2024-08-01 01:42:56 +08:00
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---
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title: Useful Mathematica functions for signal processing units
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author: peter
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date: 2024-08-01 01:40:23 +0800
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2024-10-29 17:42:47 +08:00
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categories: [Programming, University] # Blogging | Electronics | Programming | Mechanical | SelfHosting
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tags: [ELEC4402, communications systems, mathematica] # systems | embedded | rf | microwave | electronics | solidworks | automation | tip
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2024-08-01 01:42:56 +08:00
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# image: assets/img/2024-08-01-Useful-Mathematica-f/preview.png
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---
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I will update this as I add more functions.
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Using it for the unit ELEC4402 Communication Systems
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```mathematica
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(* Signal power *)
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SigPower[expr_, t_] :=
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2024-08-14 15:54:38 +08:00
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Limit[1/(2 T) Integrate[expr^2, {t, -T, T}], T -> Infinity]
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2024-08-01 01:42:56 +08:00
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2024-08-14 15:54:38 +08:00
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(* Normalized sinc function,default Sinc in Mathematica is not \
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normalized *)
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2024-08-01 01:42:56 +08:00
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SincNorm[Infinity] := Sinc[Pi Infinity]
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SincNorm[t_?NumericQ] := Sinc[Pi t]
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2024-08-14 15:54:38 +08:00
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(* Fourier transform,frequency in Hz *)
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2024-08-01 01:42:56 +08:00
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FTfreq[varargs__] :=
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FourierTransform[varargs,
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FourierParameters -> {0, -2*Pi}] /. {Sinc[f_] :>
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SincNorm[Simplify[f/Pi]]}
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2024-08-14 15:54:38 +08:00
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(* Inverse Fourier transform,frequency in Hz *)
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2024-08-01 01:42:56 +08:00
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IFTfreq[varargs__] :=
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InverseFourierTransform[varargs,
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FourierParameters -> {0, -2*Pi}] /. {Sinc[f_] :>
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SincNorm[Simplify[f/Pi]]}
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```
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