Generate an Autoregressive Order 1 sequence given \(\phi\) and \(\sigma^2\).
gen_ar1(N, phi = 0.3, sigma2 = 1)An unsigned integer for signal length.
A double that contains autocorrection.
A double that contains process variance.
A vec containing the AR(1) process.
The Autoregressive order 1 (AR1) process with non-zero parameter \(\phi \in (-1,+1)\) and \(\sigma^2 \in {\rm I\!R}^{2}\). This process is defined as: $${X_t} = {\phi _1}{X_{t - 1}} + {\varepsilon_t} $$, where $${\varepsilon_t}\mathop \sim \limits^{iid} N\left( {0,\sigma^2} \right)$$ AR(1) processes are sometimes used as an approximation for Bias Instability noises.
The function first generates a vector of White Noise with length \(N+1\) using gen_wn and then obtains the
autoregressive values under the above process definition.
The \(X_0\) (first value of \(X_t\)) is discarded.
The function implements a way to generate the AR(1)'s \(x_t\) values without calling the general ARMA function.
Thus, the function is able to generate values much faster than gen_arma.