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Ideal Lowpass Filter Revisited

The ideal lowpass filter of Fig.4.1 can now be described by the following specifications:

  • The transition width TW is zero ( $ \omega_s=\omega_p$ in Fig.4.2).
  • The pass-band and stop-band ripples are both zero
    ( $ \delta_p = \delta_s = 0$ in Fig.4.2, and $ \hbox{SBA} = \infty$ ).
As discussed above, these specifications are not achievable by any FIR filter. It is instructive, however, to see how an optimal least-squares design comes out in this case.

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