Use different variables

project.md

@@ -21,18 +21,18 @@ $$
 Meanwhile, the Fourier transform of $$f$$ is
 
 $$
-\hat{f}(\hat{x}, \hat{y})
-= \int_\mathbb{R} \int_\mathbb{R} f(x, y) e^{-2 \pi i (\hat{x} x + \hat{y} y)} dx dy
+\hat{f}(u, v)
+= \int_\mathbb{R} \int_\mathbb{R} f(x, y) e^{-2 \pi i (u x + v y)} dx dy
 $$
 
-Note that the slice along the $$\hat{x}$$ axis in frequency space is described by
+Note that the slice along the $$u$$ axis in frequency space is described by
 
 $$
 \begin{align*}
-\hat{f}(\hat{x}, 0)
-&= \int_\mathbb{R} \int_\mathbb{R} f(x, y) e^{-2 \pi i \hat{x} x} dx dy \\
-&= \int_\mathbb{R} \left( \int_\mathbb{R} f(x, y) dy \right) e^{-2 \pi i \hat{x} x} dx \\
-&= \int_\mathbb{R} p(x) e^{-2 \pi i \hat{x} x} dx \\
-&= \hat{p}(\hat{x})
+\hat{f}(u, 0)
+&= \int_\mathbb{R} \int_\mathbb{R} f(x, y) e^{-2 \pi i u x} dx dy \\
+&= \int_\mathbb{R} \left( \int_\mathbb{R} f(x, y) dy \right) e^{-2 \pi i u x} dx \\
+&= \int_\mathbb{R} p(x) e^{-2 \pi i u x} dx \\
+&= \hat{p}(u)
 \end{align*}
 $$