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

[Aaron Lanterman]

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