Consider a signal with autocorrelation function . If is negative, what does this indicate about the signal ?Select one:a.The signal is periodic.b.The signal is non-stationary.c.The signal is deterministic.d.The signal has even symmetry.
Question
Consider a signal with autocorrelation function . If is negative, what does this indicate about the signal ?Select one:a.The signal is periodic.b.The signal is non-stationary.c.The signal is deterministic.d.The signal has even symmetry.
Solution
The autocorrelation function of a signal provides information about the similarity of a signal with a delayed version of itself. If the autocorrelation function R(τ) is negative, it indicates that the signal has a change in phase. This does not necessarily mean that the signal is periodic, non-stationary, deterministic, or has even symmetry.
a. The signal is periodic: A negative autocorrelation does not necessarily mean the signal is periodic. A periodic signal would have an autocorrelation function that is also periodic, but it could be positive or negative depending on the phase of the signal.
b. The signal is non-stationary: A negative autocorrelation does not necessarily mean the signal is non-stationary. Non-stationary signals can have any type of autocorrelation function, depending on their statistical properties.
c. The signal is deterministic: A negative autocorrelation does not necessarily mean the signal is deterministic. Deterministic signals can have any type of autocorrelation function, depending on their specific form.
d. The signal has even symmetry: A negative autocorrelation does not necessarily mean the signal has even symmetry. Even symmetric signals would have an autocorrelation function that is also even symmetric, but it could be positive or negative depending on the phase of the signal.
Therefore, a negative autocorrelation function does not provide specific information about whether the signal is periodic, non-stationary, deterministic, or has even symmetry.
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