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In the equation xq(n)=axq(n-1)+dq(n), if a < 1 then integrator is called?

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In the equation xq(n)=axq(n-1)+dq(n), if a < 1 then integrator is called?

(a) Leaky integrator

(b) Ideal integrator

(c) Ideal accumulator

(d) Both Ideal integrator & accumulator

The question was posed to me during an interview for a job.

This key question is from Oversampling A/D Converters topic in chapter Sampling and Reconstruction of Signals of Digital Signal Processing

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The correct answer is (a) Leaky integrator

Easy explanation: In the equation xq(n)=axq(n-1)+ dq(n), a < 1 results in a ”leaky integrator”.

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