Two systems with impulse responses $h_{1}$ (t) and $h_{2}$ (t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

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Solution

$In cascade connection,$

$H(s) = H_{1} (s) . H_{2} (s)$

$\Rightarrow h(t) = h_{1} (t) * h_{2} (t)$

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Similar questions

h_{1} [n] = δ [n - 1]

h_{2} [n] = δ [n - 2]

h (n) w h e r e h_{2} (n) = u (n) - u (n - 2)

y_{1} (n)

x (n) = δ (n) - δ (n - 1) .

\sum_{n = - \infty}^{\infty} y (n) =

S_{1}, S_{2}, S_{3}, S_{4}

h_{1} (t) = 1 h_{2} (t) = u (t)

h_{3} (t) = \frac{u (t)}{t + 1} h_{4} (t) = e^{- 3 t} u (t)

A cascade system having the impulse responses

h_{1} (n) ={1, - 1} and h_{2} (n) = {1, 1}

↑

↑

is shown in the figure below, where symbol ↑ denotes the time origin.

The input sequence x(n) for which the

cascade system produces an output sequence

y(n) = {1, 2, 1, -1, -2, -1} is

↑

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