The output of a discrete-time system is related to its input x[n] as follows: y[n] =...

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The output of a discrete-time system is related to its input x[n] as follows: y[n] = @ox[n] + ax[n-1] + a₂x[n- 2] + a3x[n - 3]. Let the operator S denote a system that shifts the input x[n] by k time units to produce x[nk]. Formulate the operator H for the system relating y[n] to x[n]. Then develop a block diagram repre- sentation for H, using (a) cascade implementation and (b) parallel implementation. Show that the system BIBO stable for all ao, 4₁, 42, and a3. is The output of a discrete-time system is related to its input x[n] as follows: y[n] = @ox[n] + ax[n-1] + a₂x[n- 2] + a3x[n - 3]. Let the operator S denote a system that shifts the input x[n] by k time units to produce x[nk]. Formulate the operator H for the system relating y[n] to x[n]. Then develop a block diagram repre- sentation for H, using (a) cascade implementation and (b) parallel implementation. Show that the system BIBO stable for all ao, 4₁, 42, and a3. is

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