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Two systems with impulse responses h1(t) and h2(t) are connected in cascade.
Then the overall impulse response of the cascaded system is given by
Then the overall impulse response of the cascaded system is given by
- a)Product of h1(t) and h2(t)
- b)Sum of h1(t) and h2(t)
- c)Convolution of h1(t) and h2(t)
- d)Subtraction of h1(t) and h2(t)
Correct answer is option 'C'. Can you explain this answer?
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Two systems with impulse responses h1(t) and h2(t) are connected in ca...
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Explanation:
When two systems with impulse responses h1(t) and h2(t) are connected in cascade, the output of the first system becomes the input of the second system. The overall output of the cascaded system is the product of the individual outputs of the two systems.
Let x(t) be the input to the cascaded system and y1(t) and y2(t) be the individual outputs of the two systems. Then we can write:
y1(t) = h1(t) * x(t)
y2(t) = h2(t) * y1(t) = h2(t) * h1(t) * x(t)
Therefore, the overall output of the cascaded system is:
y(t) = y2(t) = h1(t) * h2(t) * x(t)
This means that the overall impulse response of the cascaded system is the convolution of the individual impulse responses of the two systems, which is given by option 'C'.
Therefore, the correct answer is option 'C' - Convolution of h1(t) and h2(t).
When two systems with impulse responses h1(t) and h2(t) are connected in cascade, the output of the first system becomes the input of the second system. The overall output of the cascaded system is the product of the individual outputs of the two systems.
Let x(t) be the input to the cascaded system and y1(t) and y2(t) be the individual outputs of the two systems. Then we can write:
y1(t) = h1(t) * x(t)
y2(t) = h2(t) * y1(t) = h2(t) * h1(t) * x(t)
Therefore, the overall output of the cascaded system is:
y(t) = y2(t) = h1(t) * h2(t) * x(t)
This means that the overall impulse response of the cascaded system is the convolution of the individual impulse responses of the two systems, which is given by option 'C'.
Therefore, the correct answer is option 'C' - Convolution of h1(t) and h2(t).
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Two systems with impulse responses h1(t) and h2(t) are connected in cascade.Then the overall impulse response of the cascaded system is given bya)Product ofh1(t) and h2(t)b)Sum ofh1(t) and h2(t)c)Convolution ofh1(t) and h2(t)d)Subtraction ofh1(t) and h2(t)Correct answer is option 'C'. Can you explain this answer?
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