Q6.- Let h[n] be a real-valued N-point sequence which is the impulse response of an FIR filter with generalized linear phase. We de fine the following three sequences: 81[n] = h[2n] Juln/2], even 82[n] 0, otherwise 83[n] (-1)" h[n]. (a) Does gi[n] necessarily correspond to a filter with generalized linear phase? Justify your answer with a proof or a counter-example. If your answer is "yes", does gi[n] necessarily correspond to the same type, i.e., Type I, Type II, Type III, or Type IV, of generalized linear phase filter as h[n]? (b) Does g2[n] necessarily correspond to a filter with generalized linear phase? Justify your answer with a proof or a counter-example. If your answer is "yes", does ga[n] necessarily correspond to the same type, i.e., Type I, Type II, Type III, or Type IV, of generalized linear phase filter as h[n]? (c) Does g3[n] necessarily correspond to a filter with generalized linear phase? Justify your answer with a proof or a counter-example. If your answer is "yes", does g3[n] necessarily correspond to the same type, i.e., Type I, Type II, Type III, or Type IV, of generalized linear phase filter as h[n]?