If the autocorrelation function 𝑅𝑥𝑥(𝜏) of a signal 𝑥(𝑡) is even-symmetric around 𝜏=0, it implies that the signal 𝑥(𝑡) is real and not complex. This is because the autocorrelation function of a real signal is always even-symmetric. In other words, the signal's autocorrelation function has mirror symmetry around the vertical axis (𝜏=0). This property is a consequence of the conjugate symmetry property of the Fourier transform for real-valued signals.

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If the autocorrelation function 𝑅𝑥𝑥(𝜏) of a signal 𝑥(𝑡) is even-symmetric around 𝜏=0, it implies that the signal 𝑥(𝑡) is real and not complex. This is because the autocorrelation function of a real signal is always even-symmetric. In other words, the signal's autocorrelation function has mirror symmetry around the vertical axis (𝜏=0). This property is a consequence of the conjugate symmetry property of the Fourier transform for real-valued signals.

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If the autocorrelation function 𝑅𝑥𝑥(𝜏) of a signal 𝑥(𝑡) is even-symmetric around 𝜏=0, it implies that the signal 𝑥(𝑡) is real and not complex. This is because the autocorrelation function of a real signal is always even-symmetric. In other words, the signal's autocorrelation function has mirror symmetry around the vertical axis (𝜏=0). This property is a consequence of the conjugate symmetry property of the Fourier transform for real-valued signals.

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Consider a signal 𝑥(𝑡) with autocorrelation function 𝑅𝑥𝑥(𝜏). If 𝑅𝑥𝑥(𝜏) is even-symmetric around 𝜏=0, what can be inferred about the signal 𝑥(𝑡)?

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