- #1
Jammin_James
- 49
- 0
1. What is the null-to-null bandwidth of an AM signal with a single-tone message whose duration is 10ms and whose frequency is 1kHz?
2. Relevant transforms (sorry, I don't know how to include special formula functions that are on the forum here):
x(t)cos(ft) <-> 1/2[X(f+f0)+X(f-f0)]
Also the pulse transform, I don't know how I'd type that out, sorry. : /
3. The Attempt at a Solution .
In my mind I've pictured this in the time domain as a cosine wave being multiplied by a pulse 10ms long, centered around 0s. So translated into the frequency domain this would become a Sinc function split by the cosine tone at -1kHz and +1kHz. Normally, since only the positive frequencies are considered, only 1/T of the Sinc would be involved, but because of the shift (from the cosine) both zero crossings of the Sinc function now come into play making the width of the zero crossing 2/T.
So my final answer came to 200Hz.
Does this seem right?
2. Relevant transforms (sorry, I don't know how to include special formula functions that are on the forum here):
x(t)cos(ft) <-> 1/2[X(f+f0)+X(f-f0)]
Also the pulse transform, I don't know how I'd type that out, sorry. : /
3. The Attempt at a Solution .
In my mind I've pictured this in the time domain as a cosine wave being multiplied by a pulse 10ms long, centered around 0s. So translated into the frequency domain this would become a Sinc function split by the cosine tone at -1kHz and +1kHz. Normally, since only the positive frequencies are considered, only 1/T of the Sinc would be involved, but because of the shift (from the cosine) both zero crossings of the Sinc function now come into play making the width of the zero crossing 2/T.
So my final answer came to 200Hz.
Does this seem right?