# Laguerre Filter

This study calculates and displays a Laguerre for the data given by the Input Data Input. This study is an ACSIL implementation of the Indicator given in Figures 14.5 and 14.6 of the book Cybernetic Analysis for Stocks and Futures by John Ehlers.

Let $$X$$ be a random variable denoting the Input Data, and let $$X_t$$ be the value of $$X$$ at Index $$t$$. Let the Damping Factor Input be denoted as $$\gamma$$ (Greek letter gamma).

We begin by computing the following four functions.

$$L^{(0)}_t(X,\gamma) = (1 - \gamma)X_t + \gamma L^{(0)}_{t - 1}(X,\gamma)$$
$$L^{(1)}_t(X,\gamma) = -\gamma L^{(0)}_t(X,\gamma) + L^{(0)}_{t - 1}(X,\gamma) + \gamma L^{(1)}_{t - 1}(X,\gamma)$$
$$L^{(2)}_t(X,\gamma) = -\gamma L^{(1)}_t(X,\gamma) + L^{(1)}_{t - 1}(X,\gamma) + \gamma L^{(2)}_{t - 1}(X,\gamma)$$
$$L^{(3)}_t(X,\gamma) = -\gamma L^{(2)}_t(X,\gamma) + L^{(2)}_{t - 1}(X,\gamma) + \gamma L^{(3)}_{t - 1}(X,\gamma)$$

We then denote the Laguerre Filter and Four Bar Symmetrical Finite Impulse Response Filter as $$LF_t(X,\gamma)$$ and $$X^{(S)}_t$$, respectively, and we compute them as follows.

$$LF_t(X,\gamma) = \frac{1}{6}\left(L^{(0)}_t(X,\gamma) + 2L^{(1)}_t(X,\gamma) + 2L^{(2)}_t(X,\gamma) + L^{(3)}_t(X,\gamma)\right)$$
$$X^{(S)}_t = \frac{1}{6}(X_t + 2X_{t - 1} + 2X_{t - 2} + X_{t - 3})$$

Both $$LF_t(X,\gamma)$$ and $$X^{(S)}_t$$ are displayed as Subgraphs.

#### Inputs

• Input Data
• Damping Factor: A custom Input that determines the weighting factor given to both current and previous values of the Input Data.