Frequency Domain Analysis

The frequency domain is another way to obtain the weak (wide sense) characterization of a stationary stochastic process. Consider a stationary stochastic process $y(t)$: $\mathbb{E}[y(t)]=m_y \text{…

There exists an antitrasformation: $$\gamma_y(\tau)=\frac{1}{2\pi}\int_{-\pi}^{+\pi}{\Gamma_y(\omega)e^{j\omega\tau}d\omega}$$ Notice that the variance:…

Given the $ARMA$ process $y(t)=\frac{C(z)}{A(z)}e(t)$ with $e(t) \sim WN(0,\lambda^2)$ the spectrum is given by: $$\Gamma_y(\omega)=\mid\frac{C(e^{j\omega})}{A(e^{j\omega})}\mid^2\times\lambda^2$$…