cos(a±b)=cos(a)cos(b)∓sin(a)sin(b)(B.1)
sin(a±b)=sin(a)cos(b)∓cos(a)sin(b)(B.2)
tan(a±b)=tan(a) ± tan (b)1∓tan (a) tan (b)(B.3)
cos(a) cos(b)=12cos (a+b) + 12cos (a-b)(B.4)
sin(a)sin(b)=12cos(a-b)-12cos(a+b)(B.5)
sin(a)cos(b)=12sin(a+b)+12sin(a-b)(B.6)
cos(a)+cos(b)=2 cos(a+b2)cos(a-b2)(B.7)
cos(a)-cos(b)=-2 sin (a+b2) sin (a-b2)(B.8)
sin (a)+sin(b)=2 sin (a+b2) cos (a-b2)(B.9)
sin(a) - sin(b)=2 sin (a-b2) cos (a+b2)(B.10)
cos(2a)=cos2(a)-sin2(a)(B.11)
sin(2a)=2sin(a) cos(a)(B.12)
tan(2a)=2tan(a)1-tan2(a)(B.13)
cos2(a)=12 + 12 cos(2a)(B.14)
sin2(a)=12 - 12 cos(2a)(B.15)
∫xeaxdx=ax-1a2eax(B.16)
∫1x2+a2dx=1atan-1(xa)(B.17)
∫xx2+a2dx=12ln(x2+a2)(B.18)
∫x2x2+a2dx=x-atan-1(xa)(B.19)
∫xcos(ax)dx=1a2[cos(ax)+axsin(ax)](B.20)
∫xsin(ax)=1a2[sin(ax)-axcos(ax)](B.21)
∫eaxcos(bx)dx=eaxa2+b2[acos(bx)+bsin(bx)](B.22)
∫eaxsin(bx)dx=eaxa2+b2[asin(bx)-bcos(bx)](B.23)
∫(a+bx)ndx=(a+bx)n+1b(n+1),n>0(B.24)
∫1(a+bx)ndx=-1b(n-1)(a+bx)n-1,n>1(B.25)
Signal |
Transform |
ROC |
---|---|---|
δ (t) |
1 |
all s |
u (t) |
1s |
Re {s} > 0 |
u (−t) |
-1s |
Re {s} < 0 |
1s-a |
Re {s} > a |
|
−eat u (−t) |
1s-a |
Re {s} < a |
ejω0t u (t) |
1s-jω0 |
Re {s} > 0 |
e−|t| |
-2s2-1 |
−1 < Re {s} < 1 |
Π(t-τ/2τ) |
1-e-srs |
Re {s} > −∞ |
cos (ω0t) u (t) |
ss2+ω20 |
Re {s} > 0 |
sin (ω0t) u (t) |
ω0s2+ω20 |
Re {s} > 0 |
eat cos (ω0t) u(t) |
s-a(s-a)2+ω20 |
Re {s} > a |
eat sin (ω0t) u (t) |
ω0(s-a)2+ω20 |
Re {s} > a |
Signal |
Transform |
ROC |
---|---|---|
δ[n] |
1 |
all z |
u[n] |
zz-1 |
|z| > 1 |
u[−n] |
-zz-1 |
|z| < 1 |
an u[n] |
zz-a |
|z| > |a| |
−an u[−n − 1] |
zz-a |
|z| < |a| |
cos (Ω0n) u[n] |
z[z-cos(Ω0)]z2-2cos(Ω0) z+1 |
|z| > 1 |
sin (Ω0n) u[n] |
sin(Ω0)zz2-2cos(Ω0) z+1 |
|z| > 1 |
an cos (Ω0n) u[n] |
z[z-acos(Ω0)]z2-2acos(Ω0) z+a2 |
|z| > |a| |
an sin (Ω0n) u[n] |
asin(Ω0)zx2-2acos(Ω0) z+a2 |
|z| > |a| |
nan u[n] |
az(z-a)2 |