From 255a4e8257f9d4de9ce6e72924eeebcc02695f86 Mon Sep 17 00:00:00 2001
From: Peter Tanner <git@petertanner.dev>
Date: Thu, 1 Aug 2024 01:42:56 +0800
Subject: [PATCH] New posts:
 _posts/2024-08-01-Useful-Mathematica-functions-for-signal-processing-units.md

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+---
+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]]}
+```