You are designing a signal processing system that contains a FIR filter.$$ The filter needs to pass signals with frequencies $|$f$^|<0\mathrm{.}2$ cycles per sample and attenuate signals with frequencies $|$f$^|>0\mathrm{.}22.$

Question

Which is the best choice for the impulse response?$$ Be sure you can justify your answer by describing the characteristics of each filter.

Responses

h$[$n$]=\{0\mathrm{.}25,$n$=0,1,2,30,$otherwise

h$[$n$]=\{0\mathrm{.}25,$n$=0,1,2,30,$otherwise

h$[$n$]=\{$sin$(2$$0\mathrm{.}4($n$5))$$($n$5),$n$=0,1,...,100,$otherwise

h$[$n$]=\{$sin$(2$$0\mathrm{.}4($n$5))$$($n$5),$n$=0,1,...,100,$otherwise

h$[$n$]=\{$$[$n$]$sin$(2$$0\mathrm{.}4($n$5))$$($n$5),$n$=0,1,...,100,$otherwise

h$[$n$]=\{$$[$n$]$sin$(2$$0\mathrm{.}4($n$5))$$($n$5),$n$=0,1,...,100,$otherwise

h$[$n$]=$sin$(2$$0\mathrm{.}2$n$)$n

h$[$n$]=$sin$(2$$0\mathrm{.}2$n$)$n

h$[$n$]=\{$sin$(2$$0\mathrm{.}2($n$50))$$($n$50),$n$=0,1,...,1000,$otherwise

h$[$n$]=\{$sin$(2$$0\mathrm{.}2($n$50))$$($n$50),$n$=0,1,...,1000,$otherwise

h$[$n$]=$sin$(2$$0\mathrm{.}4$n$)$n

h$[$n$]=$sin$(2$$0\mathrm{.}4$n$)$n

h$[$n$]=\{0\mathrm{.}5,$n$=0,10,$otherwise

h$[$n$]=\{0\mathrm{.}5,$n$=0,10,$otherwise

h$[$n$]=\{$sin$(2$$0\mathrm{.}4($n$50))$$($n$50),$n$=0,1,...,1000,$otherwise

h$[$n$]=\{$sin$(2$$0\mathrm{.}4($n$50))$$($n$50),$n$=0,1,...,1000,$otherwise

h$[$n$]=\{$sin$(2$$0\mathrm{.}2($n$5))$$($n$5),$n$=0,1,...,100,$otherwise