निम्नलिखित में से कौन-सा सत्य नहीं है, यदि मान लिया जाए कि “→” फूरियर ट्रांसफार्म दर्शाता है "*" संवलन दर्शाता है, x(n) → X(ejω) and y(n) → Y(ejω)

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  1. ax(n) + by(n) → aX(e) + bY(ejω)
  2. \(x\left(n-n_{d}\right) \rightarrow e^{j \omega n_{d}}\left(e^{j \omega}\right)\)
  3. \(e^{j w_{0}} x(n) \rightarrow X\left(e^{j\left(\omega-w_{0}\right)}\right)\)
  4. x(n) * y(n) → X(e). Y(e)

Answer (Detailed Solution Below)

Option 2 : \(x\left(n-n_{d}\right) \rightarrow e^{j \omega n_{d}}\left(e^{j \omega}\right)\)
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