From 814b56cd148846cde0d7ac62f702ead11c7d1d67 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Sat, 5 Feb 2022 20:24:07 -0500 Subject: Derivation had some untranslated J --- panap.bqn | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/panap.bqn b/panap.bqn index 33bd5a5..358e3c1 100644 --- a/panap.bqn +++ b/panap.bqn @@ -123,11 +123,11 @@ Get_panap_coeff ← { 𝕊 n‿rr‿f: # --------------------------------------------------------- " # Derivation # Transfer function for an all-pass filter: argument is z, -# and rs and re are (ט∘|) and (9&o.) of the complex parameter -H = (1 + (rs×ט) - 2×re&×) ÷ (ט + rs - 2×re&×) +# and rs and re are (ט|) and (2÷˜+⟜+) of the complex parameter +H = (1 + (rs×ט) - 2×re⊸×) ÷ (ט + rs - 2×re⊸×) # Derivative with respect to z -Hp = (2 × (re-˜rs&×) - H×(1-re)) ÷ (ט+rs-2×re&×) - = (2 × (× rs-H) - re×1-˜H) ÷ (ט+rs-2×re&×) +Hp = (2 × (re-˜rs⊸×) - H×(1-re)) ÷ (ט+rs-2×re⊸×) + = (2 × (× rs-H) - re×1-˜H) ÷ (ט+rs-2×re⊸×) # Definition of the phase transfer function T (⋆⍳T ω) = (H ⋆⍳ω) -- cgit v1.2.3