Question:

The LTI system is said to be initially relaxed system when

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"Initially relaxed" implies all internal memory/storage elements (like capacitors, inductors, delay units) have zero initial values.
For such a system, the output is solely due to the input applied from that point on.
Updated On: May 22, 2025
  • Zero input produces zero output
  • Zero input produces non-zero output
  • Zero input produces an output equal to unity
  • Zero input produces an infinite output
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The Correct Option is A

Solution and Explanation

An LTI system is "initially relaxed" or "at rest" if all its initial conditions are zero before an input is applied. This means there is no stored energy in the system. A consequence of being initially relaxed is that if the input to the system is zero for all time (\(x(t)=0\) or \(x[n]=0\)), then the output will also be zero for all time (\(y(t)=0\) or \(y[n]=0\)). This is known as the zero-input zero-output (ZIZO) property for a system at rest. If a zero input produces a non-zero output, it indicates the presence of non-zero initial conditions. \[ \boxed{\text{Zero input produces zero output}} \]
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