190325 commit

Lectures/Lecture - Lomb-Scargle/Lecture-Lomb-Scargle.jl

@@ -82,11 +82,11 @@ md"""
 
 # ╔═╡ 477704cc-f022-4cc5-a4a4-679387b819bd
 # ╠═╡ show_logs = false
-md"""
+cm"""
 ## A reminder of the CFT
 ***
 
-- Given a continuous signal g(t) the Fourier transform and its inverse are:
+- Given a continuous signal ``g(t)`` the Fourier transform and its inverse are:
 
 ```math
 \hat{g}(f) \equiv \int_{-\infty}^\infty g(t) e^{-2\pi i f t} dt \quad  g(t) \equiv \int_{-\infty}^\infty \hat{g}(f) e^{+2\pi i f t} df
@@ -98,7 +98,7 @@ md"""
 \mathcal{F}\{g\} = \hat{g} \quad    \mathcal{F}^{-1}\{\hat{g}\} = g
 ```
 
-- g and ĝ are know as a Fourier pair: $g \Longleftrightarrow \hat{g}$.
+- ``g`` and ``ĝ`` are know as a Fourier pair: ``g \Longleftrightarrow \hat{g}``.
 
 - The Fourier Transform (FT) is a linear operator:
 
@@ -107,22 +107,22 @@ md"""
        \mathcal{F}\{A f(t)\} = A\mathcal{F}\{f(t)\}
 ```
 
-- The FT of a sinusoid with frequency $f_0$ is a sum of delta functions at $\pm f_0$, where $\delta(f)\equiv\int_{-\infty}^\infty e^{-2\pi i x f}df$.
+- The FT of a sinusoid with frequency ``f_0`` is a sum of delta functions at ``\pm f_0``, where ``\delta(f)\equiv\int_{-\infty}^\infty e^{-2\pi i x f}df``.
 
-- We can write: $ \mathcal{F}\{e^{2\pi f_0 t}\} = \delta(f - f_0)$, and:
+- We can write: `` \mathcal{F}\{e^{2\pi f_0 t}\} = \delta(f - f_0)``, and:
 
 ```math
 \mathcal{F}\{\cos(2\pi f_0 t)\} = \frac{1}{2}\left[\delta(f - f_0) + \delta(f + f_0)\right] \quad
       \mathcal{F}\{\sin(2\pi f_0 t)\} = \frac{1}{2i}\left[\delta(f - f_0) - \delta(f + f_0)\right]
 ```
 
-- Relations that can be derived from Euler’s formula: $e^{ix} = \cos x + i\sin x$
+- Relations that can be derived from Euler’s formula: ``e^{ix} = \cos x + i\sin x``
 
-- A time shift imparts a phase in the FT:  $  \mathcal{F}\{g(t - t_0)\} = \mathcal{F}\{g(t)\} e^{-2\pi i ft_0}$.
+- A time shift imparts a phase in the FT:  ``  \mathcal{F}\{g(t - t_0)\} = \mathcal{F}\{g(t)\} e^{-2\pi i ft_0}``.
 
-- And, as we know, the squared amplitude of the FT of a continuous signal is known as the power spectral density (PSD):  $ \mathcal{P}_g \equiv \left|\mathcal{F}\{g\}\right|^2 $.
+- And, as we know, the squared amplitude of the FT of a continuous signal is known as the power spectral density (PSD):  `` \mathcal{P}_g \equiv \left|\mathcal{F}\{g\}\right|^2 ``.
 
-    - Note that if $g$ is real-valued, it follows that $P_g$ is an even function, {i.e.} $\mathcal{P}_g(f) = \mathcal{P}_g(-f)$.
+    - Note that if ``g`` is real-valued, it follows that ``P_g`` is an even function, {i.e.} ``\mathcal{P}_g(f) = \mathcal{P}_g(-f)``.
 
 $(LocalResource("Pics/FTpairs.png"))
 """
@@ -709,7 +709,7 @@ md"""
 # ╔═╡ 9d413d79-c9fb-4c30-ac02-92380510b607
 # ╠═╡ show_logs = false
 begin
-	fg6 = Figure(size=(2000,1000))
+	fg6 = Figure(size=(700,350))
 	
 	ax1fg6 = Axis(fg6[1, 1],
 	    title="Peak scaling with number of data points (fixed S/N=10)",
@@ -837,7 +837,7 @@ begin
 	p99 = LombScargle.fapinv(lsboot7,0.99)
 	
 	
-	fg7 = Figure(size=(1000,400))
+	fg7 = Figure(size=(700,350))
 	
 	ax1fg7 = Axis(fg7[1, 1],
 	    )