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1

I would say that $R$ is an estimate of the instantaneous power in $x(t)$, as opposed to the average power. But this assumes that you implement the expectation by averaging over multiple realizations of $x(t)$. In this case, the average is still a function of time, $$ R(t) = E \left\{ x^2(t) \right\},$$ and is an estimate of the instantaneous power in $x(t)$...


1

You can see how it falls out if you work through the simple case of N=2 (I've elided the 1/N for brevity) \begin{equation} \frac{(Y_{1}X_{1}^{*}+Y_{2}X_{2}^{*})(X_{1}Y_{1}^{*}+X_{2}Y_{2}^{*})} {(X_{1}X_{1}^{*}+X_{2}X_{2}^{*})(Y_{1}Y_{1}^{*}+Y_{2}Y_{2}^{*})} \end{equation} It should be pretty obvious that there are now some cross products. Multiplying through:...


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The answer is yes. Even if we could generate several realizations of the random process by conducting the random experiment a number of times. We could only have a limited number of realizations and for a limited period of time practically. Now to take expectation of the random process we will have to take freeze time and look at the distribution of the ...


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the requestor says it's not appropriate to translate "power spectrum" as "(electric power) spectrum". And I'd agree with him. Let's start with the last of your questions: Otherwise, could someone provide better explanation? What's the layman area where one meets the term "spectrum"? Right, it's this rainbow: Zátonyi Sándor, (...


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The power spectral density (PSD) is a natural measure of the signal's power content with respect to frequency. A central part of non-parametric signal processing is to provide a "best" estimate of the "true" PSD from knowing only one or some "realizations" with finite length. By taking into account the influence of stationary ...


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I'd assume you'd divide each PSD value by the square root of the signal energy, thereby bringing the energy to 1. Energy is the sum of all squares.


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The Fourier Transform of stationary white noise exists: in fact "white" here refers to the characteristics of the Fourier Transform, in that the power spectral density will be constant over the entire spectrum, and also implies that each sample in the time domain is independent of all other samples. The distribution of the magnitude of the samples in time ...


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Note that the MATLAB result is floating point (or may be fixed point but with much higher precision) while the VSA hardware is fixed point with lower precision that also has dynamic range limitations in the analog portion of the hardware as well. To see this directly and more clearly, try these two experiments: Create a single carrier tone and capture ...


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I would strongly suggest oversampling at a frequency much higher than the bandwidth of concern, and specifically setting up the test with proper filtering to ensure that there is insignificant energy beyond half the sampling rate or $f_s/2$ (assuming real sampling). This would imply using a low pass filter prior to the sampler and also reviewing the ...


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I've ended up at a workable solution. To deal with the noise, average the CPSD results of many realizations of the noise. Pxy_AvB_mat = zeros(512/2+1,nRealizations); %preallocate Pxy_BvC_mat = zeros(512/2+1,nRealizations); %preallocate for i=1:nRealizations B = 1*(rand(length(t),1)-0.5); %new realization [Cxy_AvB,freqs_AvB] = cpsd(A,B,window,100,...


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