Re: alternating-polarity Amplitude-Modulated tone?


<cclinard@xxxxxxxxxxx> wrote in message
news:1145546603.495621.138290@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hello all,


I need to make an amplitude-modulated tone with alternating polarities
using Matlab 5.


The part I am stuck on is how to get the phase to reverse after each
cycle of the AM envelope. The phase needs to reverse at the null point
between each AM cycle.


Also, does anyone have advice on how to get the initial phase of both
frequencies to be zero?


I am new to using Matlab and would greatly appreciate any
help/advice/code.


Some general information:
sampling frequency 10,000 Hz
carrier frequency 1000 Hz
modulation frequency 84.96094 Hz
duration 1.024 seconds

Q: how to get the initial phase of both frequencies to be zero?

A: Compute them both as cosines starting at time zero.
x=cost(wct) where wc is the carrier radian frequency and t is time
[wc=2*pi*fc]
y=cos(wmt) where wm is the modulation radian frequency

Q: how to get the phase to reverse after each cycle of the AM envelope. The
phase needs to reverse at the null point between each AM cycle.

A: It would be better if you were clearer in your specification of the
objective. It depends on what you mean:

- you want the phase of the carrier to reverse after each *cycle* of the AM
envelope?
- you want the phase of the carrier to reverse at each *zero* (half-cycle)
of the AM envelope / that is, you want it to be "in phase" when the
modulation is positive and "reversed phase" when the modulation is negative.
- you want the phase of the AM envelope to reverse after each cycle of the
AM envelope?

"This phase needs to reverse at the null point between each AM cycle" So
this seems to say the phase changes at each zero-crossing or half-cycle and
not each cycle......

I will *guess* that you mean you want the phase of the carrier to reverse at
*each* null point of the AM signal. That means that you want the modulator
to be a 4-quadrant multiplier or a modulator for a "suppressed carrier" or
"double sideband" system. Here's how that works:

If the modulating signal is positive, then the output is proportional to the
modulating signal amplitude and the carrier is "in phase".
If the modulating signal is negative, then the output is proportional to the
modulating signal amplitude and the carrier is "out of phase" or, simply
multiplied by -1.

If this is what you need, then from above, the modulated signal would be
x*y.

It's a bit different than the typical "AM" because AM normally suggests that
the modulated signal is:

m1(t)= [1 + cos(wmt)]*cost(wct)

This yields 100% modulation AM. Note that the modulating signal never goes
below zero. Thus, the phase of the carrier never "switches". The spectrum
looks like a carrier of amplitude 1.0 at wc and sidebands at wc+wm and wc-wm
each with amplitudes of 0.5.

Otherwise:

m2(t) = cos(wmt)*cos(wct)

yields a spectrum that looks like lines at wc+wm and wc-wm with no visible
carrier at wc.

Fred








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