diff --git a/psets/pset6.ipynb b/psets/pset6.ipynb index 3a5e04e..8d1b21a 100644 --- a/psets/pset6.ipynb +++ b/psets/pset6.ipynb @@ -17,7 +17,7 @@ "source": [ "## Problem 1 (10+10 points)\n", "\n", - "**(a)** In class, we showed that if $\\tilde{y} = \\bar{F} y, \\tilde{a} = \\bar{F} a, \\tilde{x} = \\bar{F} x$ where $F$ is the DFT matrix, then $y = a \\circledast x$ (circular convolution) implies $\\tilde{y} = \\tilde{a} \\, \\mbox{.*} \\, \\tilde{x}$ (element-wise product). Show that the reverse is also true: show that if $\\tilde{y} = \\tilde{a} \\circledast \\tilde{x}$, then $y = a \\, \\mbox{.*} \\, x$. \n", + "**(a)** In class, we showed that if $\\tilde{y} = \\bar{F} y, \\tilde{a} = \\bar{F} a, \\tilde{x} = \\bar{F} x$ where $F$ is the DFT matrix, then $y = a \\circledast x$ (circular convolution) implies $\\tilde{y} = \\tilde{a} \\, \\mbox{.*} \\, \\tilde{x}$ (element-wise product). Show that the reverse is also true: show that if $\\tilde{y} = \\tilde{a} \\circledast \\tilde{x}$, then $y = \\alpha (a \\, \\mbox{.*} \\, x) $ for some scale factor $\\alpha = ???$. \n", "\n", "**(b)** Differentiating through convolutions, in class, involved the \"reversal\" permutation $R$:\n", "$$\n",