.. _filter-grammar:
**************
Filter grammar
**************
SeisComP supports string-based filter definitions. This section covers available
filters and their parameters.
The filter definition supports :ref:`SeisComP filters ` and
building filter chains (operator >> or ->) as well as combining them with basic mathematical operators like
* \+ : addition
* \- : subtraction
* \* : multiplitation
* \/ : division
* \^ : power / exponentiation
* \|. \| : absolute value.
Use brackets *()* to apply the operations within before the one outside.
.. note::
Filters in |scname| are recursive allowing real-time application. Therefore,
filter artefacts, e.g. ringing, are always visible at the beginning of the traces
or after data gaps.
Example
=======
.. code-block:: sh
A(1,2)>>(B(3,4)*2+C(5,6,7))>>D(8)
where A, B, C and D are different filters configured with different parameters.
In this example a sample *s* is filtered to get the final sample *sf* passing the following stages:
#. filter sample *s* with A: *sa* = A(1,2)(*s*)
#. filter *sa* with B: *sb* = B(3,4)(*sa*)
#. *sb* = *sb* \* 2
#. filter *sa* with C: *sc* = C(5,6,7)(*sa*)
#. add *sb* and *sc*: *sbc* = *sb* + *sc*
#. filter *sbc* with D: *sf* = D(8)(*sbc*)
sf = final sample.
The default filter applied by :ref:`scautopick` for making detections is
:py:func:`RMHP(10)` >> :py:func:`ITAPER(30)` >> :py:func:`BW(4,0.7,2)` >> :py:func:`STALTA(2,80)`
It first removes the offset. Then an ITAPER of 30 seconds is applied before the data
is filtered with a fourth order Butterworth bandpass with corner frequencies of 0.7 Hz and 2 Hz.
Finally an STA/LTA filter with a short-time time window of 2 seconds and a long-term time window of
80 seconds is applied.
To apply mathematical operations on original waveforms use :py:func:`self()`, e.g.:
.. code-block:: sh
self()*-1>>A(1,2)
Test filter strings
===================
Filters can be conveniently tested without much configuration. To perform such tests
#. Open waveforms in :ref:`scrttv` or the picker window of :ref:`scolv`.
#. Open a simple graphical text editor, e.g. gedit, pluma or kwrite and write down
the filter string.
#. Mark / highlight the filter string and use the mouse to drag the filter string
onto the waveforms.
#. Observe the differences between filtered and unfiltered waveforms.
.. figure:: media/scrttv-filter.png
:align: center
:width: 10cm
scrttv with raw (blue) and filtered (black) data. The applied filter string
is shown in the lower left corner.
.. _sec-filters-list:
List of filters
===============
Multiple filter functions are available. If a filter function has no
parameter, it can be given either with parentheses, e.g. :py:func:`DIFF()`,
or without, e.g. :py:func:`DIFF`.
.. warning::
All frequencies given as parameters to filters must be below the Nyquist
frequency of the original signal. Otherwise, filtering may result in undesired
behavior of modules, e.g. stopping or showing of empty traces.
.. py:function:: AVG(timespan)
Calculates the average of preceding samples.
:param timespan: Time span in seconds
.. py:function:: BW(order, lo-freq, hi-freq)
Alias for the :py:func:`Butterworth band-pass filter, BW_BP`.
.. py:function:: BW_BP(order, lo-freq, hi-freq)
Butterworth bandpass filter (BW) realized as a causal recursive IIR (infinite impulse response)
filter. An arbitrary bandpass filter can be created for given order and corner frequencies.
:param order: The filter order
:param lo-freq: The lower corner frequency
:param hi-freq: The upper corner frequency
.. py:function:: BW_BS(order, lo-freq, hi-freq)
Butterworth band stop filter realized as a causal recursive IIR (infinite impulse response) filter
suppressing amplitudes at frequencies between *lo-freq* and *hi-freq*.
:param order: The filter order
:param lo-freq: The lower corner frequency
:param hi-freq: The upper corner frequency
.. py:function:: BW_HP(order, lo-freq)
Butterworth high-pass filter realized as a causal recursive IIR (infinite impulse response) filter.
:param order: The filter order
:param lo-freq: The corner frequency
.. py:function:: BW_HLP(order, lo-freq, hi-freq)
Butterworth high-low-pass filter realized as a combination of :py:func:`BW_HP` and :py:func:`BW_LP`.
:param order: The filter order
:param lo-freq: The lower corner frequency
:param hi-freq: The upper corner frequency
.. py:function:: BW_LP(order, hi-freq)
Butterworth low-pass filter realized as a causal recursive IIR (infinite impulse response) filter.
:param order: The filter order
:param hi-freq: The corner frequency
.. py:function:: DIFF
Differentiation filter realized as a recursive IIR (infinite impulse response) differentiation
filter.
The differentiation loop calculates for each input sample `s` the output sample `s\'`:
.. code-block:: py
s' = (s-v1) / dt
v1 = s;
.. py:function:: INT([a = 0])
Integration filter realized as a recursive IIR (infinite impulse response) integration
filter. The weights are calculated according to parameter `a` in the following way:
.. code-block:: py
a0 = ((3-a)/6) * dt
a1 = (2*(3+a)/6) * dt
a2 = ((3-a)/6) * dt
b0 = 1
b1 = 0
b2 = -1
The integration loop calculates for each input sample `s` the integrated output sample s\':
.. code-block:: py
v0 = b0*s - b1*v1 - b2*v2
s' = a0*v0 + a1*v1 + a2*v2
v2 = v1
v1 = v0
:param a: Coefficient `a`.
.. py:function:: ITAPER(timespan)
A one-sided cosine taper.
:param timespan: The timespan in seconds.
.. py:function:: MAX(timespan)
Computes the maximum within the timespan preceeding the sample.
:param timespan: The timespan in seconds
.. py:function:: MEDIAN(timespan)
Computes the median within the timespan preceeding the sample. Useful, e.g.
for despiking. The delay due to the filter may be up to its timespan.
:param timespan: The timespan in seconds
.. py:function:: MIN(timespan)
Computes the minimum within the timespan preceeding the sample.
:param timespan: The timespan in seconds
.. py:function:: RM(timespan)
A running mean filter computing the mean value within *timespan*. For a given time window in seconds the running mean is
computed from the single amplitude values and set as output. This computation
is equal to :py:func:`RHMP` with the exception that the mean is not
subtracted from single amplitudes but replaces them.
.. code-block:: sh
RMHP = self-RM
:param timespan: The timespan in seconds
.. py:function:: RMHP(timespan)
A high-pass filter realized as running mean high-pass filter. For a given time window in
seconds the running mean is subtracted from the single amplitude values. This is equivalent
to high-pass filtering the data.
Running mean high-pass of e.g. 10 seconds calculates the difference to the running mean of 10 seconds.
:param timespan: The timespan in seconds
.. py:function:: self()
The original data itself.
.. py:function:: SM5([type = 1])
A simulation of a 5-second seismometer.
:param type: The data type: either 0 (displacement), 1 (velocity) or 2 (acceleration)
.. py:function:: STALTA(sta, lta)
A STA/LTA filter is the ratio of a short-time average to a long-time average calculated
continuously in two consecutive time windows. This method is the basis for many trigger
algorithm. The short-time window is for detection of transient signal onsets whereas the
long-time window provides information about the actual seismic noise at the station.
:param sta: Short-term time window
:param lta: Long-term time window
.. py:function:: WA([type = 1[,gain=2800[,T0=0.8[,h=0.8]]]])
The simulation filter of a Wood-Anderson seismometer. The data format of the waveforms has
to be given for applying the simulation filter (displacement = 0, velocity = 1, acceleration = 2),
e.g. WA(1) is the simulation on velocity data.
:param type: The data type: 0 (displacement), 1 (velocity) or 2 (acceleration)
:param gain: The gain of the Wood-Anderson response
:param T0: The eigenperiod in seconds
:param h: The damping constant
.. py:function:: WWSSN_LP([type = 1])
The instrument simulation filter of a World-Wide Standard Seismograph Network (WWSSN) long-period seismometer.
:param type: The data type: 0 (displacement), 1 (velocity) or 2 (acceleration)
.. py:function:: WWSSN_SP([type = 1])
Analog to the WWSSN_LP, the simulation filter of the short-period seismometer of the WWSSN.
:param type: The data type: 0 (displacement), 1 (velocity) or 2 (acceleration)