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Which among the below specified conditions/cases of discrete time in terms of real constant ‘a’, represents the double-sided decaying exponential signal?
1. a > 1
2. 0 < a < 1
3. a < -1
4. -1 < a < 0

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Correct Answer - Option 4 : -1 < a < 0

Real exponentials: real exponential contains no imaginary numbers and are expressed simply as

\(f\left( n \right) = B{e^{\alpha n}}\)

Where both B and α are real parameters. Unlike complex exponential that oscillates, the real exponential either decays or grows depending on the value of α.

  • Decaying exponential, when α < 0
  • Growing exponential, when α > 0
Hence, from the given options, -1 < a < 0 represents the double-sided decaying exponential signal.

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