Added noise to the in-class data set.

sdrangan · Feb 12, 2019 · 8456f2e · 8456f2e
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diff --git a/lectures/Lect05_Lasso.pdf b/lectures/Lect05_Lasso.pdf
diff --git a/lectures/Lect05_Lasso.pptx b/lectures/Lect05_Lasso.pptx
diff --git a/unit05_lasso/lasso_in_class.ipynb b/unit05_lasso/lasso_in_class.ipynb
@@ -6,7 +6,7 @@
    "source": [
     "# LASSO Regression In-Class Exercise\n",
     "\n",
-    "In this exercise, we will see how to use LASSO for pitch detection in audio.\n",
+    "In this exercise, we will see how to use LASSO for pitch detection and noise removal in audio.\n",
     "\n",
     "We load the following packages."
    ]
@@ -26,14 +26,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Load the data\n",
+    "## Load the Data\n",
     "\n",
-    "The data is taken from a sample of about 20~ms of audio from a viola.  I have already pre-processed the data.  You can load it with the following command.  The value `t` is the time (in seconds) and `y` is the sample of audio (this is a mono recording)."
+    "The data is taken from a sample of about 20 ms of audio from a viola.  I have already pre-processed the data.  You can load it with the following command.  The value `t` is the time (in seconds) and `y` is the sample of audio (this is a mono recording).  Noise has been artificially added to the sample."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -85,11 +85,14 @@
    "source": [
     "## Creating Features for a Sinusoidal Model\n",
     "\n",
-    "We will try to fit a model of the\n",
+    "We will try to fit a model of the form:\n",
     "\n",
     "    y[i] = \\sum_j a[j]*sin(2*pi*freq[j]*t[i]) + b[j]*cos(2*pi*freq[j]*t[i])\n",
     "\n",
-    "That is, `y[i]` is a sum of sinusoids.  This is a common model for audio signals.\n",
+    "That is, `y[i]` is a sum of sinusoids.  This is a common model for audio signals since an instrument, such as a viola, produces discrete tones.  \n",
+    "\n",
+    "This model is non-linear in the frequency parameters.  So, instead of trying to find the frequencies, we will fix a large number of frequencies and then require that the coefficients `a[j]` and `b[j]` are mostly sparse.  \n",
+    "\n",
     "We will use the following vector of frequencies.  This vector includes frequencies on the muscial scale as well as frequencies between the musical notes."
    ]
   },
@@ -175,9 +178,7 @@
     "We can now use LASSO regression to find the model\n",
     "* Use LASSO regression with `alpha=500` to fit the model.  \n",
     "* Find the R^2-score on the test data.\n",
-    "* Plot the predicted value of `y` for `t in [0,0.02]`.\n",
-    "* \n",
-    "\n"
+    "* Plot the predicted value of `y` for `t in [0,0.02]`."
    ]
   },
   {

diff --git a/unit05_lasso/viola_sample.p b/unit05_lasso/viola_sample.p