chapter 3. checked

Author: JacobTh98

random_signals/correlation.ipynb

@@ -18,7 +18,7 @@
     "- 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]\n",
+    "Feel free to contact the lecturer [email protected]\n",
     "\n",
     "WIP..."
    ]
@@ -88,9 +88,9 @@
    "source": [
     "## Normalization schemes for cross correlation of finite length signals\n",
     "\n",
-    "check cross correlation\n",
+    "Check cross correlation\n",
     "- of a cosine and a sine signal\n",
-    "- of a normal pdf process that exhibits some repetition"
+    "- of a normal PDF process that exhibits some repetition"
    ]
   },
   {
@@ -176,7 +176,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.2"
   }
  },
  "nbformat": 4,

random_signals/ensemble_averages.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]\n",
+    "Feel free to contact the lecturer [email protected]\n",
     "\n",
     "WIP..."
    ]
@@ -136,7 +136,7 @@
     "which reads quadratic mean is linear mean plus variance.\n",
     "\n",
     "\n",
-    "For **stationary processes** these ensemble averages are not longer time-dependent, but rather $\\mu_x[k] = \\mu_x = \\mathrm{const}$, etc. holds.\n",
+    "For **stationary processes**, these ensemble averages are no longer time-dependent, but rather $\\mu_x[k] = \\mu_x = \\mathrm{const}$, etc. holds.\n",
     "This implies that the PDF describing the random process is **not changing over time**."
    ]
   },
@@ -163,7 +163,7 @@
     "p_{xy}(\\theta_x, \\theta_y, k_x, k_y) = p_{xy}(\\theta_x, \\theta_y, \\kappa).\n",
     "\\end{equation}\n",
     "\n",
-    "For **stationary processes** two important cases lead to fundamental tools for random signal processing:\n",
+    "For **stationary processes**, two important cases lead to fundamental tools for random signal processing:\n",
     "\n",
     "- Case 1: $\\kappa = 0$, i.e. $k = k_x = k_y$\n",
     "- Case 2: $\\kappa \\neq 0$"
@@ -238,7 +238,7 @@
     "\n",
     "## Wide-Sense Ergodic\n",
     "\n",
-    "ergodicity holds for linear mapping\n",
+    "Ergodicity holds for a linear mapping\n",
     "\n",
     "\\begin{equation}\n",
     "\\overline{ x_n[k] \\cdot x_n[k-\\kappa] } = E\\{  x[k] \\cdot x[k-\\kappa]  \\} \\;\\; \\forall n\n",
@@ -278,7 +278,7 @@
     "\\lim_{K \\to \\infty} \\frac{1}{2K + 1} \\sum_{k=-K}^{K} x[k] \\cdot x[k-\\kappa].\n",
     "\\end{equation}\n",
     "\n",
-    "These equations hold for power signals, i.e. the summation yields a finite value.\n"
+    "These equations hold for power signals, i.e., the summation yields a finite value.\n"
    ]
   },
   {
@@ -372,11 +372,11 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Example: Histogram of Gaussian Noise, Cosine and Rectangular Signal\n",
+    "# Example: Histogram of Gaussian Noise, Cosine, and Rectangular Signal\n",
     "\n",
-    "Here we use the numpy histogram with fixed number of bins and really the histogram mode rather than the density mode.\n",
+    "Here, we use the numpy histogram with a fixed number of bins and really the histogram mode rather than the density mode.\n",
     "\n",
-    "We here do not strictly deal with random sample functions (for the cosine and rect), but with amplitude values over time. We do this for practical purpose however, since it is nice to get an idea what a histogram looks like for known signals."
+    "We here do not strictly deal with random sample functions (for the cosine and rect), but with amplitude values over time. We do this for practical purposes, however, since it is nice to get an idea of what a histogram looks like for known signals."
    ]
   },
   {
@@ -725,7 +725,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.2"
   }
  },
  "nbformat": 4,