2006issue C011
Constructing lowpass, highpass, and finite impulse response filters from one recurrence
One shared update forms the output from scaled current price, lagged prices, lagged outputs, and an optional subtraction of the price observed N bars earlier. Coefficient sets then select lowpass, highpass, or finite impulse response behavior. The plotted series begins only after the bar count exceeds the lookback N.
- A shared update forms the output from scaled current price, one-bar and two-bar lagged prices, one-bar and two-bar lagged outputs, and an optional subtraction of the price observed N bars earlier.
- Lowpass filter responses are selected by coefficient sets for exponential smoothing, a simple average, a Gaussian smoother, a Butterworth smoother, and a three-weight two-bar smoother.
- Highpass filter responses use one-pole and two-pole forms that initialize the output to zero on the first N bars, rather than copying price.
- Finite impulse response behavior is encoded by a lookback length N plus a coefficient that removes the price N bars earlier, and the plotted series is produced only after the bar count exceeds N.
How the construction is organized
The default input is the midpoint of each bar high and low, together with a selectable period used to derive several of the coefficients.
Editorial note: TradersWeek treats the historical workflow as a coefficient problem. Keep that ordered price input and the sampling period fixed, then switch among finite impulse response, lowpass, and highpass families by changing only the recurrence coefficients and the matching warm-up rule.
The shared update
A shared update forms the output from scaled current price, one-bar and two-bar lagged prices, one-bar and two-bar lagged outputs, and an optional subtraction of the price observed N bars earlier.
The recurrence coefficients that select a response from that update are an output scale, a lookback weight, a lookback length, three feedforward price weights, and two feedback output weights.
Period-derived smoothing
Several lowpass filter and highpass filter coefficients derive a smoothing factor from sine and cosine of a full cycle divided by the chosen period.
That period-derived smoothing factor is computed from trigonometric functions of a chosen cycle length rather than entered as an arbitrary constant.
Gaussian, Butterworth, and two-pole highpass filter rows share an intermediate equal to 2.415 times one minus the cosine of a full cycle over the chosen period.
Lowpass coefficient sets
A lowpass filter is a response built to retain slower variation in an ordered price series.
Lowpass filter responses are selected by coefficient sets for exponential smoothing, a simple average, a Gaussian smoother, a Butterworth smoother, and a three-weight two-bar smoother.
Highpass forms and the warm-up rule
A highpass filter is a response built to remove a slowly varying component of price.
Highpass filter responses are selected in one-pole and two-pole forms, and those forms initialize the output to zero on the first N bars rather than copying price.
The warm-up rule is the treatment of the first N bars, either passing price through or setting the output to zero, before the recurrence is applied.
Finite impulse response encoding
A finite impulse response filter is a response whose dependence on the input is limited to a finite lookback. The shared update subtracts the price N bars earlier and, for a simple average, weights the current price by the reciprocal of N.
Finite impulse response filter behavior is encoded by a lookback length N plus a coefficient that removes the price N bars earlier, as in the simple-average and discrete-transform coefficient sets.
When the series is plotted
The plotted series is produced only after the bar count exceeds the lookback N.
All readings on this track · 7 readings
- 2006Constructing lowpass, highpass, and finite impulse response filters from one recurrence
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- 2014Constructing a roofed stochastic from highpass and lowpass stages
- 2014The dual-K highpass roofing filter is unfinished until three choices are written together
- 2015Constructing a decycler from high-pass cancellation
- 2015Constructing decycler oscillators from highpass and bandpass filters
- 2020Finite-memory truncation for cycle filters