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

[Jerry Gray-Eskue]

>From this I gather that common sound creation and reproduction systems such
as guitar and speakers are basically linear and so do not create any
secondary signals.

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.

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 ?

Logarithmic input and Logarithmic Control Voltage = Non-Linear. - Again this
one appears easy or am I misunderstanding what a Non-Linear system is.

<<You can think of the original time-domain signals on the o-
scope as shrinking the time window to be infestimally small, and
having no frequency resolution. You can think of the Fourier transform
as stretching the window to encompass the whole signal, and you have
no time resolution.>>

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)?


Jerry


<<<
> It doesn't matter if the system is mechanical or electronic. It only
> matters if it's linear or not.

Excellent!!!
>>>

-----Original Message-----
From: synth-diy-bounces at dropmix.xs4all.nl
[mailto:synth-diy-bounces at dropmix.xs4all.nl]On Behalf Of Aaron Lanterman
Sent: Thursday, June 04, 2009 11:51 PM
To: sdiy DIY
Subject: [sdiy] Yet another try at explaining beat tones, etc.



On Jun 4, 2009, at 12:22 PM, Jerry Gray-Eskue wrote:

> Since the two frequencies are causing physical motion we can get
> reinforcement of the (a-b)/2 as the physical motions interact. So do
> we create the Beat signal here, or are the physics of the mechanical
> motion preserving the two frequencies intact?

Well - the beat signal, say when you're tuning a guitar, is never
really being created. You will not see it on any spectrum analyzer.
You're perceiving say a 0.5 Hz amplitude modulation (since your ear
can't tell the difference between the positive and negative parts of
the wave), but there's no place anywhere that a 1 Hz signal actually
exists.

In our Intro to Signal Processing class, in lab have students add two
sine waves together of close frequencies and then look at their
spectrogram in MATLAB, which gives a 2-D time-frequency plot of the
content. In the spectrogram you have to pick a window size. Small
windows give you high time resolution but low frequency resolution.
Large window sizes give you good frequency resolution but bad time
resolution. You can think of the original time-domain signals on the o-
scope as shrinking the time window to be infestimally small, and
having no frequency resolution. You can think of the Fourier transform
as stretching the window to encompass the whole signal, and you have
no time resolution.

When the students use a small time window, they see a single line at
the average of two frequencies that blinks in and out at the beat
rate. When they use a large time window, they don't see blinking -
they see two solid lines, each at the actual frequencies.

When you're tuning your guitar, if the frequencies are close, you
perceive the AM beats. As you tune them further apart, eventually you
perceive the two tones.

I've probably just confused matters more. Anyway, that's my shot at
another explanation. :)

- Aaron
_______________________________________________
Synth-diy mailing list
Synth-diy at dropmix.xs4all.nl
http://dropmix.xs4all.nl/mailman/listinfo/synth-diy