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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 () != x_dims.length ()) |
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92 { |
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93 error ("filter: dimensionality of si and x must agree"); |
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94 return y; |
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95 } |
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96 |
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97 int si_dim = 0; |
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98 for (int i = 0; i < x_dims.length (); i++) |
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99 { |
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100 if (i == dim) |
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101 continue; |
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102 |
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103 if (x_dims(i) == 1) |
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104 continue; |
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105 |
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106 if (si_dims(++si_dim) != x_dims(i)) |
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107 { |
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108 error ("filter: dimensionality of si and x must agree"); |
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109 return y; |
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110 } |
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111 } |
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112 |
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113 if (norm != 1.0) |
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114 { |
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115 a = a / norm; |
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116 b = b / norm; |
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117 } |
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118 |
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119 if (a_len <= 1 && si_len <= 0) |
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120 return b(0) * x; |
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121 |
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122 y.resize (x_dims, 0.0); |
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123 |
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124 int x_stride = 1; |
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125 for (int i = 0; i < dim; i++) |
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126 x_stride *= x_dims(i); |
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127 |
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128 int x_num = x_dims.numel () / x_len; |
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129 for (int num = 0; num < x_num; num++) |
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130 { |
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131 int x_offset; |
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132 if (x_stride == 1) |
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133 x_offset = num * x_len; |
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134 else |
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135 { |
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136 int x_offset2 = 0; |
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137 x_offset = num; |
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138 while (x_offset >= x_stride) |
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139 { |
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140 x_offset -= x_stride; |
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141 x_offset2++; |
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142 } |
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143 x_offset += x_offset2 * x_stride * x_len; |
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144 } |
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145 int si_offset = num * si_len; |
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146 |
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147 if (a_len > 1) |
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148 { |
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149 T *py = y.fortran_vec (); |
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150 T *psi = si.fortran_vec (); |
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151 |
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152 const T *pa = a.data (); |
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153 const T *pb = b.data (); |
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154 const T *px = x.data (); |
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155 |
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156 psi += si_offset; |
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157 |
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158 for (int i = 0, idx = x_offset; i < x_len; i++, idx += x_stride) |
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159 { |
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160 py[idx] = psi[0] + pb[0] * px[idx]; |
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161 |
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162 if (si_len > 0) |
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163 { |
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164 for (int j = 0; j < si_len - 1; j++) |
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165 { |
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166 OCTAVE_QUIT; |
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167 |
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168 psi[j] = psi[j+1] - pa[j+1] * py[idx] + pb[j+1] * px[idx]; |
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169 } |
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170 |
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171 psi[si_len-1] = pb[si_len] * px[idx] - pa[si_len] * py[idx]; |
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172 } |
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173 else |
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174 { |
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175 OCTAVE_QUIT; |
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176 |
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177 psi[0] = pb[si_len] * px[idx] - pa[si_len] * py[idx]; |
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178 } |
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179 } |
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180 } |
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181 else if (si_len > 0) |
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182 { |
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183 T *py = y.fortran_vec (); |
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184 T *psi = si.fortran_vec (); |
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185 |
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186 const T *pb = b.data (); |
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187 const T *px = x.data (); |
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188 |
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189 psi += si_offset; |
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190 |
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191 for (int i = 0, idx = x_offset; i < x_len; i++, idx += x_stride) |
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192 { |
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193 py[idx] = psi[0] + pb[0] * px[idx]; |
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194 |
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195 if (si_len > 1) |
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196 { |
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197 for (int j = 0; j < si_len - 1; j++) |
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198 { |
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199 OCTAVE_QUIT; |
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200 |
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201 psi[j] = psi[j+1] + pb[j+1] * px[idx]; |
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202 } |
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203 |
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204 psi[si_len-1] = pb[si_len] * px[idx]; |
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205 } |
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206 else |
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207 { |
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208 OCTAVE_QUIT; |
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209 |
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210 psi[0] = pb[1] * px[idx]; |
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211 } |
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212 } |
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213 } |
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214 } |
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215 |
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216 return y; |
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217 } |
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218 |
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219 #if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL) |
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220 extern MArrayN<double> |
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221 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, |
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222 MArrayN<double>&, int dim); |
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223 |
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224 extern MArrayN<Complex> |
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225 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, |
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226 MArrayN<Complex>&, int dim); |
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227 #endif |
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228 |
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229 template <class T> |
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230 MArrayN<T> |
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231 filter (MArray<T>& b, MArray<T>& a, MArrayN<T>& x, int dim = -1) |
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232 { |
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233 dim_vector x_dims = x.dims(); |
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234 |
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235 if (dim < 0) |
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236 { |
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237 // Find first non-singleton dimension |
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238 while (dim < x_dims.length () && x_dims(dim) <= 1) |
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239 dim++; |
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240 |
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241 // All dimensions singleton, pick first dimension |
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242 if (dim == x_dims.length ()) |
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243 dim = 0; |
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244 } |
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245 else |
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246 if (dim < 0 || dim > x_dims.length ()) |
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247 { |
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248 error ("filter: filtering over invalid dimension"); |
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249 return MArrayN<T> (); |
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250 } |
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251 |
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252 int a_len = a.length (); |
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253 int b_len = b.length (); |
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254 |
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255 int si_len = (a_len > b_len ? a_len : b_len) - 1; |
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256 dim_vector si_dims = x.dims (); |
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257 for (int i = dim; i > 0; i--) |
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258 si_dims(i) = si_dims(i-1); |
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259 si_dims(0) = si_len; |
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260 |
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261 MArrayN<T> si (si_dims, T (0.0)); |
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262 |
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263 return filter (b, a, x, si, dim); |
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264 } |
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265 |
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266 DEFUN_DLD (filter, args, nargout, |
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267 "-*- texinfo -*-\n\ |
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268 @deftypefn {Loadable Function} {y =} filter (@var{b}, @var{a}, @var{x})\n\ |
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269 @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si})\n\ |
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270 @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, [], @var{dim})\n\ |
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271 @deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si}, @var{dim})\n\ |
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272 Return the solution to the following linear, time-invariant difference\n\ |
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273 equation:\n\ |
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274 @iftex\n\ |
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275 @tex\n\ |
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276 $$\n\ |
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277 \\sum_{k=0}^N a_{k+1} y_{n-k} = \\sum_{k=0}^M b_{k+1} x_{n-k}, \\qquad\n\ |
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278 1 \\le n \\le P\n\ |
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279 $$\n\ |
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280 @end tex\n\ |
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281 @end iftex\n\ |
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282 @ifinfo\n\ |
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283 \n\ |
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284 @smallexample\n\ |
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285 N M\n\ |
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286 SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x)\n\ |
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287 k=0 k=0\n\ |
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288 @end smallexample\n\ |
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289 @end ifinfo\n\ |
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290 \n\ |
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291 @noindent\n\ |
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292 where\n\ |
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293 @ifinfo\n\ |
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294 N=length(a)-1 and M=length(b)-1.\n\ |
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295 @end ifinfo\n\ |
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296 @iftex\n\ |
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297 @tex\n\ |
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298 $a \\in \\Re^{N-1}$, $b \\in \\Re^{M-1}$, and $x \\in \\Re^P$.\n\ |
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299 @end tex\n\ |
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300 @end iftex\n\ |
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301 over the first non-singleton dimension of @var{x} or over @var{dim} if\n\ |
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302 supplied. An equivalent form of this equation is:\n\ |
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303 @iftex\n\ |
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304 @tex\n\ |
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305 $$\n\ |
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306 y_n = -\\sum_{k=1}^N c_{k+1} y_{n-k} + \\sum_{k=0}^M d_{k+1} x_{n-k}, \\qquad\n\ |
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307 1 \\le n \\le P\n\ |
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308 $$\n\ |
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309 @end tex\n\ |
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310 @end iftex\n\ |
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311 @ifinfo\n\ |
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312 \n\ |
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313 @smallexample\n\ |
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314 N M\n\ |
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315 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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316 k=1 k=0\n\ |
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317 @end smallexample\n\ |
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318 @end ifinfo\n\ |
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319 \n\ |
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320 @noindent\n\ |
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321 where\n\ |
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322 @ifinfo\n\ |
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323 c = a/a(1) and d = b/a(1).\n\ |
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324 @end ifinfo\n\ |
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325 @iftex\n\ |
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326 @tex\n\ |
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327 $c = a/a_1$ and $d = b/a_1$.\n\ |
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328 @end tex\n\ |
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329 @end iftex\n\ |
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330 \n\ |
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331 If the fourth argument @var{si} is provided, it is taken as the\n\ |
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332 initial state of the system and the final state is returned as\n\ |
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333 @var{sf}. The state vector is a column vector whose length is\n\ |
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334 equal to the length of the longest coefficient vector minus one.\n\ |
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335 If @var{si} is not supplied, the initial state vector is set to all\n\ |
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336 zeros.\n\ |
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337 \n\ |
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338 In terms of the z-transform, y is the result of passing the discrete-\n\ |
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339 time signal x through a system characterized by the following rational\n\ |
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340 system function:\n\ |
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341 @iftex\n\ |
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342 @tex\n\ |
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343 $$\n\ |
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344 H(z) = {\\displaystyle\\sum_{k=0}^M d_{k+1} z^{-k}\n\ |
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345 \\over 1 + \\displaystyle\\sum_{k+1}^N c_{k+1} z^{-k}}\n\ |
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346 $$\n\ |
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347 @end tex\n\ |
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348 @end iftex\n\ |
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349 @ifinfo\n\ |
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350 \n\ |
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351 @example\n\ |
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352 M\n\ |
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353 SUM d(k+1) z^(-k)\n\ |
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354 k=0\n\ |
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355 H(z) = ----------------------\n\ |
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356 N\n\ |
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357 1 + SUM c(k+1) z(-k)\n\ |
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358 k=1\n\ |
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359 @end example\n\ |
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360 @end ifinfo\n\ |
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361 @end deftypefn") |
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362 { |
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363 octave_value_list retval; |
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364 |
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365 int nargin = args.length (); |
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366 |
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367 if (nargin < 3 || nargin > 5) |
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368 { |
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369 print_usage ("filter"); |
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370 return retval; |
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371 } |
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372 |
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373 const char *errmsg = "filter: arguments a and b must be vectors"; |
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374 |
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375 int dim; |
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376 dim_vector x_dims = args(2).dims (); |
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377 |
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378 if (nargin == 5) |
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379 { |
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380 dim = args(4).nint_value() - 1; |
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381 if (dim < 0 || dim >= x_dims.length ()) |
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382 { |
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383 error ("filter: filtering over invalid dimension"); |
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384 return retval; |
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385 } |
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386 } |
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387 else |
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388 { |
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389 // Find first non-singleton dimension |
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390 dim = 0; |
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391 while (dim < x_dims.length () && x_dims(dim) <= 1) |
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392 dim++; |
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393 |
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394 // All dimensions singleton, pick first dimension |
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395 if (dim == x_dims.length ()) |
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396 dim = 0; |
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397 } |
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398 |
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399 if (args(0).is_complex_type () |
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400 || args(1).is_complex_type () |
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401 || args(2).is_complex_type () |
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402 || (nargin >= 4 && args(3).is_complex_type ())) |
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403 { |
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404 ComplexColumnVector b (args(0).complex_vector_value ()); |
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405 ComplexColumnVector a (args(1).complex_vector_value ()); |
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406 |
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407 ComplexNDArray x (args(2).complex_array_value ()); |
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408 |
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409 if (! error_state) |
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410 { |
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411 ComplexNDArray si; |
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412 |
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413 if (nargin == 3 || args(3).is_empty ()) |
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414 { |
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415 int a_len = a.length (); |
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416 int b_len = b.length (); |
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417 |
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418 int si_len = (a_len > b_len ? a_len : b_len) - 1; |
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419 |
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420 dim_vector si_dims = x.dims (); |
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421 for (int i = dim; i > 0; i--) |
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422 si_dims(i) = si_dims(i-1); |
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423 si_dims(0) = si_len; |
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424 |
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425 si.resize (si_dims, 0.0); |
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426 } |
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427 else |
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428 { |
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429 dim_vector si_dims = args (3).dims (); |
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430 bool si_is_vector = true; |
|
5059
|
431 for (int i = 0; i < si_dims.length (); i++) |
|
|
432 if (si_dims(i) != 1 && si_dims(i) < si_dims.numel ()) |
|
4844
|
433 { |
|
|
434 si_is_vector = false; |
|
|
435 break; |
|
|
436 } |
|
|
437 |
|
5059
|
438 si = args(3).complex_array_value (); |
|
|
439 |
|
4844
|
440 if (si_is_vector) |
|
5059
|
441 si = si.reshape (dim_vector (si.numel (), 1)); |
|
4844
|
442 } |
|
3088
|
443 |
|
|
444 if (! error_state) |
|
|
445 { |
|
4844
|
446 ComplexNDArray y (filter (b, a, x, si, dim)); |
|
3088
|
447 |
|
|
448 if (nargout == 2) |
|
4844
|
449 retval(1) = si; |
|
2928
|
450 |
|
4844
|
451 retval(0) = y; |
|
2928
|
452 } |
|
|
453 else |
|
3088
|
454 error (errmsg); |
|
2928
|
455 } |
|
|
456 else |
|
|
457 error (errmsg); |
|
|
458 } |
|
|
459 else |
|
|
460 { |
|
3419
|
461 ColumnVector b (args(0).vector_value ()); |
|
|
462 ColumnVector a (args(1).vector_value ()); |
|
4844
|
463 |
|
|
464 NDArray x (args(2).array_value ()); |
|
2928
|
465 |
|
|
466 if (! error_state) |
|
|
467 { |
|
4844
|
468 NDArray si; |
|
3088
|
469 |
|
4844
|
470 if (nargin == 3 || args(3).is_empty ()) |
|
2928
|
471 { |
|
3088
|
472 int a_len = a.length (); |
|
|
473 int b_len = b.length (); |
|
|
474 |
|
|
475 int si_len = (a_len > b_len ? a_len : b_len) - 1; |
|
|
476 |
|
4844
|
477 dim_vector si_dims = x.dims (); |
|
|
478 for (int i = dim; i > 0; i--) |
|
5059
|
479 si_dims(i) = si_dims(i-1); |
|
|
480 si_dims(0) = si_len; |
|
4844
|
481 |
|
|
482 si.resize (si_dims, 0.0); |
|
3088
|
483 } |
|
|
484 else |
|
4844
|
485 { |
|
|
486 dim_vector si_dims = args (3).dims (); |
|
|
487 bool si_is_vector = true; |
|
5059
|
488 for (int i = 0; i < si_dims.length (); i++) |
|
|
489 if (si_dims(i) != 1 && si_dims(i) < si_dims.numel ()) |
|
4844
|
490 { |
|
|
491 si_is_vector = false; |
|
|
492 break; |
|
|
493 } |
|
|
494 |
|
5059
|
495 si = args(3).array_value (); |
|
|
496 |
|
4844
|
497 if (si_is_vector) |
|
5059
|
498 si = si.reshape (dim_vector (si.numel (), 1)); |
|
4844
|
499 } |
|
3088
|
500 |
|
|
501 if (! error_state) |
|
|
502 { |
|
4844
|
503 NDArray y (filter (b, a, x, si, dim)); |
|
3088
|
504 |
|
|
505 if (nargout == 2) |
|
4844
|
506 retval(1) = si; |
|
2928
|
507 |
|
4844
|
508 retval(0) = y; |
|
2928
|
509 } |
|
|
510 else |
|
3088
|
511 error (errmsg); |
|
2928
|
512 } |
|
|
513 else |
|
|
514 error (errmsg); |
|
|
515 } |
|
|
516 |
|
|
517 return retval; |
|
|
518 } |
|
|
519 |
|
4844
|
520 template MArrayN<double> |
|
|
521 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, |
|
|
522 MArrayN<double>&, int dim); |
|
2928
|
523 |
|
4844
|
524 template MArrayN<double> |
|
|
525 filter (MArray<double>&, MArray<double>&, MArrayN<double>&, int dim); |
|
2928
|
526 |
|
4844
|
527 template MArrayN<Complex> |
|
|
528 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, |
|
|
529 MArrayN<Complex>&, int dim); |
|
2928
|
530 |
|
4844
|
531 template MArrayN<Complex> |
|
|
532 filter (MArray<Complex>&, MArray<Complex>&, MArrayN<Complex>&, int dim); |
|
2928
|
533 |
|
|
534 /* |
|
|
535 ;;; Local Variables: *** |
|
|
536 ;;; mode: C++ *** |
|
|
537 ;;; End: *** |
|
|
538 */ |
