chapter 8. checked

Author: JacobTh98

filter_design/iir_biquad.ipynb

@@ -19,7 +19,7 @@
     "- lecture: https://github.com/spatialaudio/digital-signal-processing-lecture\n",
     "- tutorial: https://github.com/spatialaudio/digital-signal-processing-exercises\n",
     "\n",
-    "Feel free to contact lecturer [email protected]"
+    "Feel free to contact the lecturer [email protected]"
    ]
   },
   {
@@ -28,8 +28,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
     "from matplotlib.markers import MarkerStyle\n",
     "from matplotlib.patches import Circle\n",
     "from scipy import signal\n",
@@ -100,8 +100,8 @@
     "\\label{eq:biquad}\n",
     "\\end{equation}\n",
     "\n",
-    "- The notation in form of the **first fraction** in above equation is suitable for identifying the structure of the filter (the necessary delay elements for the input (numerator) and the output (denominator) can directly be seen) and for creating block diagrams (direct form I/II, transposed direct forms, ...) from the difference equation.\n",
-    "- The form of the **second fraction** is more convenient for calculating poles, zeros and gain of the filter."
+    "- The notation in the form of the **first fraction** in the above equation is suitable for identifying the structure of the filter (the necessary delay elements for the input (numerator) and the output (denominator) can directly be seen) and for creating block diagrams (direct form I/II, transposed direct forms, ...) from the difference equation.\n",
+    "- The form of the **second fraction** is more convenient for calculating poles, zeros, and gain of the filter."
    ]
   },
   {
@@ -127,7 +127,7 @@
    "source": [
     "## Real Poles\n",
     "\n",
-    "For **real poles** (i.e. poles on the real-axis in the z-plane), the expression under the square root has to be positive\n",
+    "For **real poles** (i.e., poles on the real axis in the z-plane), the expression under the square root has to be positive\n",
     "\n",
     "\\begin{equation}\n",
     "z_{\\infty,1,2}=\\frac{-a_1}{2}\\pm\\frac{1}{2}\\sqrt{\\underbrace{a_1^2-4a_2}_{\\geq0}}\n",
@@ -140,7 +140,7 @@
     "a_2>|a_1|-1\n",
     "\\end{align}\n",
     "\n",
-    "must hold (try to figure out these conditions by yourself) to achieve stable IIR system with real valued coefficients $a_{1,2}$."
+    "must hold (try to figure out these conditions by yourself) to achieve a stable IIR system with real-valued coefficients $a_{1,2}$."
    ]
   },
   {
@@ -260,7 +260,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.2"
   }
  },
  "nbformat": 4,