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fir2007

kaiser example

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Unformatted text preview: ¥ ¡ £ #        ¤ ¦ ©  ¤ ¦       " # # ¤ ¨ § ¨      § ¤ ¨   # ! ¥ ©   ¤ §  § ¨   ¤ § § £ £  § ¥ ¢    ¡ ¥ ¦¤ ¤ § ¡ © Kaiser Windows Formulae are empirical ECE 600 FIR Design T.H.E OHIO S ATE T UNIVERSITY Slide # 15  ¨ ¢  § # ¢ ¢   ¡ § ¢ 1 # ¡ (0 (  " ¨ ) ¢ %3 \$ % 4 " "  # 5 %( ¡ ¡ 4  ¨ 2 2 6   0 \$  " ) "  ¢ # ¡ ! § § & %¡ ¨ ¢ ¡ ¡  ( %  ¢ ¨ ' ¡ # ! " ! ¨ ! ¡ \$ § ¢ © ¨ §  ¡ "  ¨ ¦ ¤ ¥£ ¡¢ ¡  ¢  Kaiser: Example 1 Revisited (can iteratively adjust ECE 600 FIR Design \$ and ' \$ >> h=fir1(45,0.25,kaiser(46,3.40)); for some reduction in ) T.H.E OHIO S ATE T UNIVERSITY Slide # 16 Frequency Sampled Design [Van den Enden & Verhoeckx, Prentice-Hall, 1989, section 8.2.2.] ECE 600 FIR Design T.H.E OHIO S ATE T UNIVERSITY Slide # 17 Least Squares Design   4 ¡  £ (by Parseval's theorem) £  £  ¡ ¡ 4 ¡  £  £ ¨  © ¥ ¦ §  ¢ ¦ ¨  ¢ £¡ ¥ ¦¤ § Thus, the mean squared error is minimized by trunction of the ideal impulse response. or, use a weighting function Wgt to adjust errors  ¢¡ ¥¤ § 4 "  ¢ £¡ ¥¤ §  &  ¡ ¨ Wgt ¡ ¢ £¡ ¥ ¦¤ § 4  #  ¥ ¢ © § ¡ " ¡ ¨ ¡ 4  £ ¦ ¨  © §  ¥ ¢ " ¡ ¨ ¡ 4  £  £  &  ¡ " ¨ ¡ ¢ 4 ¢ £¡ ¥ ¦¤ § ¢ £¡ ¥ ¦¤ § 4  # Integral of squared error ECE 600 FIR Design T.H.E OHIO S ATE T UNIVERSITY Slide # 18 Example Consider use of MATLAB's FIRLS command: ECE 600 FIR Design T.H.E OHIO S ATE T UNIVERSITY Slide # 19 § 4 ¡ § ¡    ¤ £ ¡ ¢  ¤ ¥ " ¡ ¨  H - approx basis vector ¢ § ¦ ¥  ¡  &  ¡ ¨ Wgt 4 ¢ £¡ ¥ ¦¤ §   # Projection Theorem ECE 600 FIR Design T.H.E OHIO S ATE T UNIVERSITY Slide # 20 Gives ECE 600 FIR Design  linear equations in  ¨ § ¨ §  &  ¡  ¨   ¤ £ ¤ ¤ £ ¤ unknowns OHIO S ATE T T.H.E U...
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