariant) systems with impulse responses h1(t) and h2(t) connected in parallel is given by the convolution of the input signal with the sum of the impulse responses. Therefore, the correct answer is:

y(t) = x(t) * (h1(t) + h2(t))

Here's a step-by-step explanation:

1. In a parallel connection of LTI systems, the input signal x(t) is applied to both systems simultaneously.

2. Each system responds to the input signal according to its impulse response, producing outputs x(t) * h1(t) and x(t) * h2(t), respectively. Here, the asterisk (*) denotes convolution.

3. The total output y(t) of the parallel connection is the sum of the individual outputs, which is the convolution of the input signal with the sum of the impulse responses.

Question

The output of two LTI (Linear Time-Invariant) systems with impulse responses h1(t) and h2(t) connected in parallel is given by the convolution of the input signal with the sum of the impulse responses. Therefore, the correct answer is:

y(t) = x(t) * (h1(t) + h2(t))

Here's a step-by-step explanation:

1. In a parallel connection of LTI systems, the input signal x(t) is applied to both systems simultaneously.

2. Each system responds to the input signal according to its impulse response, producing outputs x(t) * h1(t) and x(t) * h2(t), respectively. Here, the asterisk (*) denotes convolution.

3. The total output y(t) of the parallel connection is the sum of the individual outputs, which is the convolution of the input signal with the sum of the impulse responses.

Knowee AI · Accepted Answer

The output of two LTI (Linear Time-Invariant) systems with impulse responses h1(t) and h2(t) connected in parallel is given by the convolution of the input signal with the sum of the impulse responses. Therefore, the correct answer is:

y(t) = x(t) * (h1(t) + h2(t))

Here's a step-by-step explanation:

1. In a parallel connection of LTI systems, the input signal x(t) is applied to both systems simultaneously.

2. Each system responds to the input signal according to its impulse response, producing outputs x(t) * h1(t) and x(t) * h2(t), respectively. Here, the asterisk (*) denotes convolution.

3. The total output y(t) of the parallel connection is the sum of the individual outputs, which is the convolution of the input signal with the sum of the impulse responses.

Determine the output of two LTI systems with impulse response h1 (t) and h2 (t) are connected in parallel.Group of answer choicesy(t) = x(t) * (h1(t) h2(t))y(t) = x(t) (h1(t) + h2(t))y(t) = (x(t) h1(t)) + h2(t)y(t) = x(t) + (h1(t) + h2(t))

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Determine the output of two LTI systems with impulse response h1 (t) and h2 (t) are connected in parallel.Group of answer choicesy(t) = x(t) * (h1(t) h2(t))y(t) = x(t) *(h1(t) + h2(t))y(t) = (x(t) * h1(t)) + h2(t)y(t) = x(t) + (h1(t) + h2(t))

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Determine the output of two LTI systems with impulse response h1 (t) and h2 (t) are connected in parallel.Group of answer choicesy(t) = x(t) * (h1(t) h2(t))y(t) = x(t) (h1(t) + h2(t))y(t) = (x(t) h1(t)) + h2(t)y(t) = x(t) + (h1(t) + h2(t))