Yes - that's the obvious bit I was missing - go back to first principles and
do the actual Fourier transform on the waveform.
There ought to be a short cut, though, knowing the integral is finite and
contains total power in the signal. I had assumed the Dirichlet integral
converged, but didn't know the result, so maybe that is the way to go.
Tnx
Andy G4JNT
www.scrbg.org/g4jnt/
-----Original Message-----
From: Warren K2ORS/WD2XGJ <[email protected]>
To: [email protected] <[email protected]>;
[email protected] <[email protected]>
Cc: Andy <[email protected]>
Date: 2006/02/01 15:34
Subject: Re: LF: Can't see the wood for the trees
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" <[email protected]>
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/
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