GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 59 of 65

Marks: +1, -0

Which of the following options is true for a LTI discrete time system that obeys the difference equation:

y[n]-a y[n-1]=b_{0} x[n]-b_{1} x[n-1]

The system is necessary causal
When $x[n]=0, n<0$ , the function $y[n] ; n>0$ is solely determined by the function $x[n]$
$y[n]$ is unaffected by the values of $x[n-k] ; k>2$
The system impulse response is non-zero at infinite many instant.

Solution:

y(z)-a z^{-1} y(z)=b_{0} x(z)-b_{1} z^{-1} x(z)

\;{y(z)}/{x(z)}=\;{b_{0}-b_{1} z^{-1}}/{1-a z^{-1}}

So, system must be causal.

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