Constructing a Finite Impulse Response Filter compared with Exponential smoothing

Editorial framing

This TradersWeek editorial teaches the construction of a finite-horizon smoother as an explicit signal-processing choice. The Finite Impulse Response Filter is treated as a Lowpass filter that can be compared, term by term, with Exponential smoothing, so a reader can see how lookback, lag, and retained history are designed.

Finite impulse response construction

A Finite Impulse Response Filter is constructed so that its output depends on a finite window of input samples and then drops those samples from the average once they leave that window. A simple moving average is presented as an example of a finite impulse response construction.

Exponential smoothing construction

An exponential moving average is presented as an infinite impulse response construction because it retains earlier data through recursive averaging rather than discarding it after a fixed lookback. Exponential smoothing is constructed with a closed-form update that weights the latest close by k and the previous average by one minus k, where k equals two divided by the period count plus one.

Lowpass construction

A Lowpass filter construction is defined as the complementary operation used to isolate lower-frequency trend before a highpass residual is obtained by subtracting that filtered series from the original data.

Lag and smoothing

Filter lag is defined as the number of observations by which a constructed smoother, such as a moving average, trails its input series. Smoothing is defined as a construction that reduces excess variability while still aiming to represent the underlying trend in the input series.