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I would assume by faults you mean breaks in a signal line such that a reflection occurs. This is indeed an application of the autocorrelation: You transmit a sequence down a transmission line. If there is any change in impendance in the the line (such a break or kink etc) then a portion of your signal will be reflected back according to the reflection ...


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The typical practice with decibels is to append the unit. Unfortunately, it's informal, so you'll see things like "dBm" in RF circuits which refers to "dB with a reference of 1mW", not "dB with a reference of 1 meter". you could: Put a note in your graph that $0\mathrm{dB} = \mathrm{1 m/s^2}$ Use "dBg" (and use 1g as your reference) Just keep the y-axis ...


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Assume $x[n]$ and $y[n]$ represent two jointly WSS (wide-sense stationary) discrete-time random processes. Further assume that they have zero means, without losing the generality. If $x[n]$ and $y[n]$ are independent, then they are also uncorrelated, and since they have zero means, they are also orthogonal; i.e. $$ E\{ x[n]y^*[n-k]\} = 0 \tag{1}$$ Let $$...


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Okay, when discussing white noise or pink noise (or red noise or brown noise or flicker) or some other random process, there is this property called the power spectrum, in which white noise has a constant value for all frequencies. But we integrate the power spectrum over all frequencies (from $-\infty$ to $+\infty$) to get power. Integrating a constant, ...


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On a straight forward approach, energy of a signal given by $E = \int \limits_{-\infty}^{+\infty}|x^2(t)|dt$ is a constant number whereas PSD can be obtained from FFT which is a function of frequency. PSD is the square of the absolute value of FFT. In either case the value of energy or PSD gives an insight of the amplitude/strength of a signal.


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I think a better definition of the power spectrum is the following: The power spectrum of $x(t)$ is the Fourier transform of the autocorrelation function of $x(t)$, where $x(t)$ can be either a deterministic power signal, or a wide-sense stationary (WSS) random process. The definition of the autocorrelation function depends on the model for $x(t)$. If $x(...


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