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In the foregoing discussions, many algorithms are developed based on the assumption that the signals are complex. However, the signals received in the antennae in terms of voltage or current are real. A real sinusoid \(\cos {}(\omega t)\) may be decomposed into two complex sinusoids \(e^{j\omega t}\) and \(e^{-j\omega t}\) using the Euler’s formula \(\cos {}(\omega t) = \left (\frac {e^{j\omega t}+e^{-j\omega t}}{2}\right )\) . When the signal is assumed to be complex, a sinusoid with frequency \(\omega \) is represented as \(e^{j\omega t}\) . Hence, the input real sinusoid \(\cos {}(\omega t)\) must be preprocessed removing the \(e^{-j\omega t}\) term. Such preprocessing will be discussed in Sect. 10.2.

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Array Signal Preprocessing

  • 章节

  • 发表日期：

    2026年

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  • Yong Ching Lim,
  • Paulo S. R. Diniz,
  • Yih-Fang Huang

摘要

In the foregoing discussions, many algorithms are developed based on the assumption that the signals are complex. However, the signals received in the antennae in terms of voltage or current are real. A real sinusoid \(\cos {}(\omega t)\) may be decomposed into two complex sinusoids \(e^{j\omega t}\) and \(e^{-j\omega t}\) using the Euler’s formula \(\cos {}(\omega t) = \left (\frac {e^{j\omega t}+e^{-j\omega t}}{2}\right )\) . When the signal is assumed to be complex, a sinusoid with frequency \(\omega \) is represented as \(e^{j\omega t}\) . Hence, the input real sinusoid \(\cos {}(\omega t)\) must be preprocessed removing the \(e^{-j\omega t}\) term. Such preprocessing will be discussed in Sect. 10.2.