Chapter 11: Noise Analysis
This demo shows the Autocorrelation Function (ACF) \(\varphi_{xx}[\kappa]\) and the Power Spectral Density (PSD) \(\Phi_{xx}(\mathrm e^{\mathrm{j}\Omega})\) of a random process \(x[k]\). For a single realization \(x_i[k]\) of \(x[k]\), the ACF and PSD can be calculated as: $$\varphi_{xx}[\kappa] = \sum_{k=-\infty}^\infty x_i[k+\kappa]x_i^\ast[k]$$ and $$\Phi_{xx}(\mathrm e^{\mathrm{j}\Omega}) = \mathcal F_\ast\{\varphi_{xx}[\kappa]\} = \sum_{\kappa=-\infty}^\infty \varphi_{xx}[\kappa]\mathrm e^{-\mathrm{j}k\Omega},$$ with the normalized frequency \(\Omega=\omega T\) with sampling interval \(T=\frac{1}{f_\mathrm s}\).
Input \(x[k]\)