Better thumbnail for e360 post

_posts/2024-07-25-Echo360-Super-Speed-Userscript-released.md

@@ -4,7 +4,7 @@ author: peter
 date: 2024-07-25 02:35:04 +0800
 categories: [Programming] # Blogging | Electronics | Programming | Mechanical | SelfHosting
 tags: [extension, userscript, browser] # systems | embedded | rf | microwave | electronics | solidworks | automation | tip
-image: /assets/img/2024-07-25-Echo360-Super-Speed-/superspeed.png
+image: /assets/img/2024-07-25-Echo360-Super-Speed-/preview.png
 ---
 
 I've just made a userscript which allows you to set the speed of the Echo360 lecture player over the 2x maximum. By default, the script lets you set the player speed to 4x and 3x in addition to the default set of speeds, but you may customize the dropdown to have any speed you want (subject to browser limits).

_posts/2024-08-01-Useful-Mathematica-functions-for-signal-processing-units.md

@@ -0,0 +1,34 @@
+---
+title: Useful Mathematica functions for signal processing units
+author: peter
+date: 2024-08-01 01:40:23 +0800
+categories: [Uni] # Blogging | Electronics | Programming | Mechanical | SelfHosting
+tags: [ELEC4402] # systems | embedded | rf | microwave | electronics | solidworks | automation | tip
+# image: assets/img/2024-08-01-Useful-Mathematica-f/preview.png
+---
+
+I will update this as I add more functions.
+
+Using it for the unit ELEC4402 Communication Systems
+
+```mathematica
+(* Signal power *)
+SigPower[expr_, t_] :=
+ Limit[1/(2 T) Integrate[expr, {t, -T, T}], T -> Infinity]
+
+(* Normalized sinc function, default Sinc in Mathematica is not normalized *)
+SincNorm[Infinity] := Sinc[Pi  Infinity]
+SincNorm[t_?NumericQ] := Sinc[Pi  t]
+
+(* Fourier transform, frequency in Hz *)
+FTfreq[varargs__] :=
+ FourierTransform[varargs,
+   FourierParameters -> {0, -2*Pi}] /. {Sinc[f_] :>
+    SincNorm[Simplify[f/Pi]]}
+
+(* Inverse Fourier transform, frequency in Hz *)
+IFTfreq[varargs__] :=
+ InverseFourierTransform[varargs,
+   FourierParameters -> {0, -2*Pi}] /. {Sinc[f_] :>
+    SincNorm[Simplify[f/Pi]]}
+```