```
Hi, Leif and all.

On Sat, 28 Jun 2003, Leif Asbrink wrote:

> > By the way as pulse shape is assumed to be known perfectly though the best
> > procedure to determine pulse timing and its amplitude to be as fallows.
> > One should maximize a correlator betwin pulse function stored in memory
> > and real signal. This maximization yelds a incoming time of pulse.
> I think this has to be modified. We have a pulse, detected by a power level
> 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?

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.

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.

> 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'.

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.

>
> Linrad solves this by working with the pulse power rather than the
> pulse amplitude as a first step. This information is already
> implicitly contained in "detected by a power level above threshold."
>
> ..................................................................
>
>
> I might add that the calibration procedure where the operator selects the
> desired frequency response also means that he selects the desired pulse
> response. The optimum compromise seems to be a very complicated problem
> from a theoretical point of view but it is not very critical in situations
> that I have experience with.

Leif thanks a lot for such a detailed explanation. There is very