نموذج الإشارة ذات النطاق الضيق
عدل
في تطبيقات تشكيل الزاوية، مع تردد الموجة الحاملة f, φ هي أيضاً دالة متغير الزمن،[2] :
*يحتاج تعديل هذا القسم*
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
[3]
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mn>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mn><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mn>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mn><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
mi><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo></mrow><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo></munder></mrow><mrow class="MJX-TeXAtom-ORD"><mtext>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mtext></mrow></munder><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mrow><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mrow><mn>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mn><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mn>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mn></mfrac></mrow></mrow><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo></mrow></mrow><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo></mover></mrow><mrow class="MJX-TeXAtom-ORD"><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mn>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mn><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo></mrow></mover><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mi>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mi><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo><mo stretchy="false">
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo></mrow><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo></munder></mrow><mrow class="MJX-TeXAtom-ORD"><mtext>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mtext></mrow></munder><mo>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
</mo></mrow>
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
{\displaystyle }
sin
[
2
π
f
t
+
ϕ
(
t
)
]
=
sin
(
2
π
f
t
)
⋅
cos
[
ϕ
(
t
)
]
⏟
in-phase
+
sin
(
2
π
f
t
+
π
2
)
⏞
cos
(
2
π
f
t
)
⋅
sin
[
ϕ
(
t
)
]
⏟
quadrature
.
{\displaystyle \sin[2\pi ft+\phi (t)]\ =\ \underbrace {\sin(2\pi ft)\cdot \cos[\phi (t)]} _{\text{in-phase}}\,+\,\underbrace {\overbrace {\sin \left(2\pi ft+{\tfrac {\pi }{2}}\right)} ^{\cos(2\pi ft)}\cdot \sin[\phi (t)]} _{\text{quadrature}}.}
[4]
</img>