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The auto-correlation function Rx(τ) satisfies which one of the following properties?
- a)Rx(τ) = - Rx(-τ)
- b)Rx(τ) = Rx(-τ)
- c)Rx(τ) > - Rx(0)
- d)Rx(τ) > 1
Correct answer is option 'B'. Can you explain this answer?
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The auto-correlation function Rx(τ) satisfies which one of the fol...
T) is a mathematical function that describes how a signal or time series is correlated with itself at different time lags. It is defined as the expected value of the product of two time-shifted samples of a signal or time series, given by:
Rx(t) = E[X(t) X(t + τ)]
where X(t) is the signal or time series at time t, τ is the time lag, and E[·] denotes the expected value operator.
The auto-correlation function is a useful tool for analyzing the properties of time series data, such as their periodicity, stationarity, and spectral content. It can be used to estimate the power spectrum of a signal, which describes the distribution of its energy over different frequencies.
The auto-correlation function is related to the Fourier transform of the signal through the Wiener-Khinchin theorem, which states that the power spectral density of a stationary signal is the Fourier transform of its auto-correlation function.
In practice, the auto-correlation function is often estimated from a finite sample of data using statistical methods such as the sample auto-correlation function or the maximum likelihood estimator. These estimators are commonly used in time series analysis, signal processing, and statistical inference.
Rx(t) = E[X(t) X(t + τ)]
where X(t) is the signal or time series at time t, τ is the time lag, and E[·] denotes the expected value operator.
The auto-correlation function is a useful tool for analyzing the properties of time series data, such as their periodicity, stationarity, and spectral content. It can be used to estimate the power spectrum of a signal, which describes the distribution of its energy over different frequencies.
The auto-correlation function is related to the Fourier transform of the signal through the Wiener-Khinchin theorem, which states that the power spectral density of a stationary signal is the Fourier transform of its auto-correlation function.
In practice, the auto-correlation function is often estimated from a finite sample of data using statistical methods such as the sample auto-correlation function or the maximum likelihood estimator. These estimators are commonly used in time series analysis, signal processing, and statistical inference.
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The auto-correlation function Rx(τ) satisfies which one of the fol...
The autocorrelation function of a signal is defined as the measure of similarity or coherence between a signal and its time delayed version. Thus, autocorrelation is the correlation of a signal with itself.
Property of autocorrelation function:
- The autocorrelation function of energy signals exhibits complex conjugate symmetry, which means the real part of autocorrelation function R(τ) is an even function of delay parameter ( τ) and the imaginary part of R(τ) is an odd function of the parameter τ. Thus,
R(τ)=R∗(−τ)
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The auto-correlation function Rx(τ) satisfies which one of the following properties?a)Rx(τ) = - Rx(-τ)b)Rx(τ) = Rx(-τ)c)Rx(τ) > - Rx(0)d)Rx(τ) > 1Correct answer is option 'B'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The auto-correlation function Rx(τ) satisfies which one of the following properties?a)Rx(τ) = - Rx(-τ)b)Rx(τ) = Rx(-τ)c)Rx(τ) > - Rx(0)d)Rx(τ) > 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The auto-correlation function Rx(τ) satisfies which one of the following properties?a)Rx(τ) = - Rx(-τ)b)Rx(τ) = Rx(-τ)c)Rx(τ) > - Rx(0)d)Rx(τ) > 1Correct answer is option 'B'. Can you explain this answer?.
The auto-correlation function Rx(τ) satisfies which one of the following properties?a)Rx(τ) = - Rx(-τ)b)Rx(τ) = Rx(-τ)c)Rx(τ) > - Rx(0)d)Rx(τ) > 1Correct answer is option 'B'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The auto-correlation function Rx(τ) satisfies which one of the following properties?a)Rx(τ) = - Rx(-τ)b)Rx(τ) = Rx(-τ)c)Rx(τ) > - Rx(0)d)Rx(τ) > 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The auto-correlation function Rx(τ) satisfies which one of the following properties?a)Rx(τ) = - Rx(-τ)b)Rx(τ) = Rx(-τ)c)Rx(τ) > - Rx(0)d)Rx(τ) > 1Correct answer is option 'B'. Can you explain this answer?.
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