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1 /* |
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2 |
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3 Copyright (C) 1996, 1997 John W. Eaton |
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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 the |
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9 Free Software Foundation; either version 2, or (at your option) any |
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10 later version. |
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11 |
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12 Octave is distributed in the hope that it will be useful, but WITHOUT |
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 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, write to the Free |
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19 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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20 |
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21 */ |
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22 |
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23 // Based on Tony Richardson's filter.m. |
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24 // |
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25 // Originally translated to C++ by KH (Kurt.Hornik@ci.tuwien.ac.at) |
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26 // with help from Fritz Leisch and Andreas Weingessel on Oct 20, 1994. |
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27 // |
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28 // Rewritten to use templates to handle both real and complex cases by |
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29 // jwe, Wed Nov 1 19:15:29 1995. |
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30 |
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31 #ifdef HAVE_CONFIG_H |
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32 #include <config.h> |
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33 #endif |
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34 |
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35 #include "quit.h" |
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36 |
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37 #include "defun-dld.h" |
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38 #include "error.h" |
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39 #include "oct-obj.h" |
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40 |
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41 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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42 extern MArrayN<double> |
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43 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, int dim); |
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44 |
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45 extern MArrayN<Complex> |
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46 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, int dim); |
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47 #endif |
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48 |
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49 template <class T> |
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50 MArrayN<T> |
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51 filter (MArray<T>& b, MArray<T>& a, MArrayN<T>& x, MArrayN<T>& si, |
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52 int dim = 0) |
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53 { |
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54 MArrayN<T> y; |
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55 |
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56 int a_len = a.length (); |
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57 int b_len = b.length (); |
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58 |
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59 int ab_len = a_len > b_len ? a_len : b_len; |
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60 |
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61 b.resize (ab_len, 0.0); |
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62 if (a_len > 1) |
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63 a.resize (ab_len, 0.0); |
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64 |
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65 T norm = a (0); |
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66 |
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67 if (norm == 0.0) |
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68 { |
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69 error ("filter: the first element of a must be non-zero"); |
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70 return y; |
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71 } |
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72 |
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73 dim_vector x_dims = x.dims (); |
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74 if ((dim < 0) || (dim > x_dims.length ())) |
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75 { |
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76 error ("filter: filtering over invalid dimension"); |
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77 return y; |
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78 } |
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79 |
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80 int x_len = x_dims (dim); |
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81 |
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82 dim_vector si_dims = si.dims (); |
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83 int si_len = si_dims (0); |
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84 |
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85 if (si_len != ab_len - 1) |
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86 { |
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87 error ("filter: first dimension of si must be of length max (length (a), length (b)) - 1"); |
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88 return y; |
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89 } |
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90 |
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91 if (si_dims.length() == 1) |
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92 { |
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93 // Special case as x_dims.length() might be 2, but be a vector |
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94 if (x_dims.length() > 2 || |
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95 (x_dims.length () == 2 && ((x_dims(0) != 1 || |
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96 x_dims(1) != si_dims(0)) && |
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97 (x_dims(1) != 1 || |
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98 x_dims(0) != si_dims(0))))) |
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99 { |
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100 error ("filter: dimensionality of si and x must agree"); |
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101 return y; |
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102 } |
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103 } |
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104 else if (si_dims.length () != x_dims.length ()) |
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105 { |
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106 error ("filter: dimensionality of si and x must agree"); |
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107 return y; |
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108 } |
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109 |
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110 int si_dim = 0; |
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111 for (int i = 0; i < x_dims.length (); i++) |
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112 { |
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113 if (i == dim) |
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114 continue; |
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115 |
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116 if (x_dims(i) == 1) |
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117 continue; |
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118 |
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119 if (si_dims (++si_dim) != x_dims (i)) |
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120 { |
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121 error ("filter: dimensionality of si and x must agree"); |
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122 return y; |
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123 } |
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124 } |
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125 |
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126 if (norm != 1.0) |
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127 { |
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128 a = a / norm; |
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129 b = b / norm; |
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130 } |
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131 |
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132 if ((a_len <= 1) && (si_len <= 0)) |
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133 return b(0) * x; |
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134 |
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135 y.resize (x_dims, 0.0); |
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136 |
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137 int x_stride = 1; |
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138 for (int i = 0; i < dim; i++) |
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139 x_stride *= x_dims(i); |
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140 |
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141 int x_num = x_dims.numel () / x_len; |
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142 for (int num = 0; num < x_num; num++) |
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143 { |
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144 int x_offset; |
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145 if (x_stride == 1) |
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146 x_offset = num * x_len; |
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147 else |
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148 { |
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149 int x_offset2 = 0; |
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150 x_offset = num; |
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151 while (x_offset >= x_stride) |
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152 { |
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153 x_offset -= x_stride; |
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154 x_offset2++; |
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155 } |
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156 x_offset += x_offset2 * x_stride * x_len; |
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157 } |
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158 int si_offset = num * si_len; |
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159 |
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160 if (a_len > 1) |
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161 { |
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162 for (int i = 0; i < x_len; i++) |
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163 { |
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164 int idx = i * x_stride + x_offset; |
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165 y (idx) = si (si_offset) + b (0) * x (idx); |
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166 |
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167 if (si_len > 1) |
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168 { |
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169 for (int j = 0; j < si_len - 1; j++) |
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170 { |
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171 OCTAVE_QUIT; |
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172 |
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173 si (j + si_offset) = si (j + 1 + si_offset) - |
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174 a (j+1) * y (idx) + b (j+1) * x (idx); |
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175 } |
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176 |
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177 si (si_len - 1 + si_offset) = b (si_len) * x (idx) |
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178 - a (si_len) * y (idx); |
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179 } |
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180 else |
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181 si (si_offset) = b (si_len) * x (idx) |
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182 - a (si_len) * y (idx); |
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183 } |
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184 } |
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185 else if (si_len > 0) |
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186 { |
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187 for (int i = 0; i < x_len; i++) |
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188 { |
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189 int idx = i * x_stride + x_offset; |
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190 y (idx) = si (si_offset) + b (0) * x (idx); |
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191 |
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192 if (si_len > 1) |
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193 { |
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194 for (int j = 0; j < si_len - 1; j++) |
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195 { |
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196 OCTAVE_QUIT; |
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197 |
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198 si (j + si_offset) = si (j + 1 + si_offset) + |
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199 b (j+1) * x (idx); |
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200 } |
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201 |
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202 si (si_len - 1 + si_offset) = b (si_len) * x (idx); |
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203 } |
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204 else |
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205 si (si_offset) = b (1) * x (idx); |
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206 } |
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207 } |
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208 } |
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209 |
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210 return y; |
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211 } |
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212 |
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213 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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214 extern MArrayN<double> |
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215 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, |
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216 MArrayN<double>&, int dim); |
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217 |
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218 extern MArrayN<Complex> |
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219 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, |
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220 MArrayN<Complex>&, int dim); |
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221 #endif |
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222 |
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223 template <class T> |
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224 MArrayN<T> |
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225 filter (MArray<T>& b, MArray<T>& a, MArrayN<T>& x, int dim = -1) |
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226 { |
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227 dim_vector x_dims = x.dims (); |
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228 |
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229 if (dim < 0) |
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230 { |
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231 // Find first non-singleton dimension |
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232 while ((dim < x_dims.length()) && (x_dims (dim) <= 1)) |
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233 dim++; |
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234 |
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235 // All dimensions singleton, pick first dimension |
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236 if (dim == x_dims.length ()) |
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237 dim = 0; |
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238 } |
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239 else |
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240 if (dim < 0 || dim > x_dims.length ()) |
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241 { |
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242 error ("filter: filtering over invalid dimension"); |
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243 return MArrayN<T> (); |
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244 } |
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245 |
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246 int a_len = a.length (); |
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247 int b_len = b.length (); |
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248 |
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249 int si_len = (a_len > b_len ? a_len : b_len) - 1; |
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250 dim_vector si_dims = x.dims (); |
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251 for (int i = dim; i > 0; i--) |
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252 si_dims (i) = si_dims (i-1); |
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253 si_dims (0) = si_len; |
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254 |
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255 MArrayN<T> si (si_dims, T (0.0)); |
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256 |
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257 return filter (b, a, x, si, dim); |
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258 } |
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259 |
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260 DEFUN_DLD (filter, args, nargout, |
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261 "-*- texinfo -*-\n\ |
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262 @deftypefn {Loadable Function} {y =} filter (@var{b}, @var{a}, @var{x})\n\ |
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263 @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si})\n\ |
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264 @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, [], @var{dim})\n\ |
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265 @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si}, @var{dim})\n\ |
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266 Return the solution to the following linear, time-invariant difference\n\ |
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267 equation:\n\ |
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268 @iftex\n\ |
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269 @tex\n\ |
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270 $$\n\ |
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271 \\sum_{k=0}^N a_{k+1} y_{n-k} = \\sum_{k=0}^M b_{k+1} x_{n-k}, \\qquad\n\ |
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272 1 \\le n \\le P\n\ |
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273 $$\n\ |
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274 @end tex\n\ |
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275 @end iftex\n\ |
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276 @ifinfo\n\ |
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277 \n\ |
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278 @smallexample\n\ |
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279 N M\n\ |
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280 SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x)\n\ |
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281 k=0 k=0\n\ |
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282 @end smallexample\n\ |
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283 @end ifinfo\n\ |
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284 \n\ |
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285 @noindent\n\ |
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286 where\n\ |
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287 @ifinfo\n\ |
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288 N=length(a)-1 and M=length(b)-1.\n\ |
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289 @end ifinfo\n\ |
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290 @iftex\n\ |
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291 @tex\n\ |
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292 $a \\in \\Re^{N-1}$, $b \\in \\Re^{M-1}$, and $x \\in \\Re^P$.\n\ |
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293 @end tex\n\ |
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294 @end iftex\n\ |
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295 over the first non-singleton dimension of @var{x} or over @var{dim} if\n\ |
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296 supplied. An equivalent form of this equation is:\n\ |
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297 @iftex\n\ |
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298 @tex\n\ |
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299 $$\n\ |
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300 y_n = -\\sum_{k=1}^N c_{k+1} y_{n-k} + \\sum_{k=0}^M d_{k+1} x_{n-k}, \\qquad\n\ |
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301 1 \\le n \\le P\n\ |
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302 $$\n\ |
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303 @end tex\n\ |
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304 @end iftex\n\ |
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305 @ifinfo\n\ |
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306 \n\ |
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307 @smallexample\n\ |
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308 N M\n\ |
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309 y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k) for 1<=n<=length(x)\n\ |
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310 k=1 k=0\n\ |
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311 @end smallexample\n\ |
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312 @end ifinfo\n\ |
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313 \n\ |
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314 @noindent\n\ |
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315 where\n\ |
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316 @ifinfo\n\ |
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317 c = a/a(1) and d = b/a(1).\n\ |
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318 @end ifinfo\n\ |
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319 @iftex\n\ |
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320 @tex\n\ |
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321 $c = a/a_1$ and $d = b/a_1$.\n\ |
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322 @end tex\n\ |
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323 @end iftex\n\ |
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324 \n\ |
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325 If the fourth argument @var{si} is provided, it is taken as the\n\ |
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326 initial state of the system and the final state is returned as\n\ |
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327 @var{sf}. The state vector is a column vector whose length is\n\ |
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328 equal to the length of the longest coefficient vector minus one.\n\ |
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329 If @var{si} is not supplied, the initial state vector is set to all\n\ |
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330 zeros.\n\ |
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331 \n\ |
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332 In terms of the z-transform, y is the result of passing the discrete-\n\ |
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333 time signal x through a system characterized by the following rational\n\ |
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334 system function:\n\ |
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335 @iftex\n\ |
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336 @tex\n\ |
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337 $$\n\ |
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338 H(z) = {\\displaystyle\\sum_{k=0}^M d_{k+1} z^{-k}\n\ |
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339 \\over 1 + \\displaystyle\\sum_{k+1}^N c_{k+1} z^{-k}}\n\ |
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340 $$\n\ |
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341 @end tex\n\ |
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342 @end iftex\n\ |
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343 @ifinfo\n\ |
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344 \n\ |
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345 @example\n\ |
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346 M\n\ |
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347 SUM d(k+1) z^(-k)\n\ |
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348 k=0\n\ |
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349 H(z) = ----------------------\n\ |
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350 N\n\ |
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351 1 + SUM c(k+1) z(-k)\n\ |
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352 k=1\n\ |
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353 @end example\n\ |
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354 @end ifinfo\n\ |
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355 @end deftypefn") |
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356 { |
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357 octave_value_list retval; |
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358 |
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359 int nargin = args.length (); |
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360 |
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361 if (nargin < 3 || nargin > 5) |
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362 { |
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363 print_usage ("filter"); |
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364 return retval; |
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365 } |
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366 |
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367 const char *errmsg = "filter: arguments a and b must be vectors"; |
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368 |
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369 int dim; |
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370 dim_vector x_dims = args(2).dims (); |
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371 |
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372 if (nargin == 5) |
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373 { |
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374 dim = args(4).nint_value() - 1; |
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375 if (dim < 0 || dim >= x_dims.length ()) |
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376 { |
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377 error ("filter: filtering over invalid dimension"); |
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378 return retval; |
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379 } |
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380 } |
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381 else |
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382 { |
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383 // Find first non-singleton dimension |
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384 dim = 0; |
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385 while ((dim < x_dims.length()) && (x_dims (dim) <= 1)) |
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386 dim++; |
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387 |
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388 // All dimensions singleton, pick first dimension |
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389 if (dim == x_dims.length ()) |
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390 dim = 0; |
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391 } |
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392 |
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393 if (args(0).is_complex_type () |
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394 || args(1).is_complex_type () |
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395 || args(2).is_complex_type () |
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396 || (nargin >= 4 && args(3).is_complex_type ())) |
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397 { |
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398 ComplexColumnVector b (args(0).complex_vector_value ()); |
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399 ComplexColumnVector a (args(1).complex_vector_value ()); |
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400 |
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401 ComplexNDArray x (args(2).complex_array_value ()); |
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402 |
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403 if (! error_state) |
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404 { |
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405 ComplexNDArray si; |
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406 |
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407 if (nargin == 3 || args(3).is_empty ()) |
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408 { |
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409 int a_len = a.length (); |
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410 int b_len = b.length (); |
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411 |
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412 int si_len = (a_len > b_len ? a_len : b_len) - 1; |
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413 |
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414 dim_vector si_dims = x.dims (); |
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415 for (int i = dim; i > 0; i--) |
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416 si_dims (i) = si_dims (i-1); |
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417 si_dims (0) = si_len; |
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418 |
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419 si.resize (si_dims, 0.0); |
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420 } |
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421 else |
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422 { |
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423 dim_vector si_dims = args (3).dims (); |
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424 bool si_is_vector = true; |
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425 for (int i=0; i < si_dims.length (); i++) |
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426 if ((si_dims (i) != 1) && (si_dims (i) < si_dims.numel ())) |
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427 { |
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428 si_is_vector = false; |
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429 break; |
|
|
430 } |
|
|
431 |
|
|
432 if (si_is_vector) |
|
4901
|
433 // XXX FIXME XXX -- there must be a better way... |
|
|
434 si = ComplexNDArray (MArrayN<Complex> (ArrayN<Complex> (args(3).complex_vector_value ()))); |
|
4844
|
435 else |
|
|
436 si = args(3).complex_array_value (); |
|
|
437 } |
|
3088
|
438 |
|
|
439 if (! error_state) |
|
|
440 { |
|
4844
|
441 ComplexNDArray y (filter (b, a, x, si, dim)); |
|
3088
|
442 |
|
|
443 if (nargout == 2) |
|
4844
|
444 retval(1) = si; |
|
2928
|
445 |
|
4844
|
446 retval(0) = y; |
|
2928
|
447 } |
|
|
448 else |
|
3088
|
449 error (errmsg); |
|
2928
|
450 } |
|
|
451 else |
|
|
452 error (errmsg); |
|
|
453 } |
|
|
454 else |
|
|
455 { |
|
3419
|
456 ColumnVector b (args(0).vector_value ()); |
|
|
457 ColumnVector a (args(1).vector_value ()); |
|
4844
|
458 |
|
|
459 NDArray x (args(2).array_value ()); |
|
2928
|
460 |
|
|
461 if (! error_state) |
|
|
462 { |
|
4844
|
463 NDArray si; |
|
3088
|
464 |
|
4844
|
465 if (nargin == 3 || args(3).is_empty ()) |
|
2928
|
466 { |
|
3088
|
467 int a_len = a.length (); |
|
|
468 int b_len = b.length (); |
|
|
469 |
|
|
470 int si_len = (a_len > b_len ? a_len : b_len) - 1; |
|
|
471 |
|
4844
|
472 dim_vector si_dims = x.dims (); |
|
|
473 for (int i = dim; i > 0; i--) |
|
|
474 si_dims (i) = si_dims (i-1); |
|
|
475 si_dims (0) = si_len; |
|
|
476 |
|
|
477 si.resize (si_dims, 0.0); |
|
3088
|
478 } |
|
|
479 else |
|
4844
|
480 { |
|
|
481 dim_vector si_dims = args (3).dims (); |
|
|
482 bool si_is_vector = true; |
|
|
483 for (int i=0; i < si_dims.length (); i++) |
|
|
484 if ((si_dims (i) != 1) && (si_dims (i) < si_dims.numel ())) |
|
|
485 { |
|
|
486 si_is_vector = false; |
|
|
487 break; |
|
|
488 } |
|
|
489 |
|
|
490 if (si_is_vector) |
|
4901
|
491 // XXX FIXME XXX -- there must be a better way... |
|
|
492 si = NDArray (MArrayN<double> (ArrayN<double> (args(3).vector_value ()))); |
|
4844
|
493 else |
|
|
494 si = args(3).array_value (); |
|
|
495 } |
|
3088
|
496 |
|
|
497 if (! error_state) |
|
|
498 { |
|
4844
|
499 NDArray y (filter (b, a, x, si, dim)); |
|
3088
|
500 |
|
|
501 if (nargout == 2) |
|
4844
|
502 retval(1) = si; |
|
2928
|
503 |
|
4844
|
504 retval(0) = y; |
|
2928
|
505 } |
|
|
506 else |
|
3088
|
507 error (errmsg); |
|
2928
|
508 } |
|
|
509 else |
|
|
510 error (errmsg); |
|
|
511 } |
|
|
512 |
|
|
513 return retval; |
|
|
514 } |
|
|
515 |
|
4844
|
516 template MArrayN<double> |
|
|
517 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, |
|
|
518 MArrayN<double>&, int dim); |
|
2928
|
519 |
|
4844
|
520 template MArrayN<double> |
|
|
521 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, int dim); |
|
2928
|
522 |
|
4844
|
523 template MArrayN<Complex> |
|
|
524 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, |
|
|
525 MArrayN<Complex>&, int dim); |
|
2928
|
526 |
|
4844
|
527 template MArrayN<Complex> |
|
|
528 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, int dim); |
|
2928
|
529 |
|
|
530 /* |
|
|
531 ;;; Local Variables: *** |
|
|
532 ;;; mode: C++ *** |
|
|
533 ;;; End: *** |
|
|
534 */ |
