diff --git a/_posts/2024-08-01-Useful-Mathematica-functions-for-signal-processing-units.md b/_posts/2024-08-01-Useful-Mathematica-functions-for-signal-processing-units.md index 9bda1cb..a204623 100644 --- a/_posts/2024-08-01-Useful-Mathematica-functions-for-signal-processing-units.md +++ b/_posts/2024-08-01-Useful-Mathematica-functions-for-signal-processing-units.md @@ -14,19 +14,20 @@ 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] + Limit[1/(2 T) Integrate[expr^2, {t, -T, T}], T -> Infinity] -(* Normalized sinc function, default Sinc in Mathematica is not normalized *) +(* 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 *) +(* 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 *) +(* Inverse Fourier transform,frequency in Hz *) IFTfreq[varargs__] := InverseFourierTransform[varargs, FourierParameters -> {0, -2*Pi}] /. {Sinc[f_] :>