Re: BBC Radio 4 'Feedback' (13:30 Friday) - Discussion about move to

"Ian Jackson" <ianREMOVETHISjackson@xxxxxxxxxxxxxxxxx> wrote in
message
news:Ft6KqGJOObeKFwR2@xxxxxxxxxxxxxxxxx
In message <h5bld2$1kb$1@xxxxxxxx>, boltar2003@xxxxxxxxxxx writes
On Wed, 5 Aug 2009 10:52:26 +0100
Ian Jackson <ianREMOVETHISjackson@xxxxxxxxxxxxxxxxx> wrote:
Its just a way of deconstructing the
waveform for analysis. A pure square wave is just a pure square
wave.
It is not a sine wave with infinite number of harmonics imposed
on top
however the people who designed the equipment decided to display
it
even if thats a convenient way of working with it behind the
scenes.

Sorry. You are 100%+ wrong.

No I'm not.

That's simply because an oscilloscope views the waveform in the
time
domain. Yes, it sees the squarewave as it 'really is'.

The time domain is reality. The frequency domain is something
invented by
man unless you know of a parallel universe where its real.

I just can't believe how wrong you are. However, I'm beginning to
get a
sneaky feeling that, somehow, we are not quite talking about the
same
thing.

The harmonic components of a non-sinusoidal waveform really do
exist.
Monsieur J Fourier may have done a lot of mathematical analysis on
this
subject but, physically, these harmonics really DO exist. Honest.
The
frequency domain is not a figment of the imagination. There is no
need
for there to be parallel universes. All the harmonics exist
perfectly
well in the one we are in at the moment.

But not this time! All non-sinusoidal waveforms are the result of
the
addition of a series of phase-locked sinewaves, and the shape of
the
waveform (as seen on an oscilloscope) depends upon both the
amplitude
and phase relationship of these sinewaves. Believe me - they DO
exist!

No they don't. Thats simply how you can visualise them , thats not
what
the waveforms really are. E = mc2 is a way of understanding the
energy
in matter, buts that not what the energy actually *is*.

And if you want more proof think about this:

If you had say 10hz square wave and you sampled it at 20Hz and got
the
phasing matching exactly so the output of the sampler was 1, -1,
1, -1
etc (we're ignoring amplitude here) you could exactly reproduce the
input square wave if you fed that information though an appropriate
DAC.
But hold on , if that square wave is an infinte regression of
harmonic
sine waves in ever increasing frequency how could you possibly
reproduce
it with data from a 20hz sampler when if what you're saying is true
it
would need a sampler of infinite frequency to capture it
completely?
Answer - because in reality its a 10hz square wave, nothing more,
not a
combination of sine waves.
I'm no expert on sampling, but (simplistically), if you fed a 1:1
mark-space 10Hz squarewave signal into a gate and sampled it with a
1:1
mark-space 20Hz squarewave, you would get an output of 1, 0, 0, 0
for
each full 10Hz cycle. This is not a 1:1 squarewave and, to recover
anything like the original shape of the 10Hz signal, you would have
to
severely lowpass filter it - so much so that you would end up with
only
a 10Hz sinewave (which Herr Nyquist might have predicted).


Nyquist was Swedish:

http://en.wikipedia.org/wiki/Harry_Nyquist


For a squarewave to look anything like squarewave, it has to have at
least something like up the 7th harmonic present (70Hz), so you
would
need to sample it at least 140Hz to retain the original shape. You
would
never try and sample it at 20Hz.

Somewhere on the internet, there is a very informative 'fun' website
where you can 'build' your own waveform from its various harmonic
components (you can set the amplitudes, phases etc). Unfortunately,
I
can't find it at the moment, but I'll post it here if I do.



--
Steve - www.savefm.org - stop the BBC bullies switching off FM

www.digitalradiotech.co.uk - digital radio news & info

"It is the sheer volume of online audio content available via
internet-connected devices which terrifies the UK radio industry. I
believe that broadband-delivered radio will explode in the years to
come, offering very local, unregulated content, as well as opening a
window to the radio stations of the world." - from the Myers Report


.

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