Two discrete time systems with impulse responses h1 -n- - - -n -1- and h2 -n- - - -n -2- are connected in cascade- The overall impulse response of the cascade system is

H_1 [n] = δ [n 1] Z.T⟷ H_1 (z) = z^ 1 nbsp; h_2 [n] = δ [n 2] Z.T⟷ H_2 (z) = z^ 2 nbsp; overall impulse response in Z domain, H(z) = nbsp; H_1(z) H_2 ...

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Time Shifting Property of Z Transform

Two discrete ...

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Two discrete time systems with impulse responses $h_{1} [n] = δ [n - 1]$ and $h_{2} [n] = δ [n - 2]$ are connected in cascade. The overall impulse response of the cascade system is

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Solution

$h_{1} [n] = δ [n - 1]$ $Z . T ⟷$ $H_{1} (z) = z^{- 1}$

$h_{2} [n] = δ [n - 2]$ $Z . T ⟷$ $H_{2}$ (z) = $z^{- 2}$

overall impulse response in Z-domain,

$H (z) = H_{1} (z) H_{2} (z)$

$= z^{- 1} z^{- 2} = z^{- 3}$

Overall impulse response in discrete - time domain,

$h [n] = δ (n - 3)$

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Two discrete time systems with impulse responses h1[n]=δ[n−1] and h2[n]=δ[n−2] are connected in cascade. The overall impulse response of the cascade system is

h1[n]=δ[n−1] Z.T⟷ H1(z)=z−1 h2[n]=δ[n−2] Z.T⟷ H2 (z) = z−2 overall impulse response in Z-domain, H(z)=H1(z)H2(z) =z−1z−2=z−3 Overall impulse response in discrete - time domain, h[n]=δ(n−3)

Two discrete time systems with impulse responses $h_{1} [n] = δ [n - 1]$ and $h_{2} [n] = δ [n - 2]$ are connected in cascade. The overall impulse response of the cascade system is

$h_{1} [n] = δ [n - 1]$ $Z . T ⟷$ $H_{1} (z) = z^{- 1}$

$h_{2} [n] = δ [n - 2]$ $Z . T ⟷$ $H_{2}$ (z) = $z^{- 2}$

overall impulse response in Z-domain,

$H (z) = H_{1} (z) H_{2} (z)$

$= z^{- 1} z^{- 2} = z^{- 3}$

Overall impulse response in discrete - time domain,

$h [n] = δ (n - 3)$