[sdiy] Yet another try at explaining beat tones, etc.

[Jerry Gray-Eskue]

Thanks to all,

I think I now have a generalized idea what the difference is, obviously this
is a much more complicated subject than I anticipated and can take some
serious mathematical analysis to be certain which type of system you are
dealing with.

Jerry

-----Original Message-----
From: synth-diy-bounces at dropmix.xs4all.nl
[mailto:synth-diy-bounces at dropmix.xs4all.nl]On Behalf Of Aaron Lanterman
Sent: Friday, June 05, 2009 10:04 AM
To: sdiy DIY
Subject: Re: [sdiy] Yet another try at explaining beat tones, etc.


On Jun 5, 2009, at 9:20 AM, Jerry Gray-Eskue wrote:

>> I am still a bit fuzzy on what Makes a system non-linear so to
>> clarify lets
> use a Voltage Control Amplifier.
>
> Linear input and Linear Control Voltage = Linear system - This one
> appears
> easy and means that this form of Amplitude Modulation is linear.

Careful. You have to define what are your inputs and what are your
outputs. If you consider audio in and audio out, the system is linear
for any given choice of control signal.

> Linear input and Logarithmic Control Voltage = *** Linear or Non-
> Linear ?
> *** Is it enough that only one term (if I am using that word
> correctly) is
> non-linear ?

Again, if you consider audio in and audio out, the system is linear
for any given choice of control signal.
>
> Logarithmic input and Logarithmic Control Voltage = Non-Linear. -
> Again this
> one appears easy or am I misunderstanding what a Non-Linear system is.

If you consider anything, this is nonlinear.

For a system T defined by y(t) = T{x(t)} to be linear, the following
must hold:

T{a x1(t) + b x2(t)} = a T{x1(t)} + b T{x2(t)}

Note, interestingly, that y(t) = 5 x(t) + 3 does NOT define a linear
system, even though it's a function of a straight line. Put it in the
relation above - you'll see the additive 3 term kills the linearity.

> When you do the Fourier Transform are you not "Rotating" the signal
> sample
> points from a 2 dimensional space defined by Time vs. Amplitude (time
> domain) to a 2 dimensional space defined by Frequency vs. Amplitude
> (frequency domain)?

That's a pretty good description. Sinusoids form another "basis set"
for signals.

- Aaron
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