Provided by: gmt_4.5.11-1build1_amd64 bug


       spectrum1d - compute auto- [and cross- ] spectra from one [or two] timeseries.


       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 ]


       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:

              Power spectral density of X(t).  Units of X * X * dt.

              Power spectral density of Y(t).  Units of Y * Y * dt.

              Power spectral density of the coherent output.  Units same as ypower.

              Power spectral density of the noise output.  Units same as ypower.

              Gain spectrum, or modulus of the transfer function.  Units of (Y / X).

              Phase spectrum, or phase of the transfer function.  Units are radians.

              Admittance spectrum, or real part of the transfer function.  Units of (Y / X).

              (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.


              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.


       -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 =

       -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

       -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).


       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.


       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


       GMT(1), grdfft(1)


       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.