33 on the design of finite impulse response filters

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Unformatted text preview: &' 03 $¢ E 1 § ¡ 0 1 7    !a" d Hd  uU  f 5  ¤ d 3 H  U  U d 3 H ¤ " 3 d H  5  "d U  "   d 5 5 # £$ $! ¦(i§ # U 5 H  " 3   3 § T0 p Note that the central frequency is , the last frequency is almost This is because we have discretized the unit circle in the interval or . . In does not make much sense to talk about frequencies above radians. If fact the is the Nyquist frequency in rads. What is the meaning of frequencies above ?. Well this simple reflect the way we have discretized the unit circle when computing the DFT. 3.2. THE 2D DFT 71 ω3 ω2 ω1 11 ω0 ω5 ω7 2 3 ω0 ω4=π ω1 ω2 7 4 6 5 6 7 8 ω3 ω4=π ω5 ω6 ω7 21 2 3 2π−ω5 ω0 2π−ω6 2π−ω7 ω1 ω2 8 ω6 4 5 ω3 ω4=π Figure 3.3: Distribution of frequencies around the unit circle. The DFT can be plotted as in the interval or in the interval. 31) ¥ DA('& The 2D DFT 3  q) 3 E ¡ 3.2 The 2D Fourier transform is defined as follows: (3.31) ¥  ) & X  h £ ¢ £ ( ¨ ¢ ¡( g ' ¥% X ) ¡ ¡ ¡ 3¥ 60 ) 10¡ §X similarly, we can de...
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