Omega Element[-pi, pi]: X(e^j omega) = {L, when omega = 0 e^-j omega(L-1)/2. sin

Question

Omega Element[-pi, pi]: X(e^j omega) = {L, when omega = 0 e^-j omega(L-1)/2. sin(omega L/2)/sin(omega/2), otherwise We therefore have another example of a complex-valued DTFT. We can determine its magnitude and phase components as follows. The magnitude component is easily seen to be |X(e^j omega)| = {L, when omega = 0 |sin(omega L/2)/sin(omega/2)|, otherwise while for the phase component we need to add a correction of plusminus pi when the ratio sin(omega L/2)/sin(omega/2) is negative, i.e.. X(e^j omega) = {0, when omega = 0 -omega(L-1)/2 plusminus pi middot 1/2 (1- sign (sin(omega L/2)/sin(omega/2)) otherwise why do we need & rightarrow to account for sign of the sine functions when they have zero phase?

Explanation / Answer

For the phase calculations for sine, it should get the result in the limits of sine function defined.

The result must be in [0 pi]. For cosine the result must be in [-pi/2 , pi/2]

So to get the results in limitations of sine we add + or - pi

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.