Lately there have been many
excellent software programs developed that use an inexpensive and simple
comparator circuit to send SSTV audio over RS232 to a computer where
demodulation and display of the picture is done. In addition to this, there are
programs that utilize the sound card in the computer to generate the same
information. To date, all of these programs use the same basic demodulation
technique of counting the time between zero-crossings of the received audio to
determine frequency. Although this has worked well for many years, the SSTV
community should catch up with the current technologies and take advantage of
the available DSP techniques to do better filtering and demodulation. Not
everyone is up to speed on these technologies, but for those who are, I'm
writing this to spark some interest and experimentation.

I've been doing some development
using an Analog Devices ADSP2181 DSP processor that's available on an
evaluation board (called "EZ KIT Lite") and includes the software
development tools for under $80 (no, I have no connection with this
company...it just happens to be the processor I used). Included on the board
are stereo A/D and D/A converters, RS232 interface and power comes from a
supplied wall transformer. This board is pictured to the left. Similar boards
are also available from Motorola for their DSP processors.

The results achieved to
date look very promising with the filtering of the audio and demod being done
entirely on the DSP board. If you want to see the technical details...read on.
If you aren't familiar with DSP fundamentals...take some time to review in the
ARRL Handbook before proceeding. Most of what I cover here is discussed on page
18.14 of the 1995 handbook (my latest copy).

The technique I used to
demodulate the FM signal involves doing a quadrature mix of the audio down to
DC where in-phase and quadrature signals are generated to give both amplitude
and phase information of the signal. Refer to the block diagram at the left.
Sampling of the audio from the transceiver is done at 8 kHz. This is then
multiplied by a cosine signal at 2 kHz (Fs/4) to generate the "real"
part of the signal. Similarly, the signal is multiplied by a sine signal at 2
kHz to generate the "imaginary" part of the signal (the
multiplication is doing the same thing as the mixer in your radio). Together,
the real and imaginary signals form a complex representation of the signal with
what was at 2 kHz now "translated" to DC. With me so far?? Our signal
of interest for SSTV was between 1200Hz (sync) and 2300 Hz (white). Now, our
SSTV signal is between -300 and +800 Hz. If we had chosen a sample rate of 7
kHz we could have centered the signal around DC (which is what you would try to
do) but the example would have been more awkward. At this point you may be
asking how the sine and cosine signals were generated. Well... Fortunately,
since the frequency we chose is 1/4 of the sample frequency, we can represent a
cosine at that frequency very nicely by the sequence of samples
1,0,-1,0,1,0,-1,0......... This gives us 4 samples per cycle of a 2 kHz **cosine**
wave where the sample sequence is at a 8 kHz rate. Similarly, we can generate the
**sine** wave by using the sequence 0,1,0,-1,0,1,0,-1..... To
illustrate how we multiply our input samples by the sine and cosine sequences,
lets look at what happens to the first two samples that come in. The input
sample is multiplied by 1 to generate our first "real" (in-phase)
sample. This **same** input sample is multiplied by 0 to generate
our first "imaginary" (quadrature) sample. The next input sample gets
multiplied by 0 to generate the second real sample and by 1 to generate the
second imaginary sample....and so on. Please don't leave out the data that
comes out as 0 (it'll mess up the whole process).

__The Filters__

Both real and imaginary
signals are run through identical FIR low-pass filters to remove images. Our
filters for this example would be 800Hz low-pass FIR filters that effectively
perform the job of a bandpass filter on the SSTV signal. FIR filters have a
constant delay (linear phase) response (a big plus for FM demodulation where
you are detecting changes in phase). We can use a 23-tap filter and be down by
40+ dB at 1500 Hz and have plenty of processing horsepower left to spare.

__The Demodulator__

The rate of change of phase
of our SSTV signal will give us the SSTV FM demodulation data we are after. The
phase is simply the arctangent of (Qn/In) where Qn is the quadrature (or
imaginary part of the signal) and In is the in-phase (or real part of the
signal). The rate of change of phase with respect to time (or samples in our
case) is the frequency so all we have to do is figure out how much the phase
changes between each sample and that number will be a representation of the
frequency of our signal. Without going into the derivation, I will now give you
an equation that can be used (without doing any trig. calculations) to
accomplish just what we want. If you can do a little calculus and you're still
interested, the derivation is included at the end of this article.

Demod_{n}={Q_{n}*I_{n-1}-I_{n}*Q_{n-1}}/{I_{n}^{2}+Q_{n}^{2}}

Here "n" is used
to indicate the current sample and "n-1" is used to indicate the
sample just before the current sample. "I" is the real or in-phase
part and "Q" is the imaginary or quadrature part. This is a
"first order" detector that works very well for our slow-scan design.
Higher order implementations can be done that use more input samples but it doesn't
buy much in performance.

__The Results__

To see how it all works, I
have implemented all of the above on the ADSP2181 and sent the result out
through the DAC on the board so it can be seen on an oscilloscope. The
demodulator performed very well and seemed to offer some improvement during
noisy conditions (this type of FM demod has fairly good rejection of AM noise).
The same data can be output on the RS232 port of the DSP board to your PC where
it can be converted into a picture. I'm currently working on that part of the
project. There are a couple of SSTV developers who are trying their hand at
this method including one who is using a soundcard to generate the digitized
samples. This should work just as well with the tradeoff being the CPU cycles
that get consumed to do the DSP. Since the DSP code would be replacing the
entire zero crossing code and all the Band-Aids required to make this technique
work reasonably well, the tradeoff may be a reasonable one. There are many
advantages to this approach including that you get several demod outputs per
cycle of the input audio. In fact, the output data rate is much higher than is
needed and can be reduced by doing "decimation" of the data after the
FIR filter processing (as long as you maintain 2 samples per cycle at the
frequency where the filter is down by 30 or 40 dB). Work continues on this
project and I would be interested to hear from developers who plan to give this
a shot. If you know folks who have been developing SSTV programs, please ask
them to check this out. DSP techniques will be** the** way to do
SSTV demod (and all other kinds of demod) in future ham equipment. Similar
techniques are currently being used to do demod of digital modulation in
commercial equipment (including TNCs and cell phones). Here is an opportunity
to experiment with something that more hams should be having fun with. **See
you on the air!**

__Derivation of the
equation__**:**

Demod_{n}={Q_{n}*I_{n-1}-I_{n}*Q_{n-1}}/{I_{n}^{2}+Q_{n}^{2}}

(Note that my original article had the sign flipped. It still worked but the output
waveform was inverted.)

We know from the article that Demod_{n}=d(atan (Q_{n}/I_{n}))/dn

Since d(atan u)/dn={1/(1+u^{2})}*du/dn

Then Demod_{n}={1/(1+(Q_{n}/I_{n})^{2})}*d(Q_{n}/I_{n})/dn

Simplifying gives a general expression for FM demod (Equation 1):

Demod_{n}=[{I_{n}*d(Q_{n})/dn-Q_{n}*d(I_{n})/dn}/I_{n}^{2}]/(1+(I_{n}/Q_{n})^{2})

For a first order approximation of the derivative d/dn, we can use (Equations
2&3):

d (I_{n})/dn~I_{n}-I_{n-1}

d (Q_{n})/dn~Q_{n}-Q_{n-1}

For a better approximation of the derivative we could use a program that
generates coefficients for a higher order FIR filter that is a differentiator.
Linearity of the Demod output can be improved this way, if needed.

Back to the equation. Substitute Equations 2&3 into Equation 1 and we get:

Demod_{n}=[{I_{n}*(Q_{n}-Q_{n-1})-Q_{n}*(I_{n}-I_{n-1})}/I_{n}^{2}]/(1+(I_{n}/Q_{n})^{2})

Simplifying:

Demod_{n}={I_{n}*(Q_{n}-Q_{n-1})-Q_{n}*(I_{n}-I_{n-1})}/(I_{n}^{2}+Q_{n}^{2})

Demod_{n}={Q_{n}*I_{n-1}-I_{n}*Q_{n-1}}/{I_{n}^{2}+Q_{n}^{2}}