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.