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annotate scripts/signal/periodogram.m @ 18998:956fc864c39f

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periodogram.m: Fix bug when nfft < length (x) and "onesided" specified (bug #42859). * periodogram.m: Don't use nargin to decide when normalized frequencies should be used. Instead check whether Fs has been specified to make the decision.
author Rik <rik@octave.org>
date Thu, 07 Aug 2014 20:24:59 -0700
parents 8ac4ab4ae5f4
children
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d63878346099 maint: Update copyright notices for release.
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1995-2013 Friedrich Leisch
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2 ## Copyright (C) 2010 Alois Schloegl
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3 ## Copyright (C) 2014 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 (at
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10 ## 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 GNU
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15 ## 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 {Function File} {[@var{Pxx}, @var{w}] =} periodogram (@var{x})
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23 ## @deftypefnx {Function File} {[@var{Pxx}, @var{w}] =} periodogram (@var{x}, @var{win})
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24 ## @deftypefnx {Function File} {[@var{Pxx}, @var{w}] =} periodogram (@var{x}, @var{win}, @var{nfft})
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25 ## @deftypefnx {Function File} {[@var{Pxx}, @var{f}] =} periodogram (@var{x}, @var{win}, @var{nfft}, @var{Fs})
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26 ## @deftypefnx {Function File} {[@var{Pxx}, @var{f}] =} periodogram (@dots{}, "@var{range}")
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27 ## @deftypefnx {Function File} {} periodogram (@dots{})
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28 ##
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29 ## Return the periodogram (Power Spectral Density) of @var{x}.
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30 ##
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31 ## The possible inputs are:
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32 ##
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33 ## @table @var
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34 ## @item x
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35 ##
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36 ## data vector. If @var{x} is real-valued a one-sided spectrum is estimated.
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37 ## If @var{x} is complex-valued, or @qcode{"@var{range}"} specifies
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38 ## @qcode{"@nospell{twosided}"}, the full spectrum is estimated.
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39 ##
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40 ## @item win
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41 ## window weight data. If window is empty or unspecified a default rectangular
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42 ## window is used. Otherwise, the window is applied to the signal
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43 ## (@code{@var{x} .* @var{win}}) before computing the periodogram. The window
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44 ## data must be a vector of the same length as @var{x}.
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45 ##
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46 ## @item nfft
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47 ## number of frequency bins. The default is 256 or the next higher power of
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48 ## 2 greater than the length of @var{x}
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49 ## (@code{max (256, 2.^nextpow2 (length (x)))}). If @var{nfft} is greater
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50 ## than the length of the input then @var{x} will be zero-padded to the length
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51 ## of @var{nfft}.
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52 ##
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53 ## @item Fs
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54 ## sampling rate. The default is 1.
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55 ##
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56 ## @item range
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57 ## range of spectrum. @qcode{"@nospell{onesided}"} computes spectrum from
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58 ## [0..nfft/2+1]. @qcode{"@nospell{twosided}"} computes spectrum from
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59 ## [0..nfft-1].
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60 ## @end table
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61 ##
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62 ## The optional second output @var{w} are the normalized angular frequencies.
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63 ## For a onesided calculation @var{w} is in the range [0, pi] if @var{nfft}
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64 ## is even and [0, pi) if @var{nfft} is odd. Similarly, for a twosided
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65 ## calculation @var{w} is in the range [0, 2*pi] or [0, 2*pi) depending on
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66 ## @var{nfft}.
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67 ##
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68 ## If a sampling frequency is specified, @var{Fs}, then the output frequencies
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69 ## @var{f} will be in the range [0, @var{Fs}/2] or [0, @var{Fs}/2) for
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70 ## onesided calculations. For twosided calculations the range will be
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71 ## [0, @var{Fs}).
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72 ##
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73 ## When called with no outputs the periodogram is immediately plotted in the
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74 ## current figure window.
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75 ## @seealso{fft}
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76 ## @end deftypefn
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77
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78 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
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79 ## Description: Compute the periodogram
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80
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81 function [pxx, f] = periodogram (x, varargin)
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82
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83 ## check input arguments
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84 if (nargin < 1 || nargin > 5)
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85 print_usage ();
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86 endif
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87
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88 nfft = fs = range = window = [];
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89 j = 2;
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90 for k = 1:length (varargin)
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91 if (ischar (varargin{k}))
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92 range = varargin{k};
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93 else
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94 switch (j)
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95 case 2
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96 window = varargin{k};
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97 case 3
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98 nfft = varargin{k};
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99 case 4
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100 fs = varargin{k};
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101 endswitch
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102 j++;
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103 endif
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104 endfor
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105
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106 if (! isvector (x))
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107 error ("periodogram: X must be a real or complex vector");
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108 endif
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109 x = x(:); # Use column vectors from now on
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110
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111 n = rows (x);
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112
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113 if (! isempty (window))
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114 if (! isvector (window) || length (window) != n)
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115 error ("periodogram: WIN must be a vector of the same length as X");
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116 endif
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117 window = window(:);
8ac4ab4ae5f4 periodogram.m: Overhaul function (bug #39279, bug #42859).
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118 x .*= window;
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119 endif
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120
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121 if (isempty (nfft))
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122 nfft = max (256, 2.^nextpow2 (n));
8ac4ab4ae5f4 periodogram.m: Overhaul function (bug #39279, bug #42859).
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123 elseif (! isscalar (nfft))
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124 error ("periodogram: NFFT must be a scalar");
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125 endif
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126
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127 use_w_freq = isempty (fs);
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128 if (! use_w_freq && ! isscalar (fs))
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129 error ("periodogram: FS must be a scalar");
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130 endif
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131
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132 if (strcmpi (range, "onesided"))
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133 range = 1;
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134 elseif (strcmpi (range, "twosided"))
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135 range = 2;
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136 elseif (strcmpi (range, "centered"))
8ac4ab4ae5f4 periodogram.m: Overhaul function (bug #39279, bug #42859).
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137 error ('periodogram: "centered" range type is not implemented');
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138 else
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139 range = 2-isreal (x);
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140 endif
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141
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142 ## compute periodogram
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143
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144 if (n > nfft)
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145 Pxx = 0;
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146 rr = rem (length (x), nfft);
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147 if (rr)
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148 x = [x(:); zeros(nfft-rr, 1)];
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149 endif
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150 x = sum (reshape (x, nfft, []), 2);
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151 endif
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152
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153 if (! isempty (window))
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154 n = sumsq (window);
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155 endif;
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156 Pxx = (abs (fft (x, nfft))) .^ 2 / n;
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157
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158 if (use_w_freq)
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159 Pxx /= 2*pi;
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160 else
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161 Pxx /= fs;
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162 endif
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163
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164 ## generate output arguments
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165
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166 if (range == 1) # onesided
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167 if (! rem (nfft,2)) # nfft is even
8ac4ab4ae5f4 periodogram.m: Overhaul function (bug #39279, bug #42859).
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168 psd_len = nfft/2+1;
8ac4ab4ae5f4 periodogram.m: Overhaul function (bug #39279, bug #42859).
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169 Pxx = Pxx(1:psd_len) + [0; Pxx(nfft:-1:psd_len+1); 0];
8ac4ab4ae5f4 periodogram.m: Overhaul function (bug #39279, bug #42859).
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170 else # nfft is odd
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171 psd_len = (nfft+1)/2;
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172 Pxx = Pxx(1:psd_len) + [0; Pxx(nfft:-1:psd_len+1)];
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173 endif
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174 endif
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175
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176 if (nargout != 1)
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177 if (range == 1)
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178 f = (0:nfft/2)' / nfft;
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179 elseif (range == 2)
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180 f = (0:nfft-1)' / nfft;
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181 endif
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182 if (use_w_freq)
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183 f *= 2*pi; # generate w=2*pi*f
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184 else
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185 f *= fs;
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186 endif
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187 endif
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188
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189 if (nargout == 0)
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190 if (use_w_freq)
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191 plot (f/(2*pi), 10*log10 (Pxx));
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192 xlabel ("normalized frequency [x pi rad]");
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193 ylabel ("Power density [dB/rad/sample]");
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194 else
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195 plot (f, 10*log10 (Pxx));
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196 xlabel ("frequency [Hz]");
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197 ylabel ("Power density [dB/Hz]");
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198 endif
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199 grid on;
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200 title ("Periodogram Power Spectral Density Estimate");
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201 else
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202 pxx = Pxx;
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203 endif
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204
3191
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205 endfunction
17338
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206
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207
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208 ## FIXME: Need some functional tests
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209
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210
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211 %% Test input validation
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212 %!error periodogram ()
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213 %!error periodogram (1,2,3,4,5,6)
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214 %!error <X must be a real or complex vector> periodogram (ones (2,2))
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215 %!error <WIN must be a vector.*same length> periodogram (1:5, ones (2,2))
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216 %!error <WIN must be a vector.*same length> periodogram (1:5, 1:6)
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217 %!error <NFFT must be a scalar> periodogram (1:5, 1:5, 1:5)
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218 %!error <FS must be a scalar> periodogram (1:5, [], [], 1:5)
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219 %!error <"centered" range type is not implemented> periodogram (1:5, "centered")
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diff changeset
220