oS Rea signal w(t) cos(w.t + 8) 1[£7W(ƒ — ƒ-) +e W(ƒ + #)]
translation
“<® (w(t) is real]
Xe, Complex signal w(t) er! Wf — Sc)
C frequency
translation
T Bandpass signal Re{ g(t) e/*'} (GF -f.)+ G(-f -f)]
but Differentiation d we) ( j2nf)"W(f)
XS megmum [_ wuya (/2z/)-'W(ƒ) + †W(0) ð(ƒ)
< Convolution w,(r) * w(t) = | 10(À) Wi(f)W2(f)
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3/18/21
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Linearity @,5,[0]+a,1,[4] @,X,(Q) + 4,X,(Q)
First difference a{a]—s{a—-1) (I—e"9)X(0)
\Qiszx
I
Real sequence a{o) = x, (a) + x, [a] X(@! = A:Q) + #0)
X(- Qì = X”(G@ì
Parseval’s theorem
2 a~-
> bate? =f ieee eo
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Function Time Waveform w(t) Spectrum W(/)
+l, r>0 ]
Sinusoid cos(w.t + ¢) jel* HF — f.) + fed" HF +f)
Impulse train > &(t — kT) ho > Hf — nfo),
where fo = 1/T Scanne d with CamScanner
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Tính chất của biên đôi Laplace
Laplace-Domain Shifting e™ x(t) X(s— 50) R+Re{so}
Time/Frequency-Domain Scaling (ar) bX (£) aR
Time-Domain Convolution xX) *x2(f) X1(s)X2(s) At least Ri NR2
Property
Initial Value Theorem x(0”) = lim sX (s) Final Value Theorem lim x(t) = lim sX(s) Lan s—+0
4/13/21
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Mot so cap bién doi Laplace
11 [sin Wot] u(r) tet Re{s} >0
12 [e~@ cos@ot]u(t) Gia+a Re{s} > —a
13 [e~@ sin@ot}u(t) q r1 at Re{s} > —a
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Tinh chat cua biên đôi z
Convolution X1 *X2(n) Xj (z)X2(z) At least Ri NR>
Accumulation ) a9) = X(z) Atleast RN |z| > 1
Property
Initial Value Theorem x(0) = lim X(z) Final Value Theorem lim x(n) = lim {(z — 1)X(z)]
“IẠEJpA|
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Một số cặp biên đổi z
ff 17)
9 —na"u(—n—1) ay? z| <la
10 (cosÔon),(n) an rã |#|>]
II = (sinQen)u(n) ni mnm ld>l
l2 (a"cosQon)u(n) xB, |z| > Ja
13 (a"sinQon)u(n) 32 e|> lal
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