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1 ## Copyright (C) 1996, 1998, 2000, 2003, 2004, 2005, 2006, 2007 |
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2 ## Auburn University. All rights reserved. |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{mag}, @var{phase}, @var{w}] =} bode (@var{sys}, @var{w}, @var{out_idx}, @var{in_idx}) |
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22 ## If no output arguments are given: produce Bode plots of a system; otherwise, |
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23 ## compute the frequency response of a system data structure |
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24 ## |
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25 ## @strong{Inputs} |
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26 ## @table @var |
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27 ## @item sys |
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28 ## a system data structure (must be either purely continuous or discrete; |
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29 ## see is_digital) |
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30 ## @item w |
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31 ## frequency values for evaluation. |
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32 ## |
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33 ## if @var{sys} is continuous, then bode evaluates @math{G(jw)} where |
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34 ## @math{G(s)} is the system transfer function. |
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35 ## |
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36 ## if @var{sys} is discrete, then bode evaluates G(@code{exp}(jwT)), where |
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37 ## @itemize @bullet |
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38 ## @item @math{T} is the system sampling time |
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39 ## @item @math{G(z)} is the system transfer function. |
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40 ## @end itemize |
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41 ## |
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42 ## @strong{Default} the default frequency range is selected as follows: (These |
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43 ## steps are @strong{not} performed if @var{w} is specified) |
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44 ## @enumerate |
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45 ## @item via routine __bodquist__, isolate all poles and zeros away from |
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46 ## @var{w}=0 (@var{jw}=0 or @math{@code{exp}(jwT)}=1) and select the frequency |
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47 ## range based on the breakpoint locations of the frequencies. |
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48 ## @item if @var{sys} is discrete time, the frequency range is limited |
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49 ## to @math{jwT} in |
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50 ## @ifinfo |
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51 ## [0,2 pi /T] |
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52 ## @end ifinfo |
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53 ## @iftex |
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54 ## @tex |
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55 ## $[0,2\pi/T]$ |
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56 ## @end tex |
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57 ## @end iftex |
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58 ## @item A "smoothing" routine is used to ensure that the plot phase does |
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59 ## not change excessively from point to point and that singular |
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60 ## points (e.g., crossovers from +/- 180) are accurately shown. |
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61 ## |
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62 ## @end enumerate |
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63 ## @item out_idx |
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64 ## @itemx in_idx |
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65 ## |
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66 ## The names or indices of outputs and inputs to be used in the frequency |
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67 ## response. See @code{sysprune}. |
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68 ## |
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69 ## @strong{Example} |
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70 ## @example |
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71 ## bode(sys,[],"y_3", @{"u_1","u_4"@}); |
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72 ## @end example |
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73 ## @end table |
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74 ## @strong{Outputs} |
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75 ## @table @var |
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76 ## @item mag |
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77 ## @itemx phase |
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78 ## the magnitude and phase of the frequency response @math{G(jw)} or |
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79 ## @math{G(@code{exp}(jwT))} at the selected frequency values. |
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80 ## @item w |
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81 ## the vector of frequency values used |
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82 ## @end table |
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83 ## |
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84 ## @enumerate |
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85 ## @item If no output arguments are given, e.g., |
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86 ## @example |
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87 ## bode(sys); |
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88 ## @end example |
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89 ## bode plots the results to the screen. Descriptive labels are |
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90 ## automatically placed. |
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91 ## |
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92 ## Failure to include a concluding semicolon will yield some garbage |
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93 ## being printed to the screen (@code{ans = []}). |
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94 ## |
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95 ## @item If the requested plot is for an @acronym{MIMO} system, mag is set to |
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96 ## @math{||G(jw)||} or @math{||G(@code{exp}(jwT))||} |
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97 ## and phase information is not computed. |
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98 ## @end enumerate |
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99 ## @end deftypefn |
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100 |
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101 ## Author: John Ingram <ingraje@eng.auburn.edu> |
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102 ## Created: July 10, 1996 |
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103 ## Based on previous code by R. Bruce Tenison, July 13, 1994 |
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104 ## Modified by David Clem November 13, 1994 |
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105 ## again by A. S. Hodel July 1995 (smart plot range, etc.) |
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106 ## Modified by Kai P. Mueller September 28, 1997 (multiplot mode) |
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107 |
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108 function [mag_r, phase_r, w_r] = bode (sys, w, outputs, inputs, plot_style) |
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109 |
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110 ## check number of input arguments given |
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111 if (nargin < 1 || nargin > 5) |
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112 print_usage (); |
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113 endif |
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114 if (nargin < 2) |
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115 w = []; |
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116 endif |
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117 if (nargin < 3) |
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118 outputs = []; |
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119 endif |
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120 if (nargin < 4) |
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121 inputs = []; |
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122 endif |
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123 if (nargin < 5) |
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124 plot_style = "dB"; |
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125 endif |
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126 |
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127 if (strcmp (plot_style, "dB")) |
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128 do_db_plot = 1; |
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129 elseif (strcmp (plot_style, "mag")) |
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130 do_db_plot = 0; |
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131 else |
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132 error ("bode: invalid value of plot_style specified"); |
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133 endif |
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134 |
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135 [f, w, sys] = __bodquist__ (sys, w, outputs, inputs, "bode"); |
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136 bode_nin = sysdimensions (sys, "in"); |
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137 bode_nout = sysdimensions (sys, "out"); |
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138 |
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139 [stname, inname, outname] = sysgetsignals (sys); |
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140 systsam = sysgettsam (sys); |
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141 |
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142 ## Get the magnitude and phase of f. |
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143 mag = abs (f); |
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144 phase = unwrap (arg (f)) * 180.0 / pi; |
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145 |
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146 if (nargout < 1), |
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147 ## Plot the information |
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148 if (is_digital (sys)) |
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149 xlstr = sprintf ("Digital frequency w=rad/sec. pi/T=%g", pi/systsam); |
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150 tistr = "(exp(jwT)) "; |
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151 else |
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152 xlstr = "Frequency in rad/sec"; |
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153 tistr = "(jw)"; |
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154 endif |
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155 |
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156 wv = [min(w), max(w)]; |
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157 |
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158 is_siso_sys = is_siso (sys); |
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159 max_mag_positive = max (mag) > 0; |
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160 |
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161 if (is_siso_sys) |
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162 subplot (2, 1, 1); |
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163 endif |
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164 |
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165 if (do_db_plot) |
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166 md = 20 * log10 (mag); |
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167 semilogx (w, md); |
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168 if (max_mag_positive) |
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169 ylabel ("Gain in dB"); |
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170 axvec = axis2dlim ([w(:), md(:)]); |
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171 axvec(1:2) = wv; |
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172 axis (axvec); |
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173 endif |
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174 else |
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175 loglog (w, mag); |
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176 ylabel ("Gain |Y/U|") |
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177 endif |
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178 xlabel (xlstr); |
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179 grid ("on"); |
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180 |
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181 if (is_siso_sys) |
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182 title (sprintf ("|[Y/U]%s|, u=%s, y=%s", tistr, inname{1}, outname{1})); |
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183 else |
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184 title (sprintf ("||Y(%s)/U(%s)||", tistr, tistr)); |
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185 disp ("MIMO plot from") |
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186 disp (__outlist__(inname," ")); |
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187 disp ("to") |
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188 disp (__outlist__(outname," ")); |
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189 endif |
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190 |
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191 if (is_siso_sys) |
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192 subplot (2, 1, 2); |
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193 axvec = axis2dlim ([w(:), phase(:)]); |
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194 axvec(1:2) = wv; |
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195 semilogx (w, phase); |
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196 axis (axvec); |
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197 xlabel (xlstr); |
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198 ylabel ("Phase in deg"); |
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199 title (sprintf ("phase([Y/U]%s), u=%s, y=%s", |
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200 tistr, inname{1}, outname{1})); |
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201 grid ("on"); |
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202 endif |
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203 else |
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204 mag_r = mag; |
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205 phase_r = phase; |
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206 w_r = w; |
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207 endif |
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208 |
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209 endfunction |
