The output of a system is given in difference equation form as $$y\left( k \right) = \,a\,\,y\left( {k - 1} \right) + x\left( k \right),$$ where $$x\left( k \right)$$ is the input. If $$x\left( k \right)$$ $$\, = \,\,0$$ for $$k\, \ne \,0,\,\,x\left( 0 \right)\, = \,1,$$ and $$y\left( 0 \right)\, = \,0,$$ find $$y\left( k \right)$$ for all $$k.$$ Determine the range of $$'a'$$ for which $$y\left( k \right)\,$$ is bounded.

GATE 1988 Electronics & Communication PYQ — Signals and Systems

GATE 19881988PYQOTHERanswer pendingexplanation soonmedium

Signals and Systems · Z-Transform

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Recurring concept

Z-Transform has appeared in GATE Electronics & Communication 40 times across 22 years (2016, 2018, 2020, 2024, 2025, ...).