TABTREND(1NEMO) manual page

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Name

tabtrend - difference rows from previous rows

Description

tabtrend takes a single column from an ASCII table, and differences subsequent values, creating a new column that is thus one row shorter.

Note that for a gaussian signal, differencing subsequent elements will create a distribution with a noise sqrt(2) larger than the input signal.

The parameter delta= is the distance in rows to compute the trend, which enables one to compute the phase structure function of the signal (see EXAMPLES below).

Parameters

The following parameters are recognized in order; they may be given in any order if the keyword is also given. Use --help to confirm this man page is up to date.

in=: Input file name. No default.
xcol=: Column(s) to use [1]
cumul=t|f: Cumulative, instead of differences. Default: false
delta=N: How far should the neighbor in the trend analysis be? [1]
orig=t|f: Also show the original column (if selected it will be shown after the trend column [f]
first=t|f: Add the first row? [Default: f]

Examples

Create 10000 numbers gaussian distributed with dispersion 1, here are a few sequences showing a few operations that modify the observed dispersion:

n=10000
seq $n | tabmath - - ’rang(0,1)’ all seed=-1 |                             tabhist
- 
# sigma=1
seq $n | tabmath - - ’rang(0,1)’ all seed=-1 | tabsmooth - |               tabhist
-
# sigma=0.612 (sqrt(3/8)?)
seq $n | tabmath - - ’rang(0,1)’ all seed=-1 | tabtrend -  |               tabhist
-
# sigma=1.414 (sqrt(2))
seq $n | tabmath - - ’rang(0,1)’ all seed=-1 | tabsmooth - | tabtrend -  | tabhist
-
# sigma=0.5
seq $n | tabmath - - ’rang(0,1)’ all seed=-1 | tabtrend -  | tabsmooth - | tabhist
-
# sigma=0.5

Note that smoothing and trending are related, so their resulting dispersions in the last two examples do not multiply.

This also means if you don’t know if a signal had been applied a Hanning smoothing, compute the sigma before and after a difference operator. If that ratio is sqrt(2) , it means it was not, it was a pure un-correllated gaussian. However, if the ratio is sqrt(2/3) = 0.816, it was a Hanning smoothed signal to begin with.

By using different values of the delta= parameter, one can study the correlation length of the noise, .e.g to look at correlations on a scale of up to 64:

    rm -f rms.tab
    seq 10000 | tabmath - - ’rang(0,1),%2+10*sind(%1*2)’ > tab1
    for i in $(seq 64); do
       rms=(tabtrend tab1 delta=$i |tabstat - qac=t | txtpar - p0=QAC,1,4)
       echo $i $rms >> rms.tab
    done
    tabplot rms.tab

Author

Peter Teuben

Update History

26-Nov-2012    finally documented    PJT
13-oct-2014    better examples        PJT
15-jun-2016    added cumul=        PJT
26-may-2020    added orig=        PJT
1-may-2022    remove nmax= for table V2    PJT
6-jun-2022    add delta=    PJT

Table of Contents

Name
Synopsis
Description
Parameters
Examples
See Also
Author
Update History