[RTTY] RTTY Rx filter bandwidth

[Kok Chen]

On Jan 10, 2013, at 1:28 PM, Joe Subich, W4TV wrote:

> 370Hz is very close to the theoretical limit - one can debate whether
> the 3rd, 5th or 7th harmonic of the 22.727 Hz "clock" are required to adequately reproduce the edges of the keying waveshape - for minimum
> ISI. 

As explained by Victor Poor, ex-K3NIO, W5SMM SK, way back in a 1964 RTTY Bulletin article, a filter that has no ISI has nothing to do with how many harmonics the filter passes. 

For those not familiar, ISI is intersymbol interference.  In simple language, a signal is smeared to the point where it interferes with itself.

The number of harmonics determines the shape of the waveform that comes out of the filter.  But as a data filter, we only need the mid-bit and the zero crossings of the waveform to be precisely correct.  We don't care what the waveform does in between those points.

Freedom from ISI is based upon Harry Nyquist's work back in the 1920's (Nyquist was working on wire telegraphy).

Examples of a Nyquist filter (i.e., a filter that has no ISI) is a Matched filter and, for a rectangular data pulse, the Raised Cosine filter.

Most profession world transmits with what is called a square-root Raised Cosine filter and receive also with a square-root Raised Cosine, so the cascaded path also has no ISI (yep, that is what is inside your trusty cell phone :-).  By doing that, their transmit waveforms are much narrower than even the waveshaped AFSK stuff Andy K0SM showed.

You can get a concise explanation of ISI and RTTY filters here:

http://w7ay.net/site/Technical/RTTY%20Demodulators/Contents/filters.html

And yes, not all ISI free filters are equal either, the Matched Filter (used in RITTY and in cocoaModem) is a bit more sensitive than the Raised Cosine under AWGN conditions.  You can see that in Figure 4 here:

http://w7ay.net/site/Technical/Extended%20Nyquist%20Filters/index.html

You can see that at -7 dB SNR (3 kHz noise bandwidth), the Raised Cosine throws almost twice as many errors as the Matched Filter under AWGN conditions.

If you scroll down to Figures 5 and 6, you can see how using a filter that is too narrow and a filter that is too wide affects the error rates.  For the same -7 dB SNR, a filter that is 20% too narrow for example throws 4 times (!) more errors than the Raised Cosine that is designed for 45.45 baud (or about 6 or 7 times more errors than the Matched Filter).

The Matched Filter is very wide, so that is where the trade off comes.  When there is QRM, you would want to switch to the Raised Cosine.  Or apply a flat top roofing filter ahead of the Matched Filter.  But the "Extended Nyquist Filters" article shows a better alternative than switching to a simple Raised Cosine or using a flat top roofing filter ahead of a Matching Filter.

73
Chen, W7AY