Science > Physics > Frequency Modulation: Bandwidth of information signal To Bandwidth of modulated Signal
| Topic: |
Science > Physics |
| User: |
"Nano" |
| Date: |
27 Apr 2006 11:32:50 PM |
| Object: |
Frequency Modulation: Bandwidth of information signal To Bandwidth of modulated Signal |
Greetings to All,
With FM I've learned that the Bessel defines the number of sidebands
in the FM signal with respect to the modulation index of the modulated
signal (delta F/ Fm). My question has to do with the signal's spectral
content. Basically I see FM as an amplitude to frequency converter, the
higher the amplitude, the higher the frequency, the lower the amplitude
the lower the frequency (so 0 for amplitude is the center frequency).
Now, if I create a resonator with a variable centre frequency, and vary
the center frequency over a range of frequencies (let us assume that
this frequency sweep is a sinusoidal periodic waveform with a frequency
of "Fsweep"). Then the upper 3db cutoff of the highest centre frequency
and the lower 3db cutoff of the lowest center frequency would define my
system's bandwidth. For this example we need to assume no harmonic
distortion in the resonator to eliminate harmonic influence to the
spectrum. Now, why is it when the frequency "Fsweep" is increased or
decreased that we decrease or increase the amplitudes of the sidebands
(respectively)? Also, why are these sidebands even created, if the
energy of a given signal is changing over a finite set of frequencies?
Are the sidebands a result of the energy in a given signal changing
frequency (meaning the frequency (Fsweep) of the "changing frequency")?
If so wouldn't an increase in the frequency (Fsweep) of the "changing
frequency" result in more sidebands, (as this would appear to be using
more of the signal's energy?) Because according to the modulation index
& Bessel formula, the number of sidebands are inversely proportional to
the modulating frequency (Fsweep), but proportional to the changing
frequency. Or could the sidebands be a result of a spectrum analyzer
not being able to sample the spectrum fast enough to properly show the
majority of the energy created by the "variable center frequency
resonator" as it shifts at some frequency (Fsweep) about the spectrum,
thus appearing as sidebands but actually is distortion? Also, if the
sinusoids at frequencies of the sidebands, and with their respective
amplitudes and phases are summed together, will the resultant time
domain function be the replication of the time domain FM signal? And
finally we know that a pure periodic signal is a sinusoidal signal, and
a FM signal would appear to be a pure periodic sinusoid with a changing
period, thus should there even be sidebands?
Sorry for the lengthy email, I thought I'd ask the experts as this
has been troubling my mind for quite some time.
Nate
.
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| User: "Charles" |
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| Title: Re: Frequency Modulation: Bandwidth of information signal To Bandwidth of modulated Signal |
28 Apr 2006 02:42:30 AM |
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On 27 Apr 2006 21:32:50 -0700, "Nano" <nanonut@gmail.com> wrote:
Greetings to All,
With FM I've learned that the Bessel defines the number of sidebands
in the FM signal with respect to the modulation index of the modulated
signal (delta F/ Fm). My question has to do with the signal's spectral
content. Basically I see FM as an amplitude to frequency converter, the
higher the amplitude, the higher the frequency, the lower the amplitude
the lower the frequency (so 0 for amplitude is the center frequency).
Now, if I create a resonator with a variable centre frequency, and vary
the center frequency over a range of frequencies (let us assume that
this frequency sweep is a sinusoidal periodic waveform with a frequency
of "Fsweep"). Then the upper 3db cutoff of the highest centre frequency
and the lower 3db cutoff of the lowest center frequency would define my
system's bandwidth. For this example we need to assume no harmonic
distortion in the resonator to eliminate harmonic influence to the
spectrum. Now, why is it when the frequency "Fsweep" is increased or
decreased that we decrease or increase the amplitudes of the sidebands
(respectively)? Also, why are these sidebands even created, if the
energy of a given signal is changing over a finite set of frequencies?
Are the sidebands a result of the energy in a given signal changing
frequency (meaning the frequency (Fsweep) of the "changing frequency")?
If so wouldn't an increase in the frequency (Fsweep) of the "changing
frequency" result in more sidebands, (as this would appear to be using
more of the signal's energy?) Because according to the modulation index
& Bessel formula, the number of sidebands are inversely proportional to
the modulating frequency (Fsweep), but proportional to the changing
frequency. Or could the sidebands be a result of a spectrum analyzer
not being able to sample the spectrum fast enough to properly show the
majority of the energy created by the "variable center frequency
resonator" as it shifts at some frequency (Fsweep) about the spectrum,
thus appearing as sidebands but actually is distortion? Also, if the
sinusoids at frequencies of the sidebands, and with their respective
amplitudes and phases are summed together, will the resultant time
domain function be the replication of the time domain FM signal? And
finally we know that a pure periodic signal is a sinusoidal signal, and
a FM signal would appear to be a pure periodic sinusoid with a changing
period, thus should there even be sidebands?
Sorry for the lengthy email, I thought I'd ask the experts as this
has been troubling my mind for quite some time.
Nate
I'm just an old retread technician, but I may have a few useful
comments.
The number of side frequencies in an FM modulated carrier are
infinite, but they drop off in level fairly quickly, so for most
purposes they can be ignored. Your definition of the 3 dB point is
arbitrary, we used the ten dB point. Neither has a basis in theory,
they are arbitrary choices.
If you set us a signal generator for an FM signal and look at it with
a spectrum analyzer you may see a spectrum of frequencies with nothing
changing, or you may see what looks like a single frequency moving
back and forth across the screen, two way of looking at the same
thing. If you can do the math, they come out to be the same thing, I
never could, so I just accept it as being the same thing, looked at in
a different manner.
A thing to keep in mind, it is impossible to change the frequency of a
sine wave, by definition the sine wave is forever without change, The
way to have the effect of changing a frequency is to add other sine
waves in the proper amplitude and phase relationship. The composite
wave then has the appearance of a signal changing in frequency.
.
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| User: "Helmut Wabnig" |
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| Title: Re: Frequency Modulation: Bandwidth of information signal To Bandwidth of modulated Signal |
28 Apr 2006 02:28:54 AM |
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On 27 Apr 2006 21:32:50 -0700, "Nano" <nanonut@gmail.com> wrote:
Greetings to All,
snip long technobabble
Sorry for the lengthy email, I thought I'd ask the experts as this
has been troubling my mind for quite some time.
Nate
Would you re-state your question in 1(one) clear sentence?
BTW, did you ever have the opportunity to play with
a reasonable good modern spectrum analyzer?
Watch the FM spectrum as the lines come and go.
What do you see on an unmodulated FM signal?
What is the difference to AM or SSB?
w.
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| User: "Jan Panteltje" |
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| Title: Re: Frequency Modulation: Bandwidth of information signal To Bandwidth of modulated Signal |
28 Apr 2006 04:44:46 AM |
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On a sunny day (27 Apr 2006 21:32:50 -0700) it happened "Nano"
<nanonut@gmail.com> wrote in
<1146198770.437356.6830@y43g2000cwc.googlegroups.com>:
Greetings to All,
The 'logical' explanaion of the 'infinite' number (it is not infinite*) sidebands:
*In order to change the frequency of a pure sinewave, you will have to change its waveform.*
Try drawing [sine] periods on paper, and thne [advance towards] more per inch etc.
This requires a 'distortion' of the pure sinewave, it can now be seen as composed of more then one
pure sinewaves (see Fourrier).
This is the (almost never heard) time domain explanation.
The other is mathematicaly:
write out
v = ac sin(w1 +M sin w2 )
Where M is the 'modulation index'.
http://cnyack.homestead.com/files/modulation/modfm.htm
*noise is your friend.
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