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<title>SPECTRUM1D</title>
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<h1 align=center>SPECTRUM1D</h1>
<a href="#NAME">NAME</a><br>
<a href="#SYNOPSIS">SYNOPSIS</a><br>
<a href="#DESCRIPTION">DESCRIPTION</a><br>
<a href="#REQUIRED ARGUMENTS">REQUIRED ARGUMENTS</a><br>
<a href="#OPTIONS">OPTIONS</a><br>
<a href="#ASCII FORMAT PRECISION">ASCII FORMAT PRECISION</a><br>
<a href="#EXAMPLES">EXAMPLES</a><br>
<a href="#SEE ALSO">SEE ALSO</a><br>
<a href="#REFERENCES">REFERENCES</a><br>
<hr>
<a name="NAME"></a>
<h2>NAME</h2>
<p style="margin-left:11%; margin-top: 1em">spectrum1d
− compute auto− [and cross− ] spectra from
one [or two] timeseries.</p>
<a name="SYNOPSIS"></a>
<h2>SYNOPSIS</h2>
<p style="margin-left:11%; margin-top: 1em"><b>spectrum1d</b>
[ <i>x[y]file</i> ] <b>−S</b><i>segment_size</i>] [
<b>−C</b>[<b>xycnpago</b>] ] [
<b>−D</b><i>dt</i> ] [ <b>−N</b><i>name_stem</i>
] [ <b>−V</b> ] [ <b>−W</b> ] [
<b>−b</b>[<b>i</b>|<b>o</b>][<b>s</b>|<b>S</b>|<b>d</b>|<b>D</b>[<i>ncol</i>]|<b>c</b>[<i>var1</i><b>/</b><i>...</i>]]
] [ <b>−f</b>[<b>i</b>|<b>o</b>]<i>colinfo</i> ]</p>
<a name="DESCRIPTION"></a>
<h2>DESCRIPTION</h2>
<p style="margin-left:11%; margin-top: 1em"><b>spectrum1d</b>
reads X [and Y] values from the first [and second] columns
on standard input [or <i>x[y]file</i>]. These values are
treated as timeseries X(t) [Y(t)] sampled at equal intervals
spaced <i>dt</i> units apart. There may be any number of
lines of input. <b>spectrum1d</b> will create file[s]
containing auto− [and cross− ] spectral density
estimates by Welch’s method of ensemble averaging of
multiple overlapped windows, using standard error estimates
from Bendat and Piersol.</p>
<p style="margin-left:11%; margin-top: 1em">The output
files have 3 columns: f or w, p, and e. f or w is the
frequency or wavelength, p is the spectral density estimate,
and e is the one standard deviation error bar size. These
files are named based on <i>name_stem</i>. If the
<b>−C</b> option is used, up to eight files are
created; otherwise only one (xpower) is written. The files
(which are ASCII unless <b>−bo</b> is set) are as
follows: <i><br>
name_stem</i>.xpower</p>
<p style="margin-left:22%;">Power spectral density of X(t).
Units of X * X * <i>dt</i>.</p>
<p style="margin-left:11%;"><i>name_stem</i>.ypower</p>
<p style="margin-left:22%;">Power spectral density of Y(t).
Units of Y * Y * <i>dt</i>.</p>
<p style="margin-left:11%;"><i>name_stem</i>.cpower</p>
<p style="margin-left:22%;">Power spectral density of the
coherent output. Units same as ypower.</p>
<p style="margin-left:11%;"><i>name_stem</i>.npower</p>
<p style="margin-left:22%;">Power spectral density of the
noise output. Units same as ypower.</p>
<p style="margin-left:11%;"><i>name_stem</i>.gain</p>
<p style="margin-left:22%;">Gain spectrum, or modulus of
the transfer function. Units of (Y / X).</p>
<p style="margin-left:11%;"><i>name_stem</i>.phase</p>
<p style="margin-left:22%;">Phase spectrum, or phase of the
transfer function. Units are radians.</p>
<p style="margin-left:11%;"><i>name_stem</i>.admit</p>
<p style="margin-left:22%;">Admittance spectrum, or real
part of the transfer function. Units of (Y / X).</p>
<p style="margin-left:11%;"><i>name_stem</i>.coh</p>
<p style="margin-left:22%;">(Squared) coherency spectrum,
or linear correlation coefficient as a function of
frequency. Dimensionless number in [0, 1]. The
Signal-to-Noise-Ratio (SNR) is coh / (1 - coh). SNR = 1 when
coh = 0.5.</p>
<a name="REQUIRED ARGUMENTS"></a>
<h2>REQUIRED ARGUMENTS</h2>
<p style="margin-left:11%; margin-top: 1em"><i>x[y]file</i></p>
<p style="margin-left:22%;">ASCII (or binary, see
<b>−bi</b>) file holding X(t) [Y(t)] samples in the
first 1 [or 2] columns. If no file is specified,
<b>spectrum1d</b> will read from standard input.</p>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="11%"></td>
<td width="3%">
<p style="margin-top: 1em" valign="top"><b>−S</b></p> </td>
<td width="8%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top"><i>segment_size</i>
is a radix-2 number of samples per window for ensemble
averaging. The smallest frequency estimated is
1.0/(<i>segment_size</i> * <i>dt</i>), while the largest is
1.0/(2 * <i>dt</i>). One standard error in power spectral
density is approximately 1.0 / sqrt(<i>n_data</i> /
<i>segment_size</i>), so if <i>segment_size</i> = 256, you
need 25,600 data to get a one standard error bar of 10%.
Cross-spectral error bars are larger and more complicated,
being a function also of the coherency.</p></td>
</table>
<a name="OPTIONS"></a>
<h2>OPTIONS</h2>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−C</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Read the first two
columns of input as samples of two timeseries, X(t) and
Y(t). Consider Y(t) to be the output and X(t) the input in a
linear system with noise. Estimate the optimum frequency
response function by least squares, such that the noise
output is minimized and the coherent output and the noise
output are uncorrelated. Optionally specify up to 8 letters
from the set { <b>x y c n p a g o</b> } in any order to
create only those output files instead of the default [all].
<b>x</b> = xpower, <b>y</b> = ypower, <b>c</b> = cpower,
<b>n</b> = npower, <b>p</b> = phase, <b>a</b> = admit,
<b>g</b> = gain, <b>o</b> = coh.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−D</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top"><i>dt</i> Set the
spacing between samples in the timeseries [Default = 1].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−N</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top"><i>name_stem</i>
Supply the name stem to be used for output files [Default =
"spectrum"].</p> </td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−V</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects verbose
mode, which will send progress reports to stderr [Default
runs "silently"].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−W</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Write Wavelength
rather than frequency in column 1 of the output file[s]
[Default = frequency, (cycles / <i>dt</i>)].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−bi</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects binary
input. Append <b>s</b> for single precision [Default is
<b>d</b> (double)]. Uppercase <b>S</b> or <b>D</b> will
force byte-swapping. Optionally, append <i>ncol</i>, the
number of columns in your binary input file if it exceeds
the columns needed by the program. Or append <b>c</b> if the
input file is netCDF. Optionally, append
<i>var1</i><b>/</b><i>var2</i><b>/</b><i>...</i> to specify
the variables to be read. [Default is 2 input columns].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−bo</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects binary
output. Append <b>s</b> for single precision [Default is
<b>d</b> (double)]. Uppercase <b>S</b> or <b>D</b> will
force byte-swapping. Optionally, append <i>ncol</i>, the
number of desired columns in your binary output file.
[Default is 2 output columns].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−f</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Special formatting
of input and/or output columns (time or geographical data).
Specify <b>i</b> or <b>o</b> to make this apply only to
input or output [Default applies to both]. Give one or more
columns (or column ranges) separated by commas. Append
<b>T</b> (absolute calendar time), <b>t</b> (relative time
in chosen <b><A HREF="gmtdefaults.html#TIME_UNIT">TIME_UNIT</A></b> since <b><A HREF="gmtdefaults.html#TIME_EPOCH">TIME_EPOCH</A></b>),
<b>x</b> (longitude), <b>y</b> (latitude), or <b>f</b>
(floating point) to each column or column range item.
Shorthand <b>−f</b>[<b>i</b>|<b>o</b>]<b>g</b> means
<b>−f</b>[<b>i</b>|<b>o</b>]0<b>x</b>,1<b>y</b>
(geographic coordinates).</p></td>
</table>
<a name="ASCII FORMAT PRECISION"></a>
<h2>ASCII FORMAT PRECISION</h2>
<p style="margin-left:11%; margin-top: 1em">The ASCII
output formats of numerical data are controlled by
parameters in your .gmtdefaults4 file. Longitude and
latitude are formatted according to
<b><A HREF="gmtdefaults.html#OUTPUT_DEGREE_FORMAT">OUTPUT_DEGREE_FORMAT</A></b>, whereas other values are
formatted according to <b><A HREF="gmtdefaults.html#D_FORMAT">D_FORMAT</A></b>. Be aware that the
format in effect can lead to loss of precision in the
output, which can lead to various problems downstream. If
you find the output is not written with enough precision,
consider switching to binary output (<b>−bo</b> if
available) or specify more decimals using the
<b><A HREF="gmtdefaults.html#D_FORMAT">D_FORMAT</A></b> setting.</p>
<a name="EXAMPLES"></a>
<h2>EXAMPLES</h2>
<p style="margin-left:11%; margin-top: 1em">Suppose data.g
is gravity data in mGal, sampled every 1.5 km. To write its
power spectrum, in mGal**2-km, to the file data.xpower,
use</p>
<p style="margin-left:11%; margin-top: 1em"><b>spectrum1d</b>
data.g <b>−S</b>256 <b>−D</b>1.5
<b>−N</b>data</p>
<p style="margin-left:11%; margin-top: 1em">Suppose in
addition to data.g you have data.t, which is topography in
meters sampled at the same points as data.g. To estimate
various features of the transfer function, considering
data.t as input and data.g as output, use</p>
<p style="margin-left:11%; margin-top: 1em">paste data.t
data.g | <b>spectrum1d −S</b>256 <b>−D</b>1.5
<b>−N</b>data <b>−C</b></p>
<a name="SEE ALSO"></a>
<h2>SEE ALSO</h2>
<p style="margin-left:11%; margin-top: 1em"><i><A HREF="GMT.html">GMT</A></i>(1),
<i><A HREF="grdfft.html">grdfft</A></i>(1)</p>
<a name="REFERENCES"></a>
<h2>REFERENCES</h2>
<p style="margin-left:11%; margin-top: 1em">Bendat, J. S.,
and A. G. Piersol, 1986, Random Data, 2nd revised ed., John
Wiley & Sons. <br>
Welch, P. D., 1967, The use of Fast Fourier Transform for
the estimation of power spectra: a method based on time
averaging over short, modified periodograms, IEEE
Transactions on Audio and Electroacoustics, Vol AU-15, No
2.</p>
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