Revised text

Author: spors

random_signals/introduction.ipynb

@@ -74,7 +74,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Statistical Signal Processing\n",
+    "### Processing of Random Signals\n",
     "\n",
     "In contrary to the assumption of deterministic signals in traditional signal processing, [statistical signal processing](https://en.wikipedia.org/wiki/Statistical_signal_processing) treats signals explicitly as random signals. Two prominent application examples involving random signals are"
    ]
@@ -85,11 +85,11 @@
    "source": [
     "#### Measurement of physical quantities\n",
     "\n",
-    "The measurement of physical quantities is often subject to additive noise and distortions by e.g. the amplifier. The aim of statistical signal processing is to estimate the physical quantity from the observed sensor data.\n",
+    "The measurement of physical quantities is often subject to additive noise and distortions. The additive noise models e.g. the sensor noise. The distortions, by e.g. the transmission properties of an amplifier, may be modeled by a system.\n",
     "\n",
     "![Model for the measurement of physical quantities](measurement_channel.png)\n",
     "\n",
-    "$\\mathcal{H}$ denotes an arbitrary (not necessarily LTI) system."
+    "$\\mathcal{H}$ denotes an arbitrary (not necessarily LTI) system. The aim of statistical signal processing is to estimate the physical quantity from the observed sensor data, given some knowledge on the disturbing system and the statistical properties of the noise."
    ]
   },
   {
@@ -98,9 +98,11 @@
    "source": [
     "#### Communication channel\n",
     "\n",
-    "In communications engineering a message is sent over a channel distorting the signal by e.g. multipath propagation. Additive noise is present at the receiver due to background and amplifier noise. The aim of statistical signal processing is to estimate the send message from the received message.\n",
+    "In communications engineering a message is sent over a channel distorting the signal by e.g. multipath propagation. Additive noise is present at the receiver due to background and amplifier noise.\n",
     "\n",
-    "![Model for the transmission of a message over a communication channel](communication_channel.png)"
+    "![Model for the transmission of a message over a communication channel](communication_channel.png)\n",
+    "\n",
+    "The aim of statistical signal processing is to estimate the send message from the received message, given some knowledge on the disturbing system and the statistical properties of the noise."
    ]
   },
   {
@@ -128,7 +130,7 @@
    "source": [
     "**Example - Sample functions of a random process**\n",
     "\n",
-    "The following example shows sample functions of a continuous amplitude real-valued random process. All sample functions have the same characteristics with respect to certain statistical properties."
+    "The following example shows sample functions of a continuous amplitude real-valued random process. All sample functions have the same properties with respect to certain statistical measures."
    ]
   },
   {
@@ -180,7 +182,7 @@
     "\n",
     "* What is different, what is common between the sample functions?\n",
     "\n",
-    "Solution: You should have observed that the amplitude values of the individual sample functions $x_n[k]$ differ for a fixed time instant $k$. However, the sample functions seem to share some common properties. For instance, positive and negative values seem to occur with approximately the same probability."
+    "Solution: You may have observed that the amplitude values of the individual sample functions $x_n[k]$ differ for a fixed time instant $k$. However, the sample functions seem to share some common properties. For instance, positive and negative values seem to occur with approximately the same probability."
    ]
   },
   {