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RE: [linrad] RE: Linrad

Hi again,

> > above threshold. The known pulse shape is symmetric, it is a large
> > value at t=0 and weak oscillations surrounding the pulse maybe +/-
> > 10 samples. 
> Why pulse function should be symmetric? For example if hardware is simple
> oscilator then pulse function is dumped complex exponent for t>0 and it is
> 0 for t<0. It is not symmetric function. Or You mean symmetry not with
> respect to t -> -t?
But hardware is not a simple oscillator. Linrad pulse removal will work
only for a wideband pulse. It has to have constant amplitude and absolutely
linear phase over the frequency range brought into the A/D converter.

Not when it arrives at the A/D converter, because then it has passed through
our analog hardware, but when the pulse is a free wave and arrives at
the antenna, then it has to be a "dirac pulse" as understood within the 
bandwidth we are going to process. The analog filters will lengthen the pulse
and distort the phase and amplitude functions. The calibration procedure
will result in a digital filter that removes the distortion.
The final consequence is that a dirac pulse in free space will become a
symmetric pulse within Linrad.

> > If there is a second pulse of similar amplitude somewhere
> > within +/- 10 pulses, the correlation will have a significant error,
> > it is better to use the few data points at the pulse maximum only.
Here was a misprint:If there is a second pulse of similar amplitude somewhere
within +/- 10 samples, the correlation will have a significant error,

> Certanly all of this should be done in small time window to avoid
> effect of another pulse. One should limit the time interval in correlator
> by this window. To get appropriate windows (one window for one
> pulse) aproximate time of pulses should be evaluated previously. Say from
> time of signal maxima. 
You are trying to solve a different problem.

Have a look at ..........linuxdsp/blanker/narrow.htm
Fig. 2 shows what the pulses look like when the hardware does not 
contain as good anti-alias filters as the RX2500. (his is an old
page and accuracy is much better now) For this figure I asked for
a rather wide spectrum with very steep skirts. As a consequence
the oscillations spread out over a rather wide time span here.

With RX2500 the pulses are very short.

> > 
> > This is a real world experience, the correlator was my first guess.
> > The explanation is that the significant problem is not the white noise
> > floor, it is multiple pulses.
> > 
> > Although the pulse shape is known we can not correlate it directly
> > because the phase with respect to I and Q is unknown, so is the phase 
> > with respect to the sampling clock and also the phase and amplitude 
> > ratio between the two channels (polarisation)
> Though phase with respect to sampling clock is not too worth. Using
> poliminomial interpolation (linear interpolation in simplest case)
> of stored pulse function and recieving signal it is posible to get
> all functions in 'continues time'. 
Linear interpolation certainly does not work well.
(short for does not work at all)

The Linrad "Library of pulses" contains the interpolated pulse shape
for a fine enough fractional position with respect to the sampling
clock. The interpolation has to be made at a very high order and
memory is not the the problem so Linrad will look up the interpolated
pulse from the table.  

> Certanly as amplitude can be as positive as negative when time of pulse
> is evalueted one should maximize square of correlator not 
> correlator itself. 
> If there is two polarisation channels seems sum of two squared correlators
> should be maximizied. But what is optimal is matter of math analyse.
Well, the problem is to find amplitude and phase of a pulse that has
most of it's energy in two (complex) samples. This is of course
trivial if there was no interference. The assumption about what the
interference looks like is the key to the solution of this problem.
In my experience it is not white noise. It is most probably another
pulse. Therefore "Certanly all of this should be done in small time 
window to avoid effect of another pulse. One should limit the time 
interval in correlator by this window." leads to the use of three
data points only.

I have found that a simple parabolic fit to the three data
points will give the same result as sliding the interpolated
pulse shape along the three data points looking for maximum
correlation. My attempts to improve S/N for the pulse by use of 
more data points has failed, one would have to devise a procedure for
multiple pulses.


Leif / SM5BSZ