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

[David Panseri]

I've been reading Stephen W Smith's DSP book at dspguide.com. Chapter
5 helped a lot when trying to wrap my head around what is and is not a
linear system:

http://www.dspguide.com/ch5.htm

-Dave

On Fri, Jun 5, 2009 at 9:20 AM, Jerry Gray-Eskue<jerryge at cableone.net> wrote:
>
> >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
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