, ▁Nicholas ▁L . ▁In ▁the ▁Second ▁H undred ▁Years ▁of ▁Mack ville , ▁ 1 9 4 9 – 1 9 5 9 : ▁Historical ▁Ess ays . ▁ 1 9 5 9 . ▁ ▁G ross , ▁Nicholas ▁L . ▁Mack ville ▁History ▁Cont in ued , ▁ 1 9 5 9 – 1 9 6 4 : ▁Historical ▁Ess ays . ▁ 1 9 6 5 . ▁ ▁G ross , ▁Nicholas ▁L . ▁Mack ville ▁History ▁Cont in ued , ▁ 1 9 6 4 – 1 9 7 0 : ▁Historical ▁Ess ays . ▁ 1 9 7 0 . ▁ ▁External ▁links ▁ ▁Mack ville , ▁Wisconsin ▁ ▁Category : Un in cor por ated ▁communities ▁in ▁Out ag am ie ▁County , ▁Wisconsin ▁Category : Un in cor por ated ▁communities ▁in ▁Wisconsin <0x0A> </s> ▁The ▁problem ▁of ▁reconst ruction ▁from ▁zero ▁cross ings ▁can ▁be ▁stated ▁as : ▁given ▁the ▁zero ▁cross ings ▁of ▁a ▁continuous ▁signal , ▁is ▁it ▁possible ▁to ▁re construct ▁the ▁signal ▁( to ▁within ▁a ▁constant ▁factor )? ▁Word ed ▁differently , ▁what ▁are ▁the ▁conditions ▁under ▁which ▁a ▁signal ▁can ▁be ▁re construct ed ▁from ▁its ▁zero ▁cross ings ? ▁ ▁This ▁problem ▁has ▁two ▁parts . ▁First ly , ▁prov ing ▁that ▁there ▁is ▁a ▁unique ▁reconst ruction ▁of ▁the ▁signal ▁from ▁the ▁zero ▁cross ings , ▁and ▁second ly , ▁how ▁to ▁actually ▁go ▁about ▁re construct ing ▁the ▁signal . ▁Though ▁there ▁have ▁been ▁quite ▁a