docs & refactor: update fixed-point integer lfilter specification, variable naming, A0 normalization docs, and 32-bit MCU C implementation

dea/csv_processing.py

@@ -82,23 +82,23 @@ def integer_lfilter(b_int, a_int, x_float, shift_in, shift_out, shift_b, shift_a
     round_offset_out = (1 << (out_shift - 1)) if (use_round and out_shift > 0) else 0
 
     for n in range(len(x_int)):
-        acc = 0
+        sum_b = 0
         # Feedforward: 前饋完全不位移，結果為 Q_{in + b}
         for i in range(nb):
             if n - i >= 0:
-                acc += b_int[i] * x_int[n - i]
+                sum_b += b_int[i] * x_int[n - i]
                 
         # Feedback: 歷史紀錄為 Q_{in + b}，係數為 Q_a，乘積為 Q_{in + b + a}
-        fb_sum = 0
+        sum_a = 0
         for j in range(1, na):
             if n - j >= 0:
-                fb_sum += a_int[j] * y_hist[n - j]
+                sum_a += a_int[j] * y_hist[n - j]
                 
-        # Feedback 縮放：除以 A0 (即 >> shift_a)，結果退回 Q_{in + b} 完美對齊
+        # Feedback 縮放：前提 A0 = 1 (或者代表放大了 Q_a 倍的常數)，除以 A0 (即 >> shift_a) 歸一化
         # Python 的 // 等同於硬體的 SRA (Arithmetic Right Shift)，會向負無窮大 Floor
-        fb_shifted = (fb_sum + round_offset_a) // A0
+        sum_a_scaled = (sum_a + round_offset_a) // A0
         
-        acc -= fb_shifted
+        acc = sum_b - sum_a_scaled
         
         # 將超高精度的 acc 直接存入歷史變數
         y_hist[n] = acc