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The error function E(ω) should exhibit at least how many extremal frequencies in S?

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The error function E(ω) should exhibit at least how many extremal frequencies in S?

(a) L

(b) L-1

(c) L+1

(d) L+2

This question was posed to me in homework.

My query is from Design of Optimum Equi Ripple Linear Phase FIR Filters topic in chapter Digital Filters Design of Digital Signal Processing

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Best answer
The correct option is (d) L+2

Best explanation: According to Alternation theorem, a necessary and sufficient condition for P(ω) to be unique, best weighted chebyshev approximation, is that the error function E(ω) must exhibit at least L+2 extremal frequencies in S.

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