Merge pull request #11 from mgirola/L06_Q4_pull_request

Pull request for solution of L06 Q4 - fixed simple display bug in LaTeX display of one equation
dgerosa · Sep 23, 2024 · 5940ce9 · 5940ce9
2 parents f35338e + 3791d03
commit 5940ce9
Showing 1 changed file with 17 additions and 18 deletions.
diff --git a/lectures/L04_scipy.ipynb b/lectures/L04_scipy.ipynb
@@ -3043,24 +3043,23 @@
    "source": [
     "A convolution is defined as:  \n",
     "\n",
-    "  \\begin{equation}                                                                           \n",
-    "    (f \\star g)(t) \\equiv \\int_{-\\infty}^{\\infty} f(\\tau) g(t - \\tau) d\\tau                   \n",
-    "  \\end{equation}                                                                             \n",
-    "\n",
-    "  It is easy to compute this with FFTs, via the _convolution theorem_,                                                                        \n",
-    "  \\begin{equation}                                         \n",
-    "    \\mathcal{F}\\{f \\star g\\} = \\mathcal{F}\\{f\\} \\, \\mathcal{F}\\{g\\}                                          \n",
-    "  \\end{equation}                                         \n",
-    "  That is: the Fourier transform of the convolution of $f$ and $g$ is simply\n",
-    "  the product of the individual transforms of $f$ and $g$.  This allows us\n",
-    "  to compute the convolution via multiplication in Fourier space and then take\n",
-    "  the inverse transform, $\\mathcal{F}^{-1}\\{\\}$, to recover the convolution in real space:\n",
-    "  \n",
-    "  \\begin{equation}\n",
-    "  f \\star g = \\mathcal{F}^{-1}\\{ \\mathcal{F}\\{f\\} \\, \\mathcal{F}\\{g\\}\\}\n",
-    "  \\end{equation}\n",
-    "  \n",
-    "A common use of a convolution is to smooth noisy data, for example by convolving noisy data with a Gaussian.  We'll do that here."
+    "\\begin{equation}  \n",
+    "  (f \\star g)(t) \\equiv \\int_{-\\infty}^{\\infty} f(\\tau) g(t - \\tau) d\\tau \\tag{1}  \n",
+    "\\end{equation}  \n",
+    "\n",
+    "It is easy to compute this with FFTs, via the _convolution theorem_,  \n",
+    "\n",
+    "\\begin{equation}  \n",
+    "  \\mathcal{F}\\{f \\star g\\} = \\mathcal{F}\\{f\\} \\, \\mathcal{F}\\{g\\} \\tag{2}  \n",
+    "\\end{equation}  \n",
+    "\n",
+    "That is: the Fourier transform of the convolution of $f$ and $g$ is simply the product of the individual transforms of $f$ and $g$. This allows us to compute the convolution via multiplication in Fourier space and then take the inverse transform, $\\mathcal{F}^{-1}\\{\\}$, to recover the convolution in real space:\n",
+    "\n",
+    "\\begin{equation}  \n",
+    "  f \\star g = \\mathcal{F}^{-1}\\{ \\mathcal{F}\\{f\\} \\, \\mathcal{F}\\{g\\}\\} \\tag{3}  \n",
+    "\\end{equation}  \n",
+    "\n",
+    "A common use of a convolution is to smooth noisy data, for example by convolving noisy data with a Gaussian. We'll do that here.\n"
    ]
   },
   {