What a delight it is to be on this list. LF could well stand for Literate
and Febrile
I am digital-techniques ill informed and not sure if you are using ^ to
mean "to the power of "
but is your question : "what is the integral of sin(y)/y where y=x squared
?" ?
between what values of x?
Bryan - g3gvb
----- Original Message -----
From: "Andy talbot" <[email protected]>
To: "Rsgb_Lf_Group (E-mail)" <[email protected]>
Sent: 10 December 2003 08:51
Subject: LF: Related Technical Query - Soundcard calibrator
Is there anyone who can answer this...
I want to make a calibrator to enable accurate (better than 0.5%) absolute
audio measurements using a soundcard - ie. at audio frequencies to 20kHz.
Generating a square wave from CMOS logic with a precisely 5V p-p (2.5v
peak)
waveform is trivial and can be measured accurately to doubl;e check. The
levels of the odd harmonic tones are all precisely defined by :
RMS Amplitude = 2.5V * 4 / PI / SQRT(2) / N
Where N is the (odd) harmonic number, so the fundamental has an amplitude
of
2.251 Vrms which can be potted down with an accurate potential divider -
straightforward, all harmonics can be used at known levels...
Now, here is the complicated bit, I also want to include a calibrated
noise
source for accurate S/N measurements and evaluation of various decoding
techniques. To remove the need for accurate true RMS measurement to set
up
this unit, I am going to use Pseudo Random Sequence generated from a shift
register clocked very much faster than the frequencies of interest. It is
straightforward to make a 2^32-1 bit long sequence clocked at, say, 5MHz
which
will have a repeat cycle of 14 minutes, suitable for most purposes - even
Argo
calibration ! By filtering to a bandwidth significantly less than the
clock
rate (20kHz max vs. 5MHz) the result will be sufficiently Gaussian to act
as if
it were true noise. In practice, any real hardware filtering won't be
necessary as the soundcard itself will do the job; but there will be some
basic
filtering to keep out the nasty birdies likely to be generated.
Now, here is the bit I'm less sure how to work out. How do I calculate the
noise density of the PN sequence in the area of interest? Assumimg the
PRN
Sequence has 1:1 mark/space ratio (with 2^32 bits it will be certainly
near
enough) and assuming a perfect square edged waveform up to several 5MHz
clocks
away (guaranteed by using HC series logic) the TOTAL power over the
(almost)
infinite spectrum from DC to several clock multiples is defined exactly by
the
RMS value of the waveform; and for a squarewave this is equal to the peak
value
- here 2.5V.
This TOTAL power is spread out in a SIN(x^2)/x^2 pattern. Since it will
be
filtered to, essentially, just a small part of the first spectral lobe,
the
calculation really comes down to calculating the height of this lobe which
will
can be assumed to be sufficiently flat over the small bandwidth of
interest.
Once that is done, the noise power, and hence the RMS value can be
defined in
Volts / SQRT(Hz) which can be added to the signal / test tone of interest
in
variouis proportions, with the S/N then known exactly.
I'm quite incapable of integrating SIN(x^2)/x^2 from first principles (or
any
other way for that matter :-) to calculate the level of the main lobe.
Can
anyone point out the best way to do this calculation ? Instinct says
that
for a small bandwidth segment, BW, close to zero frequency, the power
will be
proportional to BW / Fclock, but I haven't a clue what scaling factors
will
be included in this, and they are what matter for an absolute level
calibrator.
Andy G4JNT
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