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maint: Merge stable to default.
author John W. Eaton <jwe@octave.org>
date Wed, 22 Feb 2017 12:58:07 -0500
parents ef4d915df748 3ac9f9ecfae5
children 194eb4bd202b
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1 ## Copyright (C) 1995-2017 Friedrich Leisch
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2 ## Copyright (C) 2010 Alois Schloegl
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3 ## Copyright (C) 2014-2016 Drew Abbot
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4 ##
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5 ## This file is part of Octave.
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6 ##
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7 ## Octave is free software; you can redistribute it and/or modify it
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8 ## under the terms of the GNU General Public License as published by
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9 ## the Free Software Foundation; either version 3 of the License, or
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10 ## (at your option) any later version.
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11 ##
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12 ## Octave is distributed in the hope that it will be useful, but
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13 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 ## GNU General Public License for more details.
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16 ##
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17 ## You should have received a copy of the GNU General Public License
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18 ## along with Octave; see the file COPYING. If not, see
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19 ## <http://www.gnu.org/licenses/>.
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20
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21 ## -*- texinfo -*-
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22 ## @deftypefn {} {[@var{Pxx}, @var{w}] =} periodogram (@var{x})
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23 ## @deftypefnx {} {[@var{Pxx}, @var{w}] =} periodogram (@var{x}, @var{win})
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24 ## @deftypefnx {} {[@var{Pxx}, @var{w}] =} periodogram (@var{x}, @var{win}, @var{nfft})
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25 ## @deftypefnx {} {[@var{Pxx}, @var{f}] =} periodogram (@var{x}, @var{win}, @var{nfft}, @var{Fs})
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26 ## @deftypefnx {} {[@var{Pxx}, @var{f}] =} periodogram (@dots{}, "@var{range}")
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27 ## @deftypefnx {} {} periodogram (@dots{})
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28 ## Return the periodogram (Power Spectral Density) of @var{x}.
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29 ##
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30 ## The possible inputs are:
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31 ##
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32 ## @table @var
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33 ## @item x
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34 ##
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35 ## data vector. If @var{x} is real-valued a one-sided spectrum is estimated.
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36 ## If @var{x} is complex-valued, or @qcode{"@var{range}"} specifies
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37 ## @qcode{"@nospell{twosided}"}, the full spectrum is estimated.
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38 ##
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39 ## @item win
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40 ## window weight data. If window is empty or unspecified a default rectangular
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41 ## window is used. Otherwise, the window is applied to the signal
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42 ## (@code{@var{x} .* @var{win}}) before computing the periodogram. The window
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43 ## data must be a vector of the same length as @var{x}.
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44 ##
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45 ## @item nfft
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46 ## number of frequency bins. The default is 256 or the next higher power of
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47 ## 2 greater than the length of @var{x}
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48 ## (@code{max (256, 2.^nextpow2 (length (x)))}). If @var{nfft} is greater
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49 ## than the length of the input then @var{x} will be zero-padded to the length
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50 ## of @var{nfft}.
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51 ##
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52 ## @item Fs
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53 ## sampling rate. The default is 1.
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54 ##
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55 ## @item range
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56 ## range of spectrum. @qcode{"@nospell{onesided}"} computes spectrum from
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57 ## [0..nfft/2+1]. @qcode{"@nospell{twosided}"} computes spectrum from
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58 ## [0..nfft-1].
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59 ## @end table
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60 ##
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61 ## The optional second output @var{w} are the normalized angular frequencies.
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62 ## For a one-sided calculation @var{w} is in the range [0, pi] if @var{nfft}
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63 ## is even and [0, pi) if @var{nfft} is odd. Similarly, for a two-sided
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64 ## calculation @var{w} is in the range [0, 2*pi] or [0, 2*pi) depending on
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65 ## @var{nfft}.
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66 ##
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67 ## If a sampling frequency is specified, @var{Fs}, then the output frequencies
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68 ## @var{f} will be in the range [0, @var{Fs}/2] or [0, @var{Fs}/2) for
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69 ## one-sided calculations. For two-sided calculations the range will be
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70 ## [0, @var{Fs}).
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71 ##
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72 ## When called with no outputs the periodogram is immediately plotted in the
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73 ## current figure window.
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74 ## @seealso{fft}
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75 ## @end deftypefn
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76
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77 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
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78 ## Description: Compute the periodogram
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79
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80 function [pxx, f] = periodogram (x, varargin)
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81
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82 ## check input arguments
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83 if (nargin < 1 || nargin > 5)
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84 print_usage ();
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85 endif
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86
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87 nfft = fs = range = window = [];
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88 j = 2;
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89 for k = 1:length (varargin)
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90 if (ischar (varargin{k}))
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91 range = varargin{k};
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92 else
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93 switch (j)
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94 case 2
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95 window = varargin{k};
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96 case 3
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97 nfft = varargin{k};
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98 case 4
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99 fs = varargin{k};
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100 endswitch
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101 j += 1;
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102 endif
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103 endfor
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104
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105 if (! isvector (x))
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106 error ("periodogram: X must be a real or complex vector");
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107 endif
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108 x = x(:); # Use column vectors from now on
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109
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110 n = rows (x);
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111
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112 if (! isempty (window))
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113 if (! isvector (window) || length (window) != n)
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114 error ("periodogram: WIN must be a vector of the same length as X");
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115 endif
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116 window = window(:);
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117 x .*= window;
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118 endif
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119
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120 if (isempty (nfft))
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121 nfft = max (256, 2.^nextpow2 (n));
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122 elseif (! isscalar (nfft))
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123 error ("periodogram: NFFT must be a scalar");
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124 endif
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125
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126 use_w_freq = isempty (fs);
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127 if (! use_w_freq && ! isscalar (fs))
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128 error ("periodogram: FS must be a scalar");
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129 endif
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130
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131 if (strcmpi (range, "onesided"))
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132 range = 1;
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133 elseif (strcmpi (range, "twosided"))
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134 range = 2;
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135 elseif (strcmpi (range, "centered"))
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136 error ('periodogram: "centered" range type is not implemented');
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137 else
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138 range = 2-isreal (x);
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139 endif
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140
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141 ## compute periodogram
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142
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143 if (n > nfft)
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144 Pxx = 0;
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145 rr = rem (length (x), nfft);
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146 if (rr)
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147 x = [x(:); zeros(nfft-rr, 1)];
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148 endif
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149 x = sum (reshape (x, nfft, []), 2);
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150 endif
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151
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152 if (! isempty (window))
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153 n = sumsq (window);
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154 endif;
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155 Pxx = (abs (fft (x, nfft))) .^ 2 / n;
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156
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157 if (use_w_freq)
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158 Pxx /= 2*pi;
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159 else
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160 Pxx /= fs;
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161 endif
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162
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163 ## generate output arguments
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164
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165 if (range == 1) # onesided
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166 if (! rem (nfft,2)) # nfft is even
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167 psd_len = nfft/2+1;
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168 Pxx = Pxx(1:psd_len) + [0; Pxx(nfft:-1:psd_len+1); 0];
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169 else # nfft is odd
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170 psd_len = (nfft+1)/2;
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171 Pxx = Pxx(1:psd_len) + [0; Pxx(nfft:-1:psd_len+1)];
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172 endif
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173 endif
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174
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175 if (nargout != 1)
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176 if (range == 1)
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177 f = (0:nfft/2)' / nfft;
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178 elseif (range == 2)
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179 f = (0:nfft-1)' / nfft;
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180 endif
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181 if (use_w_freq)
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182 f *= 2*pi; # generate w=2*pi*f
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183 else
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184 f *= fs;
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185 endif
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186 endif
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187
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188 if (nargout == 0)
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189 if (use_w_freq)
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190 plot (f/(2*pi), 10*log10 (Pxx));
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191 xlabel ("normalized frequency [x pi rad]");
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192 ylabel ("Power density [dB/rad/sample]");
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193 else
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194 plot (f, 10*log10 (Pxx));
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195 xlabel ("frequency [Hz]");
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196 ylabel ("Power density [dB/Hz]");
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197 endif
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198 grid on;
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199 title ("Periodogram Power Spectral Density Estimate");
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200 else
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201 pxx = Pxx;
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202 endif
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203
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204 endfunction
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205
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206
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207 ## FIXME: Need some functional tests
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208
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209
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210 ## Test input validation
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211 %!error periodogram ()
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212 %!error periodogram (1,2,3,4,5,6)
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213 %!error <X must be a real or complex vector> periodogram (ones (2,2))
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214 %!error <WIN must be a vector.*same length> periodogram (1:5, ones (2,2))
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215 %!error <WIN must be a vector.*same length> periodogram (1:5, 1:6)
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216 %!error <NFFT must be a scalar> periodogram (1:5, 1:5, 1:5)
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217 %!error <FS must be a scalar> periodogram (1:5, [], [], 1:5)
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218 %!error <"centered" range type is not implemented> periodogram (1:5, "centered")