DragonFly On-Line Manual Pages
SPECTRUM1D(1) Generic Mapping Tools SPECTRUM1D(1)
NAME
spectrum1d - compute auto- [and cross- ] spectra from one [or two]
timeseries.
SYNOPSIS
spectrum1d [ x[y]file ] -Ssegment_size] [ -C[xycnpago] ] [ -Ddt ] [
-Nname_stem ] [ -V ] [ -W ] [ -b[i|o][s|S|d|D[ncol]|c[var1/...]] ] [
-f[i|o]colinfo ]
DESCRIPTION
spectrum1d reads X [and Y] values from the first [and second] columns
on standard input [or x[y]file]. These values are treated as
timeseries X(t) [Y(t)] sampled at equal intervals spaced dt units
apart. There may be any number of lines of input. spectrum1d 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.
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 name_stem. If the -C option is used, up to eight files are created;
otherwise only one (xpower) is written. The files (which are ASCII
unless -bo is set) are as follows:
name_stem.xpower
Power spectral density of X(t). Units of X * X * dt.
name_stem.ypower
Power spectral density of Y(t). Units of Y * Y * dt.
name_stem.cpower
Power spectral density of the coherent output. Units same as
ypower.
name_stem.npower
Power spectral density of the noise output. Units same as
ypower.
name_stem.gain
Gain spectrum, or modulus of the transfer function. Units of (Y
/ X).
name_stem.phase
Phase spectrum, or phase of the transfer function. Units are
radians.
name_stem.admit
Admittance spectrum, or real part of the transfer function.
Units of (Y / X).
name_stem.coh
(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.
REQUIRED ARGUMENTS
x[y]file
ASCII (or binary, see -bi) file holding X(t) [Y(t)] samples in
the first 1 [or 2] columns. If no file is specified, spectrum1d
will read from standard input.
-S segment_size is a radix-2 number of samples per window for
ensemble averaging. The smallest frequency estimated is
1.0/(segment_size * dt), while the largest is 1.0/(2 * dt). One
standard error in power spectral density is approximately 1.0 /
sqrt(n_data / segment_size), so if segment_size = 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.
OPTIONS
-C 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 { x y c n p a g o } in any order to create
only those output files instead of the default [all]. x =
xpower, y = ypower, c = cpower, n = npower, p = phase, a =
admit, g = gain, o = coh.
-D dt Set the spacing between samples in the timeseries [Default =
1].
-N name_stem Supply the name stem to be used for output files
[Default = "spectrum"].
-V Selects verbose mode, which will send progress reports to stderr
[Default runs "silently"].
-W Write Wavelength rather than frequency in column 1 of the output
file[s] [Default = frequency, (cycles / dt)].
-bi Selects binary input. Append s for single precision [Default is
d (double)]. Uppercase S or D will force byte-swapping.
Optionally, append ncol, the number of columns in your binary
input file if it exceeds the columns needed by the program. Or
append c if the input file is netCDF. Optionally, append
var1/var2/... to specify the variables to be read. [Default is
2 input columns].
-bo Selects binary output. Append s for single precision [Default
is d (double)]. Uppercase S or D will force byte-swapping.
Optionally, append ncol, the number of desired columns in your
binary output file. [Default is 2 output columns].
-f Special formatting of input and/or output columns (time or
geographical data). Specify i or o 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 T
(absolute calendar time), t (relative time in chosen TIME_UNIT
since TIME_EPOCH), x (longitude), y (latitude), or f (floating
point) to each column or column range item. Shorthand -f[i|o]g
means -f[i|o]0x,1y (geographic coordinates).
ASCII FORMAT PRECISION
The ASCII output formats of numerical data are controlled by parameters
in your .gmtdefaults4 file. Longitude and latitude are formatted
according to OUTPUT_DEGREE_FORMAT, whereas other values are formatted
according to D_FORMAT. 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 (-bo if available) or
specify more decimals using the D_FORMAT setting.
EXAMPLES
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
spectrum1d data.g -S 256 -D 1.5 -N data
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
paste data.t data.g | spectrum1d -S 256 -D 1.5 -N data -C
SEE ALSO
GMT(1), grdfft(1)
REFERENCES
Bendat, J. S., and A. G. Piersol, 1986, Random Data, 2nd revised ed.,
John Wiley & Sons.
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.
GMT 4.5.14 1 Nov 2015 SPECTRUM1D(1)