Width - The weighting exponent to alter the bandwidth of the
filter.
Freq - Adjusts how responsive the filter is to variations in the
input signal.
Description:
LOWPASS is a zero lag low bandpass filter similar to the Jurik
indicator. It uses a Fast Fourier Transform to translate the input to
the frequency domain, applies a low bandpass filter and returns the
filtered signal in the real domain. It is useful a general
indicator similar to a moving average without the attendant lag.
It is extremely useful for smoothing other indicators with a
configurable delay.
The Lowpass filter comes out of Digital Signal Possessing (DSP) where
the intent is to sample a comlex (analog) waveform and filter or
decompose it into its various frequency components. The width and freq
parameters have real mathematical meanings having to do with
determining the Nyquist frequency (i.e. one half of the bandwidth of
the input signal) and the cutoff frequency for the filter. All of which
are probably not appropriate for this forum. A net search on "DSP",
"Nyquist Theorem", "Time Series Analysis", "DSP Filters", etc. will
provide a reading list for the next few years. The best book I know on
the subject is: Neural, Novel & Hybrid Algorithms for Time Series
Prediction by Timothy Masters.
As a practical matter, the standard low bandpass filters like SMA or
EMA induce a lag from the input signal while the DSP version minimizes
the lag and (in theory) makes for more responsive indicators. I would
suggest experimentation. Plot and SMA, compare with Lowpass then play
around with the parameters (ignoring the absolute values) to see if you
find it useful.
There are two input parameters:
Width (0.0 to 0.5) adjusts the weighting exponent to alter the
bandwidth of the filter i.e. the range of points considered by the
filter.
Freq (0.001 to 0.2) (in frequency units) adjusts how responsive the
filter is to variations in the input signal. Experimentation is
suggested to find the best values. (note: if the fractional ranges turn
out to be a problem for users, perhaps a range of arbitrary values
could be mapped into the acceptable ones.)
The FFT routine used was written by Laurent de Soras and freely
available for use (see notes in code).
Formula Reference:
Syntax
LOWPASS(ARRAY INPUT, Freq, Width)
Function
ARRAY INPUT can be either an
array of bars or a formula variable array of data.