Using the following definitions of lowpass, highpass, bandpass, and bandstop, classify the systems whose transfer functions have the pole-zero diagrams in Figure E.43. (Some may not be classifiable.) In each case the transfer function is H(z) .
LP: H (1) ? 0 and H (?1) = 0 HP: H (1) = 0 and H (?1) ? 0
BP: H (1) = 0 and H (?1) = 0 and H (z) ? 0 for some range of |z| = 1
BS: H (1) ? 0 and H (?1) ? 0 and H (z) = 0 for at least one |z| = 1
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