الموجات متوافقة الطور والعامودية

في الهندسة الكهربائية ، يمكن تفكيك أو توليف الدالة الجيبية [ $\sin (x)$ ] ذات تشكيل زاوي (angle modulation) من دالتين جيبية مشكّلة بالسعة (amplitude-modulated) التي يتم تعويضها في الطور بربع دورة ( $π$ / 2 راديان). جميع الدوال الثلاث لها نفس التردد. تعرف الدوال الجيبية المشكلة بالسعة بالموجات العامودية متوافقة الطور. في بعض السياقات يكون من الملائم أكثر الإشارة إلى تشكيل السعة (القاعدي) فقط بهذه الشروط.^[1]

نموذج الإشارة ذات النطاق الضيق

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)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

^[3]

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mn>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mn><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mn>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mn><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

mi><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo></mrow><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo></munder></mrow><mrow class="MJX-TeXAtom-ORD"><mtext>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mtext></mrow></munder><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mrow><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mrow><mn>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mn><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mn>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mn></mfrac></mrow></mrow><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo></mrow></mrow><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo></mover></mrow><mrow class="MJX-TeXAtom-ORD"><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mn>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mn><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo></mrow></mover><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mi>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mi><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo><mo stretchy="false">

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo></mrow><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo></munder></mrow><mrow class="MJX-TeXAtom-ORD"><mtext>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mtext></mrow></munder><mo>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

</mo></mrow>

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

\sin [2 π f t + ϕ (t)] = \underset{in-phase}{\underset{⏟}{\sin (2 π f t) \cdot \cos [ϕ (t)]}} + \underset{quadrature}{\underset{⏟}{\overset{\cos (2 π f t)}{\overset{⏞}{\sin (2 π f t + \frac{π}{2})}} \cdot \sin [ϕ (t)]}} .

^[4]

</img>

مراجع

^ Gast, (2005). 802.11 wireless networks : the definitive guide (ط. 2nd ed). Sebastopol, CA: O'Reilly. ISBN:0596100523. OCLC:58828461. مؤرشف من الأصل في 2019-12-12. {{استشهاد بكتاب}}: |طبعة= يحتوي على نص زائد (مساعدة)صيانة الاستشهاد: علامات ترقيم زائدة (link)
^ Wade, J. G. (John Graham), (1994). Signal coding and processing (ط. 2nd ed). Cambridge: Cambridge University Press. ISBN:0521412307. OCLC:28927715. مؤرشف من الأصل في 2019-12-12. {{استشهاد بكتاب}}: |طبعة= يحتوي على نص زائد (مساعدة)صيانة الاستشهاد: أسماء متعددة: قائمة المؤلفين (link) صيانة الاستشهاد: علامات ترقيم زائدة (link)
^ Karimi-Ghartemani، M.؛ Karimi، H.؛ Iravani، M. R. (2004-4). "A magnitude/phase-locked loop system based on estimation of frequency and in-phase/quadrature-phase amplitudes". IEEE Transactions on Industrial Electronics. ج. 51 ع. 2: 511–517. DOI:10.1109/TIE.2004.825282. ISSN:0278-0046. مؤرشف من الأصل في 2019-04-01. {{استشهاد بدورية محكمة}}: تحقق من التاريخ في: |تاريخ= (مساعدة)
^ Naidu, Prabhakar (2003). Modern digital signal processing : an introduction. Pangbourne: Alpha Science. ISBN:1842651331. OCLC:50876694. مؤرشف من الأصل في 2019-12-12.

انظر أيضا

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I /Q D ata for Dummies

بوابة هندسة

[1] Gast, (2005). 802.11 wireless networks : the definitive guide (ط. 2nd ed). Sebastopol, CA: O'Reilly. ISBN:0596100523. OCLC:58828461. مؤرشف من الأصل في 2019-12-12. {{استشهاد بكتاب}}: |طبعة= يحتوي على نص زائد (مساعدة)صيانة الاستشهاد: علامات ترقيم زائدة (link)

[2] Wade, J. G. (John Graham), (1994). Signal coding and processing (ط. 2nd ed). Cambridge: Cambridge University Press. ISBN:0521412307. OCLC:28927715. مؤرشف من الأصل في 2019-12-12. {{استشهاد بكتاب}}: |طبعة= يحتوي على نص زائد (مساعدة)صيانة الاستشهاد: أسماء متعددة: قائمة المؤلفين (link) صيانة الاستشهاد: علامات ترقيم زائدة (link)

[3] Karimi-Ghartemani، M.؛ Karimi، H.؛ Iravani، M. R. (2004-4). "A magnitude/phase-locked loop system based on estimation of frequency and in-phase/quadrature-phase amplitudes". IEEE Transactions on Industrial Electronics. ج. 51 ع. 2: 511–517. DOI:10.1109/TIE.2004.825282. ISSN:0278-0046. مؤرشف من الأصل في 2019-04-01. {{استشهاد بدورية محكمة}}: تحقق من التاريخ في: |تاريخ= (مساعدة)

[4] Naidu, Prabhakar (2003). Modern digital signal processing : an introduction. Pangbourne: Alpha Science. ISBN:1842651331. OCLC:50876694. مؤرشف من الأصل في 2019-12-12.

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الموجات متوافقة الطور والعامودية

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