- #1
DragonPetter
- 830
- 1
If I modulate a pulse X(t) with a.) a sine wave or b.) a cosine wave, I have the frequency spectrum expressions
[tex]
a.) \frac{1}{2j}[X(f-f_0)-X(f+f_0)]
[/tex]
[tex]
b.) \frac{1}{2}[X(f-f_0)+X(f+f_0)]
[/tex]
When I plot these for a pulse, I see a difference in the magnitude spectrum, but I should not expect to see this since this is simply a phase shift of [tex]\pi/2[/tex]
I would think if I multiplied b.) by [tex]e^{-j\pi/2}[/tex], I would get what I see in a.) but this is not the case.
Can anyone help me with what I'm missing?
[tex]
a.) \frac{1}{2j}[X(f-f_0)-X(f+f_0)]
[/tex]
[tex]
b.) \frac{1}{2}[X(f-f_0)+X(f+f_0)]
[/tex]
When I plot these for a pulse, I see a difference in the magnitude spectrum, but I should not expect to see this since this is simply a phase shift of [tex]\pi/2[/tex]
I would think if I multiplied b.) by [tex]e^{-j\pi/2}[/tex], I would get what I see in a.) but this is not the case.
Can anyone help me with what I'm missing?