Changing the sampling rate of an audio signal.

Why aren't you both guys dealing with something more earthbound?I never
bothered to deal with diracian functions.You should better persuade people
*not* to use airconditions but use fans instead, preferably with some
arguments (the chilling effect the fans work with) etc.

--
Tzortzakakis Dimitrios
major in electrical engineering, freelance electrician
FH von Iraklion-Kreta, freiberuflicher Elektriker
dimtzort AT otenet DOT gr
? <quiasmox@yahoo.com> ?????? ??? ??????
news:1124568442.442918.246850@g47g2000cwa.googlegroups.com...
>
> Polymath wrote:
> > A good question indeed!
> >
> > And a question that the so-called experts and authors in this
> > field fail to answer time and time again.
> >
> > The Diracian, or Unit Impulse is a very good mathematical tool
> > to analyse the response of systems once a mathmatical model of
> > those systems had been produced.
> >
> > It is, however, a poor mathematical claim to make that such
> > impulses are found to be part of a system when neither the
> > area nor the magnitude of such impulses are found anywhere in such
> > systems.
> >
> > To those who ask, "Who cares? I get good results." , I suggest that
> > their approach is unscientific and compares to the religious
> > loonies who sacrifice goats and virgins to stop the Sun falling
> > out of the sky and justify the continuing practice by the Sun
> > remaining in the sky.
> >
> > So.....is the world of DSP a world of scientific men, or is
> > it a world of snake-oil charlatans and of religious loonies?
> >
> > Where do these Diracian impulses come from?
>
> They're all the same, so they come right off dirac.
> --
> john
>

Dimitrios Tzortzakakis wrote:
> Why aren't you both guys dealing with something more earthbound?I never
> bothered to deal with diracian functions.You should better persuade people
> *not* to use airconditions but use fans instead, preferably with some
> arguments (the chilling effect the fans work with) etc.

It's no good. The arguments just add heat.
--
john

Talking of snake-oil, where did the factor of "T" come from in your
opening lines?

 Consider a 16-bit ADC capable of 100 M Samples per sec. In the first
 instance we'll use it to sample a geophysical signal of bandwidth
 limited
 to 300 HZ and sample at 1 kHz, with suitable analogue instrumentation
 to match the input signal to the full range of the ADC. If we now
 keep the circuit the same, but now sample at 65.536 MHZ, your claimed
 factor of "T" will result in the 16 bit range being compressed down
 to one bit. We know this doesn't happen -there will be more samples,
 but they'll still be of the same magnitude and 16-bit range.

Assuming that we were able to generate a Diracian, and then produce
a comb of them by delays and auperposition, there wouldn't be a factor
of "T" in such superposition, so where does yours come from?

>
> robert bristow-johnson wrote:
> >
> >                   x(t)*q(t) = T*SUM{x[k]*d(t-k*T)}   .------.
> >     x(t)--->(*)------------------------------------->| H(f) |---> x(t)
> >              ^                                       '------'
> >              |
> >              |                  +inf
> >              '------- q(t) = T * SUM{ d(t - k*T) }
> >                                k=-inf
> >
> >
> > where:   d(t) = 'dirac' impulse function
> >   and       T = 1/Fs = sampling period
> >            Fs = sampling frequency
> >
> >
> >                +inf
> >     q(t) = T * SUM{ d(t - k*T) }  is the "sampling function", is periodic
> >               k=-inf              with period T, and can be expressed as a
> >                                   Fourier series.  It turns out that ALL of
> >                                   the Fourier coefficients are equal to 1.