The foundational link between the shofar and the call to repentance is articulated by Mishneh Torah, Repentance 3:4, which teaches that although the blowing of the shofar on Rosh Hashana is a Scriptural decree, it carries a deep allusion: 'Awaken, O sleepers, from your sleep, and you who slumber, rouse yourselves from your slumber — examine your deeds and return in teshuvah and remember your Creator,' addressed to those who have forgotten the truth in the vanities of time.
The Hasidic sources develop this further into a two-tiered, upper-and-lower structure: Maamarim Melukatim, ליל ערב ראש-השנה ה'תשמ"ג holds that when Israel sounds the shofar below, an upper shofar-sounding is produced above, and the lower human performance of the commandment draws forth and actualizes its corresponding reality in the supernal realms — which is why the recitation of shofar verses persists even when the actual sounding is suspended on Rosh Hashana that falls on Shabbat outside the Temple.
Maamarim Melukatim, ש"פ האזינו, שבת שובה ה'תש"מ grounds the season's teshuvah in the call of Shabbat Shuvah — 'Shuva Yisrael ad Hashem Elokecha' — explaining that the word 'ad' (until) points to a supreme level of teshuvah that unifies the divine names Havayah and Elokim, rectifying and elevating all the Shabbatot of the entire year, the highest register of teshuvah עילאה.
Tzitz Eliezer 18:38 rules that the shofar sounded below draws its power from those who repent, and by its sounding it awakens the Upper Shofar, which is itself the secret of teshuvah, thereby bringing about the divine acceptance of all who return in repentance.
