# Filter grammar¶

SeisComP supports string-based filter definitions. This section covers available filters and their parameters.

The filter definition supports 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 SeisComP 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¶

```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:

1. filter sample s with A: sa = A(1,2)(s)

2. filter sa with B: sb = B(3,4)(sa)

3. sb = sb * 2

4. filter sa with C: sc = C(5,6,7)(sa)

5. add sb and sc: sbc = sb + sc

6. filter sbc with D: sf = D(8)(sbc)

sf = final sample.

The default filter applied by scautopick for making detections is

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 `self()`, e.g.:

```self()*-1>>A(1,2)
```

## Test filter strings¶

Filters can be conveniently tested without much configuration. To perform such tests

1. Open waveforms in scrttv or the picker window of scolv.

2. Open a simple graphical text editor, e.g. gedit, pluma or kwrite and write down the filter string.

3. Mark / highlight the filter string and use the mouse to drag the filter string onto the waveforms.

4. Observe the differences between filtered and unfiltered waveforms. scrttv with raw (blue) and filtered (black) data. The applied filter string is shown in the lower left corner.

## List of filters¶

Multiple filter functions are available. If a filter function has no parameter, it can be given either with parentheses, e.g. `DIFF()`, or without, e.g. `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.

`AVG`(timespan)

Calculates the average of preceding samples.

Parameters

timespan – Time span in seconds

`BW`(order, lo-freq, hi-freq)

Alias for the `Butterworth band-pass filter, BW_BP`.

`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.

Parameters
• order – The filter order

• lo-freq – The lower corner frequency

• hi-freq – The upper corner frequency

`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.

Parameters
• order – The filter order

• lo-freq – The lower corner frequency

• hi-freq – The upper corner frequency

`BW_HP`(order, lo-freq)

Butterworth high-pass filter realized as a causal recursive IIR (infinite impulse response) filter.

Parameters
• order – The filter order

• lo-freq – The corner frequency

`BW_HLP`(order, lo-freq, hi-freq)

Butterworth high-low-pass filter realized as a combination of `BW_HP()` and `BW_LP()`.

Parameters
• order – The filter order

• lo-freq – The lower corner frequency

• hi-freq – The upper corner frequency

`BW_LP`(order, hi-freq)

Butterworth low-pass filter realized as a causal recursive IIR (infinite impulse response) filter.

Parameters
• order – The filter order

• hi-freq – The corner frequency

`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':

```s' = (s-v1) / dt
v1 = s;
```
`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:

```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':

```v0 = b0*s - b1*v1 - b2*v2
s' = a0*v0 + a1*v1 + a2*v2
v2 = v1
v1 = v0
```
Parameters

a – Coefficient a.

`ITAPER`(timespan)

A one-sided cosine taper.

Parameters

timespan – The timespan in seconds.

`MAX`(timespan)

Computes the maximum within the timespan preceeding the sample.

Parameters

timespan – The timespan in seconds

`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.

Parameters

timespan – The timespan in seconds

`MIN`(timespan)

Computes the minimum within the timespan preceeding the sample.

Parameters

timespan – The timespan in seconds

`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 `RHMP` with the exception that the mean is not subtracted from single amplitudes but replaces them.

```RMHP = self-RM
```
Parameters

timespan – The timespan in seconds

`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.

Parameters

timespan – The timespan in seconds

`self`()

The original data itself.

`SM5`([type = 1])

A simulation of a 5-second seismometer.

Parameters

type – The data type: either 0 (displacement), 1 (velocity) or 2 (acceleration)

`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.

Parameters
• sta – Short-term time window

• lta – Long-term time window

`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.

Parameters
• type – The data type: 0 (displacement), 1 (velocity) or 2 (acceleration)

• gain – The gain of the Wood-Anderson response

• T0 – The eigenperiod in seconds

• h – The damping constant

`WWSSN_LP`([type = 1])

The instrument simulation filter of a World-Wide Standard Seismograph Network (WWSSN) long-period seismometer.

Parameters

type – The data type: 0 (displacement), 1 (velocity) or 2 (acceleration)

`WWSSN_SP`([type = 1])

Analog to the WWSSN_LP, the simulation filter of the short-period seismometer of the WWSSN.

Parameters

type – The data type: 0 (displacement), 1 (velocity) or 2 (acceleration)