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Dirac delta function has a continuous argument, but Kronecker delta function has a discrete argument.
Your example is a discrete signal so Kronecker delta is used.
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I assume you are working with discrete-time, since continuous-time white noise has infinite power ($\sigma^2$).
First, remember that the power of a stationary process is always equal to the autocorrelation at 0 ($P_x = R_x[0]$); and the variance is the autocovariance at 0 ($\sigma^2_x = \rm{Cov}_x[0]$). These 2 expressions are equal for processes with 0 ...
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I just don't think you're thinking this through all the way, and using the toolbox in MATLAB before you understand the basics. SNR is signal-to-noise ratio and is defined as $\text{SNR}=\frac{\text{Signal Power}}{\text{Noise Power}}$. When you call snr(signal, noise) in MATLAB, all it is doing is calculating the signal power, mean(abs(signal).^2), and the ...
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Below is a function which I wrote long back, when I needed to generate AWGN time-domain samples given Noise PSD in dBm/Hz.
AWGN_NOISE() : Generates Additive White Gaussian Noise of PSD power in dBm/Hz
AWGN has Gaussian PDF with 0 mean and $\sigma^{2} = N_{o}/2$
Noise Spectrum in $dBm/Hz = 10*log_{10}(BW*N_o/2)$, hence
$\sigma$ = $\sqrt{No/2} = \sqrt{10^{...
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See "ePeriodicity: Mining Event Periodicity from Incomplete Observations" by Zhenhui Li, Jingjing Wang, and Jiawei Han (2013); preprint at https://faculty.ist.psu.edu/jessieli/Publications/tkde14.pdf
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