We wish to design an optimal (Parks–McClellan) zero-phase Type I FIR lowpass filter with...

We wish to design an optimal (Parks–McClellan) zero-phase Type I FIR lowpass filter with passband frequency ω_p = 0.3π and stopband frequency ω_s = 0.6π with equal error weighting in the passband and stopband. The impulse response of the desired filter has length 11; i.e., h[n] = 0 for n < −5 or n > 5. Figure P7.8 shows the frequency response H(e^jω) for two different filters. For each filter, specify how many alternations the filter has, and state whether it satisfies the alternation theorem as the optimal filter in the minimax sense meeting the preceding specifications.