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Date: Thu, 2 Aug 2001 21:01:25 +0300 (EEST)
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To: rsgb_lf_group@blacksheep.org
From: "Paul Keindnen" <keinanen@sci.fi>
Subject: Decimation (Was: Re: LF: LF Receivers)
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Reply-To: rsgb_lf_group@blacksheep.org
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>The BFO at 456kHz is derived by extracting the 57th harmonic of the 10MHz
>divided down to 8kHz.  This was actually extremely simple and the most
>satisfying part of the breadboarding process to get going !.  

Very interesting design !

However, looking at the large number of odd frequencies required and also
looking at other suggestions of generating these or similar frequencies
using DDS etc., I just wondered, if the reception could be simplified by
sampling directly the input frequency.

In this way, only a single accurate frequency (the sampling clock) would be
required.

Of course, sampling at or above 300 kHz ( to satisfy the Nyquist criterion)
is out of the question, due to the availability of such high sampling rate
ADCs and the huge dynamic range required and also the huge processing power
required.

However, if the input signal is decimated (undersampled) at some convinient
sampling rate (say 6 kHz), the raw data rate would be managable. This will
create a large number of images falling on the passband, but if the input
spectrum is band limited (say 250 .. 2100 Hz bandwidth), only a single image
is produced.

Making such LC filters with sufficient stop band attenuation outside the
passband would be very hard at 136 kHz and making crystal filters for such
low frequencies would also be problematic. How about applying the wave
analyzer principle, ie. using a VFO to mix _up_ the input passband to any
convinient filter frequency (such as 455 kHz, 3.57, 9.0, 10.7 MHz). After
running the signal through a suitable crystal filter, it is mixed _down_ to
the original (RF) frequency using the _same_ VFO. Thus, any frequency error
created by the VFO is canceled. The long term VFO (or VCXO)  frequency
stability needs only be better than the crystal frequency bandwidth and
since there is a propagation delay (in the order of 1 ms) through the narrow
band filter, the VFO short term (1 ms) stability must be quite good in order
to avoid generating any frequency errors, thus, a good phase noise
performance is required. 

When the VFO is tuned, the very narrow crystal filter bandwidth moves around
the input (and output) RF frequency band, effectively creating a tunable
front end filter, with, say 250 Hz bandwidth. When this signal is sampled at
some low frequency, some alias (image) will fall somewhere in the audio
passband (possibly with an inverted spectrum). The digital signal could then
be multiplied within a processor with a LO signal generated by a software
NCO (Numerically Controlled Oscillator) to generate very low frequency I and
Q signals. 

Normally NCO/DDS constructions use sin(x) tables with sizes that are powers
of 2 (256, 4096 etc.), which is addressed simply by truncating some bits
from the NCO phase accumulator.  If the processor has a fast divide/modulo
instruction, any convinient sin(x) table, such as 1000 element (0..999)
table could be used, thus, nice frequency steps could be generated even if
the sample rate is some nice number, such as 6 or 12 kHz :-).

These are just not random ideas that have not been tested in practice, but I
hope these inspire others to think about non-conventional ways of receiving
LF signals.

Paul OH3LWR