Laguerre Filter


The Laguerre Filter (LF) is a Smoothing filter based on Laguerre polynomials.
Its first term is an EMA, which is then further smoothened with a damping factor.

The damping factor may take any value between 0 and 1.
When the damping factor is set to 0, the Laguerre Filter becomes a finite impulse response (FIR) filter.
When the damping factor is set to a value close to 1, the filter becomes dramatically smoother, but will have a significant lag.

The smoothing is controlled by an alpha factor which is the alpha for the EMA and also damps the further terms.
Alpha can range from 1 to follow prices almost exactly, down to 0 for a very slow response.

The Laguerre filter (same length) has virtually the same crossing signals but is much smoother due to the introduction of the dampening factor (gamma).
If you set gamma to 0 Laguerre will be identical to the FIR filter. This filter can be used to dampen other indicators with similar results.