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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## usage: kaiser (n, beta) |
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18 ## |
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19 ## Returns the filter coefficients of the n-point Kaiser window with |
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20 ## parameter beta. |
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21 ## |
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22 ## For the definition of the Kaiser window, see A. V. Oppenheim & |
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23 ## R. W. Schafer, "Discrete-Time Signal Processing". |
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24 ## |
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25 ## The continuous version of width n centered about x=0 is: |
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26 ## |
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27 ## besseli(0, beta * sqrt(1-(2*x/n).^2)) |
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28 ## k(x) = -------------------------------------, n/2 <= x <= n/2 |
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29 ## besseli(0, beta) |
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30 ## |
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31 ## See also: kaiserord |
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32 |
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33 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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34 ## Description: Coefficients of the Kaiser window |
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35 |
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36 ## 2000-02 Paul Kienzle (pkienzle@kienzle.powernet.co.uk) |
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37 ## use besseli rather than jybess |
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38 ## note, although Oppenheim & Schafer, 2nd edition has a formula |
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39 ## which looks completely different than the one herein, it gives |
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40 ## identical results |
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41 |
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42 function w = kaiser (n, beta) |
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43 |
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44 if (nargin != 2) |
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45 usage ("kaiser (n, beta)"); |
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46 endif |
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47 |
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48 if !(is_scalar (n) && (n == round (n)) && (n > 0)) |
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49 error ("kaiser: n has to be a positive integer"); |
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50 endif |
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51 if !(is_scalar (beta) && (beta == real (beta))) |
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52 error ("kaiser: beta has to be a real scalar"); |
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53 endif |
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54 |
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55 if (n == 1) |
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56 w = 1; |
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57 else |
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58 m = n - 1; |
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59 k = (0 : m)'; |
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60 k = 2 * beta / m * sqrt (k .* (m - k)); |
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61 w = besseli (0, k) / besseli (0, beta); |
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62 endif |
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63 |
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64 endfunction |
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65 |
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66 %!demo |
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67 %! % use demo("kaiserord"); |
