# filter1d¶

Time domain filtering of 1-D data tables

## Synopsis¶

**gmt filter1d** [ *table* ]
**-F****type***width*[**+h**]
[ **-D***increment* ]
[ **-E** ]
[ **-L***lack_width* ]
[ **-N***t_col* ]
[ **-Q***q_factor* ]
[ **-S***symmetry_factor* ]
[ **-T**[*min/max*/]*inc*[**+a**][**+e**|**i**|**n**] |**-T***file*|*list* ]
[ **-V**[*level*] ]
[ **-a**flags ]
[ **-b**binary ]
[ **-d**nodata[**+c***col*] ]
[ **-e**regexp ]
[ **-f**flags ]
[ **-g**gaps ]
[ **-h**headers ]
[ **-i**flags ]
[ **-j**flags ]
[ **-o**flags ]
[ **-q**flags ]
[ **-:**[**i**|**o**] ]
[ **--PAR**=*value* ]

**Note:** No space is allowed between the option flag and the associated arguments.

## Description¶

**filter1d** is a general time domain filter for multiple column time
series data. The user specifies which column is the time (i.e., the
independent variable). (See **-N** option below). The fastest operation
occurs when the input time series are equally spaced and have no gaps or
outliers and the special options are not needed. **filter1d** has
options **-L**, **-Q**, and **-S** for unevenly sampled data with gaps.
For spatial series there is an option to compute along-track distances
and use that as the independent variable for filtering.

## Required Arguments¶

*table*One or more ASCII (or binary, see

**-bi**[*ncols*][*type*]) data table file(s) holding a number of data columns. If no tables are given then we read from standard input.

**-F****type***width*[**+h**]Sets the filter

**type**. Choose among convolution and non-convolution filters. Append the filter code followed by the full filter*width*(i.e., \(6 \sigma\)) in same units as time column. By default we perform low-pass filtering. Append**+h**to select high-pass filtering. Some filters allow for optional arguments and a modifier. Available convolution filter types are:(

**b**) Boxcar: All weights are equal.(

**c**) Cosine Arch: Weights follow a cosine arch curve.(

**f**) Custom: Instead of*width*, give name of a one-column file with your own weight coefficients.(

**g**) Gaussian: Weights are given by the Gaussian function.Non-convolution filter types are:

(

**m**) Median: Returns median value.(

**p**) Maximum likelihood probability (a mode estimator): Return modal value. If more than one mode is found we return their average value. Append**+l**or**+u**if you rather want to return the lowermost or uppermost of the modal values.(

**l**) Lower: Return the minimum of all values.(

**L**) Lower: Return minimum of all positive values only.(

**u**) Upper: Return maximum of all values.(

**U**) Upper: Return maximum of all negative values only.Upper case type

**B**,**C**,**F**,**G**,**M**and**P**will use robust filter versions: i.e., before filtering we replace outliers (2.5 x L1 scale off the median, using 1.4826 * median absolute deviation [MAD] as L1 scale) with the median during filtering.In the case of

**L**|**U**it is possible that no data will pass the initial sign test; in that case the filter will return 0.0. Apart from custom coefficients (**f**), the other filters may accept variable filter widths by passing*width*as a two-column time-series file with filter widths in the second column. The filter-width file does not need to be co-registered with the data as we obtain the required filter width at each output location via interpolation. For multi-segment data files the filter file must either have the same number of segments or just a single segment to be used for all data segments.

## Optional Arguments¶

**-D***increment**increment*is used when series is**not**equidistantly sampled. Then*increment*will be the abscissae resolution, i.e., all abscissae will be rounded off to a multiple of*increment*. Alternatively, resample data with sample1d.

**-E**Include Ends of time series in output. Default loses half the filter-width of data at each end.

**-L***lack_width*Checks for Lack of data condition. If input data has a gap exceeding

*width*then no output will be given at that point [Default does not check Lack].

**-N***t_col*Indicates which column contains the independent variable (time). The left-most column is 0, while the right-most is (

*n_cols*- 1) [Default is 0].

**-Q***q_factor*Assess Quality of output value by checking mean weight in convolution. Enter

*q_factor*between 0 and 1. If mean weight <*q_factor*, output is suppressed at this point [Default does not check Quality].

**-S***symmetry_factor*Checks symmetry of data about window center. Enter a factor between 0 and 1. If ( (abs(n_left - n_right)) / (n_left + n_right) ) >

*factor*, then no output will be given at this point [Default does not check Symmetry].

**-T**[*min/max*/]*inc*[**+a**][**+e**|**i**|**n**] |**-T***file*|*list*Make evenly spaced time-steps from

*min*to*max*by*inc*[Default uses input times]. For details on array creation, see Generate 1-D Array.

**-V**[*level*]Select verbosity level [

**w**]. (See full description) (See cookbook information).

**-a**[[*col*=]*name*[,*…*]] (more …)Set aspatial column associations

*col*=*name*.

**-bi***record*[**+b**|**l**] (more …)Select native binary format for primary table input.

**-bo***record*[**+b**|**l**] (more …)Select native binary format for table output. [Default is same as input].

**-d**[**i**|**o**][**+c***col*]*nodata*(more …)Replace input columns that equal

*nodata*with NaN and do the reverse on output.

**-e**[**~**]*“pattern”*|**-e**[**~**]/*regexp*/[**i**] (more …)Only accept data records that match the given pattern.

**-f**[**i**|**o**]*colinfo*(more …)Specify data types of input and/or output columns.

**-g****x**|**y**|**z**|**d**|**X**|**Y**|**D***gap*[**u**][**+a**][**+c***col*][**+n**|**p**] (more …)Determine data gaps and line breaks.

**-h**[**i**|**o**][*n*][**+c**][**+d**][**+m***segheader*][**+r***remark*][**+t***title*] (more …)Skip or produce header record(s).

**-i***cols*[**+l**][**+d***divisor*][**+s***scale*|**d**|**k**][**+o***offset*][,*…*][,**t**[*word*]] (more …)Select input columns and transformations (0 is first column,

**t**is trailing text, append*word*to read one word only).

**-je**|**f**|**g**(more …)Determine how spherical distances are calculated.

**-o***cols*[,…][,**t**[*word*]] (more …)Select output columns (0 is first column;

**t**is trailing text, append*word*to write one word only).

**-q**[**i**|**o**][~]*rows*|*limits*[**+c***col*][**+a**|**t**|**s**] (more …)Select input or output rows or data limit(s) [all].

**-:**[**i**|**o**] (more …)Swap 1st and 2nd column on input and/or output.

**-^**or just**-**Print a short message about the syntax of the command, then exit (

**Note**: on Windows just use**-**).**-+**or just**+**Print an extensive usage (help) message, including the explanation of any module-specific option (but not the GMT common options), then exit.

**-?**or no argumentsPrint a complete usage (help) message, including the explanation of all options, then exit.

**--PAR**=*value*Temporarily override a GMT default setting; repeatable. See gmt.conf for parameters.

## Units¶

For map distance unit, append *unit* **d** for arc degree, **m** for arc
minute, and **s** for arc second, or **e** for meter [Default unless stated otherwise], **f**
for foot, **k** for km, **M** for statute mile, **n** for nautical mile,
and **u** for US survey foot. By default we compute such distances using
a spherical approximation with great circles (**-jg**) using the authalic radius
(see PROJ_MEAN_RADIUS). You can use **-jf** to perform
“Flat Earth” calculations (quicker but less accurate) or **-je** to perform
exact geodesic calculations (slower but more accurate; see
PROJ_GEODESIC for method used).

## ASCII Format Precision¶

The ASCII output formats of numerical data are controlled by parameters
in your gmt.conf file. Longitude and latitude are formatted
according to FORMAT_GEO_OUT, absolute time is
under the control of FORMAT_DATE_OUT and
FORMAT_CLOCK_OUT, whereas general floating point values are formatted
according to FORMAT_FLOAT_OUT. Be aware that the format in effect
can lead to loss of precision in ASCII output, which can lead to various
problems downstream. If you find the output is not written with enough
precision, consider switching to binary output (**-bo** if available) or
specify more decimals using the FORMAT_FLOAT_OUT setting.

## Generate 1-D Array¶

We will demonstrate the use of options for creating 1-D arrays via gmtmath.
Make an evenly spaced coordinate array from *min* to *max* in steps of *inc*, e.g.:

```
gmt math -o0 -T3.1/4.2/0.1 T =
3.1
3.2
3.3
3.4
3.5
3.6
3.7
```

Append **+b** if we should take log2 of *min* and *max*, get their nearest integers,
build an equidistant log2-array using *inc* integer increments in log2, then undo
the log2 conversion. E.g., **-T**3/20/1**+b** will produce this sequence:

```
gmt math -o0 -T3/20/1+b T =
4
8
16
```

Append **+l** if we should take log10 of *min* and *max* and build an
array where *inc* can be 1 (every magnitude), 2, (1, 2, 5 times magnitude) or 3
(1-9 times magnitude). E.g., **-T**7/135/2**+l** will produce this sequence:

```
gmt math -o0 -T7/135/2+l T =
10
20
50
100
```

For output values less frequently than every magnitude, use a negative integer *inc*:

```
gmt math -o0 -T1e-4/1e4/-2+l T =
0.0001
0.01
1
100
10000
```

Append **+i** if *inc* is a fractional number and it is cleaner to give its reciprocal
value instead. To set up times for a 24-frames per second animation lasting 1 minute, run:

```
gmt math -o0 -T0/60/24+i T =
0
0.0416666666667
0.0833333333333
0.125
0.166666666667
...
```

Append **+n** if *inc* is meant to indicate the *number* of equidistant coordinates
instead. To have exactly 5 equidistant values from 3.44 and 7.82, run:

```
gmt math -o0 -T3.44/7.82/5+n T =
3.44
4.535
5.63
6.725
7.82
```

Alternatively, let *inc* be a *file* with output coordinates in the first column,
or provide a comma-separated *list* of specific coordinates, such as the first 6
Fibonacci numbers:

```
gmt math -o0 -T0,1,1,2,3,5 T =
0
1
1
2
3
5
```

**Note**: Should you need to ensure that the coordinates are unique and sorted (in case the
*file* or *list* are not sorted or have duplicates) then supply the **+u** modifier.

If you only want a *single* value
then you must append a comma to distinguish the list from the setting of an increment.

If the module allows you to set up an absolute time series, append a valid time unit from the list
**y**ear, m**o**nth, **d**ay, **h**our, **m**inute, and **s**econd
to the given increment; add **+t** to ensure time column (or use **-f**). **Note**: The internal time
unit is still controlled independently by TIME_UNIT. The first 7 days of March 2020:

```
gmt math -o0 -T2020-03-01T/2020-03-07T/1d T =
2020-03-01T00:00:00
2020-03-02T00:00:00
2020-03-03T00:00:00
2020-03-04T00:00:00
2020-03-05T00:00:00
2020-03-06T00:00:00
2020-03-07T00:00:00
```

A few modules allow for **+a** which will paste the coordinate array to the output table.

Likewise, if the module allows you to set up a spatial distance series (with distances computed
from the first two data columns), specify a new increment as *inc* with a geospatial distance unit from the list
**d**egree (arc), **m**inute (arc), **s**econd (arc), m**e**ter, **f**oot, **k**ilometer,
**M**iles (statute), **n**autical miles, or s**u**rvey foot; see **-j** for calculation mode.
To interpolate Cartesian distances instead, you must use the special unit **c**.

Finally, if you are only providing an increment and will obtain *min* and *max* from the data, then it is
possible (*max* - *min*)/*inc* is not an integer, as required. If so, then *inc* will be adjusted to fit the range.
Alternatively, append **+e** to keep *inc* exact and adjust *max* instead (keeping *min* fixed).

## Examples¶

**Note**: Below are some examples of valid syntax for this module.
The examples that use remote files (file names starting with `@`

)
can be cut and pasted into your terminal for testing.
Other commands requiring input files are just dummy examples of the types
of uses that are common but cannot be run verbatim as written.

To filter the remote CO2 data set in the file MaunaLoa_CO2.txt (year, CO2) with a 5 year Gaussian filter, try

gmt filter1d @MaunaLoa_CO2.txt -Fg5 > CO2_trend.txt

Data along track often have uneven sampling and gaps which we do not want to interpolate using sample1d. To find the median depth in a 50 km window every 25 km along the track of cruise v3312, stored in v3312.txt, checking for gaps of 10 km and asymmetry of 0.3:

gmt filter1d v3312.txt -FM50 -T0/100000/25 -L10 -S0.3 > v3312_filt.txt

To smooth a noisy geospatial track using a Gaussian filter of full-width 100 km and not shorten the track, and add the distances to the file, use

gmt filter1d track.txt -Tk+a -E -Fg200 > smooth_track.txt