Envelope-to: dave@picks.force9.co.uk
Delivery-date: Wed, 01 Feb 2006 15:26:34 +0000
From: Warren K2ORS/WD2XGJ <k2ors@comcast.net>
To: rsgb_lf_group@blacksheep.org,  rsgb_lf_group@blacksheep.org
Cc: "Andy" <actalbot@southsurf.com>
Date: Wed, 01 Feb 2006 15:25:56 +0000
Message-Id: <020120061525.20807.43E0D303000D69250000514722064244130B97010D0A020E06979D0E03@comcast.net>
Subject: Re: LF: Can't see the wood for the trees
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Andy,

      Unless I'm missing the meaning of your question, I believe you want the fourier coefficients to determine the amplitudes of the components making up the pulse train. Also, should you feel the need to integrate sin(x)/x, the so-called Dirichlet integral, it does converge and the definite integral from 0 to infinity of sin(x)/x = pi/2.  For reference see:
http://www.pupress.princeton.edu/books/maor/chapter_10.pdf

 I'm in the middle of a project at the moment but let me know if I'm on the right track - I could help with the fourier coefficients perhaps this evening.

--
73 Warren K2ORS/WD2XGJ
FN42hi
http://www.w4dex.com/wd2xgj.htm

 -------------- Original message ----------------------
From: "Andy" <actalbot@southsurf.com>
> Can someone help with what should be obvious.
> 
> I have a train of constant width pulses at a fixed repetition rate.   In the
> frequency domain these appear as a spectral comb with spacing at the
> repetition rate, whose amplitude  follows a SIN(X) / X shape depending on
> the pulse width, ie. the first null occuring at at 1/width and so on.
> 
> What I'm getting tied up in knots trying to calculate is :
> 
> What is the absolute amplitude (power) of just one individual tooth of the
> comb at any particular spacing.
> 
> Assume the pulse waveform has, say,  1mW or 0dBm mean amplitude, and
> consists of 500us pulses at 40Hz PRI.   The duty cycle is 0.02, so the
> individual pulse power would have to be 50mW or 17dBm to get this mean.
> But what is the amplitude of the component at, say, 1kHz, or 1040Hz, or
> 10kHz ??
> 
> It must be obvious, but I keep feeling the urge to integrate SIN(X) / X
> which is not funny and way beyond my maths capabilities!!
> 
> The figures given above are those for the 5MHz beacon sounder sequence.
> The amplitude trace on the monitoring software during the sounder sequence
> is measuring just one line of the comb ( F = 0,  the carrier) , and appears
> to suggest this is about 30 - 35dB down on the CW part.  That is -17dB from
> the peak/mean  as above, but where does the other 13 - 18dB come from?
> 
> Tearing hair out
> 
> Andy  G4JNT
> www.scrbg.org/g4jnt/
> 
> 
>