signal.py

Created by famille-bvc

Created on October 20, 2023

1.06 KB


** TF de cos(2pif0t) **

= exp (2pijF0t) + exp(-2ppijF0t)
avec formule deuler on a 
TF(exp..) = delta(f-f0)
= X(t) = delta(f-f0) + delta(f-f0) le tout sur 2

///////////////////////////////
TF de y(t) = A * rect sur delta

donc Y(F)= integrale de A*rect sur delta * exp(-2pijf0t) dt
Y(F) = integrale de delta/-2 a delta/2 de 
A*exp(...) = A*exp(...) / -2pif
Y(F) = Adeltasinc(pifdelta)

*calcul du coef de F Zn
convolue (*) entouré

z(t) = somme rect(t-nT) sur delta
z periodique donc on ecrit : 
= rect/delta convolue somme delta(t-nT)

on TF
Z(t) = somme ZnTF(exp(2pijnT)) 
= deltasinc(pifdelta)* TF(delta(t-nT)
Z(t) = somme Zn dlta(f - n/T) 
= somme des delta sinc(pi n/t delta) * delta(f - n/T)
Zn = delta/T * sinc(pi n/T delta)

*calculer et dessiner le spectre
*de cos(2pijf0t)*Z(t)

on fait zn x cos... 
on convolue les deux resultats precedents 
TF de delta(t-nTe) = 1/Te somme delta(f - n/Te)

convolution de Arect/delta convolue arect/delta

Arect'/DELTA convolue Arect/delta
= A^2 rect ( t + delta/2) / delta - A^2 rect(t-delta/2)/delta
= A^2 delta . tri/2delta

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