Re: Is it possible to reproduce a small bandwidth (~10 hz) audio signal using a sine wave of variable frequency and amplitude?

maxplanck wrote:
Ron N. wrote:
On Dec 5, 8:05 am, Jerry Avins <j...@xxxxxxxx> wrote:
maxplanck wrote:

...

Does anyone have any more to say about this?
Does my approach make sense or is it flawed? If so, how can I fix
it?
Is there a better way to go about doing what I'm trying to do?
There may be something to it, but if so it eludes me. You have a
waveform you know how to describe, yet for the sake of "simplicity"
you
are looking for an alternate description so complex that it eludes
you.
Unfortunately, humans are not so simple, and what they
might perceive could very well seem closer to the far more
complex (hah!) description (slightly changing frequencies
with an variational beat pattern). Interestingly enough,
it might elude you, but not your ears.
The sound might stimulate my ears, but the hoped-for description
doesn't

stimulate my brain. The description, if Maxie ever finds and refines
it,

may have surpassing beauty. I tried to explain that those of us who
don't get it have no reason to respond to him.

Jerry

I'm hoping that you guys who know a lot more about complex baseband
representation etc. than i do will tell me more about what you think?

Does what i posted earlier make any sense? If not, where am i coming
off
the rails?

I can read and learn more about complex baseband representation, dig
more
to find out what the derivative of the two valued arctan function is,
etc., but i'm hoping that you guys who know a lot about these kind of
things will tell me whether i would be attempting something
insurmountable.

Thanks very much for all of your responses so far.



In case anyone missed my earlier posts, here they are, summed up:


----------------------------------------------

I have an audio signal which i created by summing 3 sine waves:

Sine Wave 1: Amplitude=1, Frequency=55 hz
Sine Wave 2: Amplitude=0.39, Frequency=52.87 hz
Sine Wave 3: Amplitude=0.34, Frequency=57.54 hz

The starting phase for all 3 sine waves is zero.

This signal sounds very interesting when played through a speaker. I
want
to represent it in a model which is as simple and intuitive as
possible,
and which can be easily manipulated through variables whose audible
properties are already understood by the human hearing/audio
processing
mechanism. Since amplitude and frequency are properties which the
human
ear intuitively understands, I figure these quantities would be ideal
for
variables in such a model.

My ultimate goal is to map the frequency and amplitude components onto
a
carrier whose frequency equals the MIDI note # nearest to my analyzed
signal's power spectrum. (For the signal that I described above, this
frequency would be 55 hz, which is MIDI note # 33.) By mapping the
frequency and amplitude components onto this carrier, I hope to
reproduce
my original signal. The benefit of doing this is that now I can
examine
the signal in terms that my ear and brain intuitively understands,
which
I can easily and intuitively manipulate.

Your ear can't understand a tritone?

I'm assuming that such a model, when used to describe a small
bandwidth
signal such as the one that i described above (bandwidth=~5hz), would
not
involve an amplitude modulator that would produce any sidebands far in
frequency from the carrier..

The total bandwidth around the carrier of an AM signal is twice the
highest modulating frequency. The sideband frequencies are symmetrical
about the carrier, so your signal can't be generated by amplitude
modulation alone. FM (and PM) sidebands aren't in general symmetrical;
the asymmetry depends on the particular modulating frequencies.

I assume this because I know that the bandwidth of a single sine
carrier,
single sine modulator AM signal is equal to twice the modulator's
frequency. Since half the bandwidth of my audio signal is ~2.5 hz, the
modulator would have to be around 2.5 hz. (sounds right?)

Yes, but AM won't cut it.

I confirmed this for myself by tracking my signal's amplitude envelope
(calculated by drawing a line between adjacent local maxima), this
envelope has a fundamental frequency of around 2.5 hz, and a beat
frequency of ~0.4 hz. (by "beat frequency," i mean like this:
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/beat.html#c3 ). This
beat frequency corresponds to the difference in beat frequency between
the carrier and the lower frequency sideband, and the carrier and the
upper frequency sideband.

57.54 - 55 = 2.54
55 - 52.87 = 2.13

2.54-2.13 = .39 = ~0.4


However, i think this signal is more than a simple one carrier, one
modulator, constant frequency and amplitude AM signal. I think this
because the power spectrum is asymmetric around the carrier. I also
think
this because when I track the frequency of this signal using Scilab by
simply measuring each successive period's time interval and converting
to
a frequency value to assign to that period's time interval, I can see
that this frequency varies over time.

It's this frequency variation that I hope to capture by
differentiating
the phase component of the signal with respect to time.

--

Assuming that i can represent the signal using an initial phase value,
a
variable amplitude component, and a variable frequency component (which
i
can get by differentiating the phase component with respect to time),
then
i need to figure out how to do this differentiation.

Please correct me if i'm doing something wrong here..

A combination of AM and PM might reproduce your waveform pretty well,
but change *anything* about it and you will probably need to start over.

...

Jerry




You mean that if i differentiate the phase component with respect to time
in an attempt to calculate frequency, then this method won't work?

Or do you mean that if I change my waveform at all then i will simply need
to reanalyze it?
.

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