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annotate scripts/signal/periodogram.m @ 10984:58c57161626d

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extend periodogram, thanks to Alois Schloegl
author Jaroslav Hajek <highegg@gmail.com>
date Thu, 16 Sep 2010 07:37:07 +0200
parents f084ba47812b
children d9c8916bb9dd
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1 ## Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2007
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2 ## Friedrich Leisch
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3 ## Copyright (C) 2010 Alois Schloegl
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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} {[Pxx,w]} = periodogram (@var{x})
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23 ## For a data matrix @var{x} from a sample of size @var{n}, return the
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24 ## periodogram. w returns the angular frequency.
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25 ##
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26 ## [Pxx,w] = periodogram (@var{x}).
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27 ##
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28 ## [Pxx,w] = periodogram (@var{x},win).
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29 ##
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30 ## [Pxx,w] = periodogram (@var{x},win,nfft).
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31 ##
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32 ## [Pxx,f] = periodogram (@var{x},win,nfft,Fs).
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33 ##
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34 ## [Pxx,f] = periodogram (@var{x},win,nfft,Fs,"range").
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35 ##
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36 ## @itemize
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37 ## @item x: data; if real-valued a one-sided spectrum is estimated,
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38 ## if complex-valued or range indicates "twosided", the full spectrum is estimated.
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39 ##
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40 ## @item win: weight data with window, x.*win is used for further computation,
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41 ## if window is empty, a rectangular window is used.
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42 ##
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43 ## @item nfft: number of frequency bins, default max(256, 2.^ceil(log2(length(x)))).
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44 ##
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45 ## @item Fs: sampleing rate, default 1.
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46 ##
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47 ## @item range: "onesided" computes spectrum from [0..nfft/2+1].
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48 ## "twosided" computes spectrum from [0..nfft-1]. These strings can appear at any
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49 ## position in the list input arguments after window.
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50 ##
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51 ## @item Pxx: one-, or two-sided power spectrum.
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52 ##
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53 ## @item w: angular frequency [0..2*pi) (two-sided) or [0..pi] one-sided.
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54 ##
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55 ## @item f: frequency [0..Fs) (two-sided) or [0..Fs/2] one-sided.
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56 ## @end itemize
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57 ##
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58 ##
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59 ## @end deftypefn
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60
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61 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
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62 ## Description: Compute the periodogram
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63
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64 function [pxx, f] = periodogram (x, varargin)
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65
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66 ## check input arguments
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67
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68 if (nargin < 1 || nargin > 5)
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69 print_usage ();
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70 endif
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71
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72 nfft = []; fs = []; range = []; window = [];
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73 j = 1;
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74 for k = 1:length (varargin)
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75 if (ischar (varargin{k}))
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76 range = varargin{k};
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77 else
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78 switch (j)
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79 case 1
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80 window = varargin{k};
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81 case 2
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82 nfft = varargin{k};
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83 case 3
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84 fs = varargin{k};
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85 case 4
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86 range = varargin{k};
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87 endswitch
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88 j++;
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89 endif
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90 endfor
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91
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92 [r, c] = size (x);
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93 if (r == 1)
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94 r = c;
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95 endif
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96
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97 if (ischar (window))
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98 range = window;
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99 window = [];
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100 endif;
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101 if (ischar (nfft))
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102 range = nfft;
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103 nfft = [];
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104 endif;
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105 if (ischar (fs))
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106 range = fs;
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107 fs = [];
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108 endif;
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109
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110 if (! isempty (window))
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111 if (all (size (x) == size (window)))
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112 x .*= window;
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113 elseif (size (x, 1) == size (window, 1) && size (window, 2) == 1)
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114 x .*= window (:,ones (1,c));
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115 endif;
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116 endif
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117
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118 if (numel (nfft)>1)
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119 error ("nfft must be scalar");
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120 endif
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121 if (isempty (nfft))
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122 nfft = max (256, 2.^ceil (log2 (r)));
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123 endif
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124
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125 if (strcmp (range, "onesided"))
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126 range = 1;
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127 elseif strcmp (range, "twosided")
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128 range = 2;
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129 else
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130 range = 2-isreal (x);
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131 endif
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132
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133 ## compute periodogram
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134
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135 if (r>nfft)
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136 Pxx = 0;
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137 rr = rem (length (x), nfft);
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138 if (rr)
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139 x = [x(:);zeros (nfft-rr, 1)];
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140 end
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141 x = sum (reshape (x, nfft, []), 2);
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142 endif
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143
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144 if (isempty (window))
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145 n = r;
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146 else
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147 n = sumsq (window);
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148 end;
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149 Pxx = (abs (fft (x, nfft))) .^ 2 / n ;
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150
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151 if (nargin<4)
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152 Pxx /= 2*pi;
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153 elseif (! isempty (fs))
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154 Pxx /= fs;
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155 endif
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156
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157 ## generate output arguments
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158
58c57161626d extend periodogram, thanks to Alois Schloegl
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159 if (range == 1) # onesided
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160 Pxx = Pxx(1:nfft/2+1) + [0; Pxx(end:-1:(nfft/2+2)); 0];
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161 endif
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162
58c57161626d extend periodogram, thanks to Alois Schloegl
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163 if (nargout != 1)
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164 if (range == 1)
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165 f = (0:nfft/2)"/nfft;
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166 elseif (range == 2)
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167 f = (0:nfft-1)"/nfft;
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168 endif
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169 if (nargin<4)
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170 f *= 2*pi; # generate w=2*pi*f
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171 elseif (! isempty (fs))
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172 f *= fs;
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173 endif
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174 endif
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175
58c57161626d extend periodogram, thanks to Alois Schloegl
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176 if (nargout == 0)
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177 if (nargin<4)
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178 plot (f/(2*pi), 10*log10 (Pxx));
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179 xlabel ("normalized frequency [x pi rad]");
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180 ylabel ("Power density [dB/rad/sample]");
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181 else
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182 plot (f, 10*log10 (Pxx));
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183 xlabel ("frequency [Hz]");
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184 ylabel ("Power density [dB/Hz]");
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185 end
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186 grid on;
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187 title ("Periodogram Power Spectral Density Estimate");
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188 else
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189 pxx = Pxx;
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190 endif
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3238
diff changeset
191
3191
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe]
jwe
parents:
diff changeset
192 endfunction