For a rational system, ROC is bounded by poles.Here, we give explicit formulae for solutions of some systems of difference equations, which extend some very particular recent results in the literature and give natural explanations for them, which were omitted in the previous literature. Reason (R): For a rational system, ROC is bounded by polesĬlarification: For the rational transfer function H (z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane. Reason (R): For a causal stable system all the poles should be outside the unit circle in the z-plane.ī.ěoth A and R are true bit R is NOT the correct explanation of AĬlarification: A causal system LTI system is stable if and only if all of poles of H(z) lie inside the unit circle.ġ0.Ěssertion (A.: For the rational transfer function H(z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane. So, x(n) series has alternate zeros n =1,3,5……ĩ.Ěssertion (A.: The stability of the system is assured if the ROC includes the unit circle in z-plane. If X(z) =(z+z -3)/(z+z -1), then x(n) series has:Ĭlarification: Using the long division method divide from denominator. Only inside the unit circle but not at z =0Ĭlarification: For stable systems the poles in z plane must lie inside or on the unit circle and Minimum number of delay elements = (Maximum power of z)-(minimum power of z).Ĩ. The poles of a digital filter with linear phase response can lieĬ. Since, the characteristic equation has roots outside the unit circle, hence the system is unstable.ħ. The characteristic equation has roots z =2, 3. Reason (R): A system is unstable if the roots of the characteristic equation lie outside the unit circle.Ī.ěoth A and R are true and R is the correct explanation of Aī.ěoth A and R are true but R is NOT the correct explanation of AĬlarification: Difference equation is y (n+2)-5 y (n+1) + 6 y (n) =x (n). Numerical analysis of continuous time systemsĬlarification: Equation in discrete time systems can be difference equation which are similar to the differentiation in the continuous time systems and difference equation results in sampled data system and numerical analysis of continuous system.Ĭlarification: Difference equation are similar to the differentiation in the continuous systems and they have same function in discrete time systems and is used in discrete time analysis.ģ.ĝifference equation in discrete systems is similar to the _ in continuous systems.Ĭlarification: Difference equation are the equations used in discrete time systems and difference equations are similar to the differential equation in continuous systems.Ĥ.ĝifference equation solution yields at the sampling instants only:Ĭlarification: Difference equation are the equations used in discrete time systems and difference equations are similar to the differential equation in continuous systems solution yields at the sampling instants only.ĥ.ĝifference equation technique for higher order systems is used in:Ĭlarification: For higher order systems Z- transform which is transforming discrete time domain into z domain and is technique is convenient for analysis and design of linear sampled data systems.Ħ.Ěssertion (A.: An LTI discrete system represented by the difference equation. Control Systems Multiple Choice Questions on “Difference Equations”.ī.
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