Consider the design of a low pass linear-phase FIR filter by means of the Parks–McClellan algorithm. Use the alternation theorem to argue that the approximation must decrease monotonically in the “don’t care” region between the passband and the stopband approximation intervals. Hint: Show that all the local maxima and minima of the trigonometric polynomial must be in either the passband or the stopband to satisfy the alternation theorem.
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