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Question

# Which of the following properties of Power spectral density is/are correct?

A
The power spectral density of a stationary process is always non-negative
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B
The mean square value of a stationary process equals the total area under the graph of the power spectral density.
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C
The power spectral density of a real-valued random process is an even function of frequency.
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D
The zero frequency value of the power spectral density of a stationary process equals the total area under the graph of the autocorrelation function.
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Solution

## The correct option is D The zero frequency value of the power spectral density of a stationary process equals the total area under the graph of the autocorrelation function.(a) Sx(0)=∫∞∞Rx(τ)dτwhere Rx(τ)=Autocorrelation functionSx(f)=Power spectral density(b) E[X2(t)]=Rx(0)=∫∞−∞Sx(f)df(c) Sx(f)≥0(d) Sx(−f)=Sx(f)

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