In notation of Z-transform, we can create the quadrature mirror filter formula_3 to (original) filter formula_4 by substitution formula_5 with formula_6 in the transfer function of formula_4.
ɪ n WORD_BOUNDARY n oʊ t eɪ ʃ ə n WORD_BOUNDARY ʌ v WORD_BOUNDARY z iː t ɹ æ n s f ɔ ɹ m WORD_BOUNDARY w iː WORD_BOUNDARY k æ n WORD_BOUNDARY k ɹ iː eɪ t WORD_BOUNDARY ð ə WORD_BOUNDARY k w ɑ d ɹ ə t̠ʃ ə ɹ WORD_BOUNDARY m ɪ ɹ ə ɹ WORD_BOUNDARY f ɪ l t ə ɹ WORD_BOUNDARY f ɔ ɹ m j ʊ l ə WORD_BOUNDARY θ ɹ iː WORD_BOUNDARY t ʊ WORD_BOUNDARY ə ɹ ɹ ɪ d̠ʒ ɪ n ə l WORD_BOUNDARY f ɪ l t ə ɹ WORD_BOUNDARY f ɔ ɹ m j ʊ l ə WORD_BOUNDARY f ɔ ɹ WORD_BOUNDARY b aɪ WORD_BOUNDARY s ʌ b s t ɪ t uː ʃ ə n WORD_BOUNDARY f ɔ ɹ m j ʊ l ə WORD_BOUNDARY f aɪ v WORD_BOUNDARY w ɪ ð WORD_BOUNDARY f ɔ ɹ m j ʊ l ə WORD_BOUNDARY s ɪ k s WORD_BOUNDARY ɪ n ð ə WORD_BOUNDARY t ɹ æ n s f ɜː WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY ʌ v WORD_BOUNDARY f ɔ ɹ m j ʊ l ə WORD_BOUNDARY f ɔ ɹ WORD_BOUNDARY