Subject: Re: [Elecraft] RTTY filter for K3

[Alan Bloom]

"Nyquist" in this context does not refer to the Nyquist criterion (i.e.
that the sample rate must be more than twice the highest signal
frequency).  It just means a filter that has no inter-symbol
interference at a certain symbol rate (baud rate).

It turns out that if you start with completely unfiltered symbols (a
series of infinitely-narrow impulses, one per symbol) a Nyquist filter
has the property that the frequency response is anti-symmetrical around
1/2 the symbol rate.  One example of a Nyquist filter is a raised-cosine
filter.  The frequency response (plotted on a linear, not dB scale) is
1.0 from zero Hz up to (1-alpha) * symbol_rate/2 and is zero for all
frequencies above (1+alpha) * symbol_rate/2.  Between 1-alpha and
1+alpha, the frequency response has the shape of a raised cosine,
smoothly going from 1.0 to 0.0.  If you plot that on graph paper, you
can see that the frequency response is anti-symmetrical about
symbol_rate/2.  (Alpha is a design parameter - the smaller the alpha the
sharper the cutoff.)

It is much easier to make a Nyquist filter digitally than with analog
components, but you could approximate one with coils and capacitors. 
Actually, even the digital filter is an approximation since it
theoretically has to have an impulse response that extends from
-infinity to +infinity.

That's probably more than you wanted to know.  :=)

Al N1AL


On Mon, 2008-05-19 at 18:35, Art wrote:
> I must be confused by this filter discussion. Is not a Nyquist filter by 
> its very definition a digital filter? Not directly comparable to the 
> crystal filters in the K3 or any other rig.
> 
> I would have supposed a Nyquist filter is one that samples at least 
> twice per cycle at the highest observed frequency.
> 
> As to what comes out of crystal filters, i.e. rtty tones, different 
> discussion. If I have the processing chain figured correctly crystal 
> filter output is then sampled by the audio card.
> 
> I'm not a filter designer. Just asking based on previous experiences.
> 
> 73 Art
> _______________________________________________
> Elecraft mailing list
> Post to: Elecraft at mailman.qth.net
> You must be a subscriber to post to the list.
> Subscriber Info (Addr. Change, sub, unsub etc.):
>  http://mailman.qth.net/mailman/listinfo/elecraft    
> 
> Help: http://mailman.qth.net/subscribers.htm
> Elecraft web page: http://www.elecraft.com