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signals Cheat Sheet (DRAFT) by

cheat sheet for signals

This is a draft cheat sheet. It is a work in progress and is not finished yet.

properties of the DTFT

Property
Aperidic signal
FT
 
x[n],y[n]
X(ejw),Y(ejw) peroid of 2PI
linearity
ax[n]+by[n]
aX(ejw)+bY(ejw)
time sifthing
x[n-n0]
e-jwn0X(ejw)
frequncey shift
ejw0nx[n]
X(ej(w-wo))
conjug­ation
x*[n]
X*(e-jw)
time reversal
x[-n]
X(ejw)
time expansion
x(k)[n­]={­x[n/k], if n=multiple of k
o, if n=/ multiple of k
X(ejkw)
convol­ution
x[n]*y[n]
X(ejw)Y(ejw)
Multip­lic­ation
x[n]y[n]
2pi\1i­nte­gra­l<2­pi>X(ejØ)Y(ej(w-Ø))dØ
differ­encing in time
x[n]-x­[n-1]
(1-e-jw)X(ejw)
accumu­lation
(k=-∞∑n) x[k]
(1-e-jw)\1X(ejw)+piX(ej0)(k=-∞∑∞) δ(w-2pik)
differ­enition in frequncy
nx[n]
J(dX(ejw))/dw
 

DTFT pairs

singnal
fourier tran
coeffi­cients
k=<­N>∑akejk(2n/N)n
(2pi)k­=-∞­∑∞(­akδ­(w-­N\2­pik)))
ak
ejwon
(2pi)L­=-∞­∑∞(­δ(w­-wo­-2piL)
w0=2pim/N