> If one computes the number of taps of a FIR decimation
> filter with a decent performance (say 0.1 dB in-band ripple
> and 100 dB alias image rejection) he discover a simple
> rule of thumb:
> N =(about) 4*D/(1-B/Fco)
> N is the required decimation filter number of taps
> D is the decimation factor
> B/Fco is ratio between the desired output alias free bandwidth and the output sampling frequency.
> Since after filtering the decimator takes one output every D
> input samples, the output impulse response is no more
> than N/D samples long, that's to say:
> N/D =(about) 4/(1-B/Fco)
> Note that the length of the output impulse response
> *does not* depend on the output sampling frequency, but just on the B/Fco ratio.
> If such a ratio is high the output pulse can be quite long.
I am afraid you apply a "conventional" model which is
not applicable in the QRN-fighting context.
Consider a sampling rate of 4 MHz.
Apply a FIR filter that has say 0.1 dB in-band ripple
and a -1 dB point at say 0.8 MHz. The -20 dB point should
be at 2 MHz and the -100 dB point at 3.2 MHz. The alias-free
range (-100 dB) would be +/- 0.8 MHz but a clever DSP software
could compensate for the fall-off between say 0.8 and 1.6 MHz
to provide a perfectly flat passband of 3.2 MHz or so. The alias
suppression at the corner frequencies would be poor. Maybe 20 dB,
but I do not think that would impair the noise-fighting.
The useful bandwidth for receiving would be 1.6 MHz only and
not any improvement over the 2 MHz sampling. The purpose of the
faster sampling would only be to eliminate certain interference
> In Perseus the decimation filter has been designed so that
> the alias-free bandwidth is 80% the output sampling frequency
> (1.6 MHz when the sampling rate is 2 MS/s) which is a good
> compromise between the decimation filters complexity and
> the efficiency of the digital signal processing made on the PC.
> At such a B/Fco ratio you can expect that each output pulse
> due to an istantaneous glitch at the receiver input is
> approximately 4/(1-0.8) = 20 samples long whatever the
> output sampling frequency is.
> You can't really resolve it into a single pulse even if
> the output sampling frequency were 40 MS/s. It will
> always be 20 samples long.
In Linrad, the PC software will take the fourier transform of the
input data stream, divide it by the fourier transform of the
impulse response of the hardware and multiply it by a "desired
pulse response" This way the pulse length is made shorter than 20
samples and at the same time the ~0.1 dB ripple is removed.
The length of the pulse is determined by the "desired pulse response"
which depends on the skirt steepness that the user has decided.
The smart blanker knows the exact shape of the pulse and its length
so it does not matter that the pulse is long in terms of samples.
I am aware that very few operators use Linrad and that only
a very small fraction of the users care to calibrate their
systems properly. I have tried to explain the theory, but I
do not think I have been sucessful at all. I am interested
in static rain at high bandwidth because I have a feeling
recordings would show a dramatic difference between the
Linrad blanker and other blankers.
> Of course 20 samples at 40 MS/s are a 0.5us interval,
> which is a much shorter time interval than that obtained
> if the sample rate were 2 MS/s but instead of increasing
> the output sample rate one can obtain the same result
> simply relaxing the B/Fco requirement.
> If the B/Fco ratio were 60% instead of 80% the output
> pulse lenght would be the half the original, if it were
> 40% one third and if it were 20% one fourth of it, a
> mere 5 samples interval (2.5us @ 2MS/s), which is even
> the half of what one could obtain attempting to double
> the output sampling frequency (and mantaining the
> original 80% B/Fco ratio).
> The penalty is that the the alias free bandwidth
> is much less than the output sample rate...
Yes:-) This is what I advocate. 4 MHz sampling and
40% alias-free bandwidth. I also want the -10 dB point
to be fairly high, maybe 80% of Nyquist.
> but who cares if we would just be satisfied to (carefully)
> clean-up a not-so-wide 200 kHz bandwidth out of a 2 MS/s
> IQ stream?
> And if it works, wouldn't it be better than obtaining the
> same result using 4 MS/s maybe overloading a poor man CPU?
As far as I undersdtand it is impossible to clean up a 200 kHz
wide segment of a 2MS/s IQ stream if the (random) secondary
pulses can not be resolved. From old experience as well as from
the one and only wideband recording at my disposal a bandwidth
of 1.6 MHz is marginal. It may or it may not work.
> BTW, making a new 4MS/s DDC would not be impossible but
> as I haven't implemented it yet I can't say that what
> was initially conceived for a much smaller output sample
> rate could sustain it (in 2008 I was even not sure that
> the 2 MS/s rate could really work).
Five years later it is very likely that a factor of two is OK:-)