(a) Consider an IIR system $y(n)=a y(n-1)+x(n)$. Let the product be quantized to 4 bits (excluding sign bit) by upward rounding and assume $\mathrm{y}^{\prime}(\mathrm{n})=0, \mathrm{n}<0, \mathrm{a}=+1 / 2 \mathrm{x}(\mathrm{n})=(15 / 16) \delta(\mathrm{n})$ Illustrate the possible Limit Cycle Oscillation and dead band effect in this case.
Explanation
The Limit Cycle Oscillation and dead band effect occur due to the nonlinear nature of the system. The system becomes nonlinear when the product is quantized to 4 bits (excluding sign bit) by upward rounding. The nonlinear system can exhibit Limit Cycle Oscillation and dead band effect.
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