Purpose

To determine the affect clipping has on the modulated SSTV waveform.

Method

The following steps were performed by computer programs:

Generation of a six line piecewise linear baseband SSTV signal
Generation of the FM signal corresponding to the result of step 1 above
Clipping of the FM signal from step 2 above
Lowpass filtering the results from steps 2 and 3 above
Demodulation of the results of step 4 above
Lowpass filtering the results of step 5 above

In addition to the clipped and un-clipped versions, two additional factors were varied. They were the maximum slew rate of the baseband signal, and whether or not step 4 above (lowpass filtering in the modulator) was done. Three tests were used to evaluate the factors of interest. In the first two tests (numbers 9 and 10), the maximum slew rate corresponds to 3000 Hz per millisecond in the passband. In the last test (number 11), this limit was reduced to 1000 Hz per millisecond.

In the first test, no lowpass filtering was used in the modulator. In the last two tests, a sample rate of 40 KHz was used in the modulator. Also, a lowpass filter was used to atttenuate those frequencies between 2400z and 20 KHz (produced by clipping) so that the filtered signal could be adequately represented at a sample rate of 10 KHz.

The differences between the tests are summarized below:

Test Number 9
- Modulator clock rate of 10 KHz
- No anti-aliasing filter after modulation or clipping
- Slew rate corresopnding to 3000 Hz per millisecond
Test Number 10
- Modulator clock rate of 40 KHz
- Anti-aliasing filter after modulation and clipping (sample rate reduced to 10 KHz)
- Slew rate corresopnding to 3000 Hz per millisecond
Test Number 11
- Modulator clock rate of 40 KHz
- Anti-aliasing filter after modulation and clipping (sample rate reduced to 10 KHz)
- Slew rate corresopnding to 1000 Hz per millisecond

A clipping level of 10% of the real amplitude was used in all of these tests. For a real amplitude of 1.0, all signal levels greater than 0.1 were set to 0.1; all signal levels less than -0.1 were set to -0.1.

Demodulation

The major steps used to demodulate the test signals were:

Multiplication of the passband signal by the sin and cos of 1750 Hz
Lowpass filtering both products resulting from step 1 above
Calculation of the angle at each sample time, from results of step 2 above
The C code used to do this calculation is reproduced below.
```
/* calculate angle */
  for (si=0; si< fap; si++)
  {Ang[si]= (float)((double)(twopi)-atan2((double)(Lo1s[si]), (double)(Lo1c[si])));}
    
```
The lowpass filtered sin products are in the Lo1s array; the lowpass filtered cos products are in the Lo1c array.
Estimating frequency by the rate of change of angle
The C code used to do this for one buffer's worth of data is reproduced below.
```
    
  for (si=0; si<val_to_write; si++)
  {/* calculate frequency in Hz. */
   diff= Ang[si]- ang_co;
   ang_co= Ang[si];
   if(diff > pi) diff-= twopi;
   else {if(diff<-pi) diff+=twopi;}
   fprintf(otf,"%7.2f\n", lo1hz + diff*kf);
  }
```
Here, lo1hz is the 1st local oscillator frequency, 1750 Hz (only 1 local oscillator is used in this particular pragram); kf is the conversion factor from radians per sample period to Hz.
Lowpass filtering of the result of step 4 above

Filter Characteristics

Modulator anti-aliasing filter

The filter used in the modulator to attenuate the frequencies between 2400 Hz and 20 KHz is a single stage "decimation by 4" lowpass filter. A graph of the interesting part of its gain characteristic is just below.

Demodulator IF filter

The lowpass filter used on the products of the passband signal and the sin and cos of the local oscillator is a two stage "decimation by 4" lowpass filter. A graph of the gain characteristic for the first stage is just below.

The input sampling frequency for the second stage of this filter is 5 KHz. A graph of its gain characteristic is just below.

A two stage interpolation filter is then used to produce the lowpass filtered result at the original sample rate. Graphs of this interpolation filter characteristic are not shown here.

Post demodulation lowpass filter

A single stage lowpass filter was used after the demodulation. The following two graphs show its gain characteristic.

Using an expanded vertical scale, to show the ripple in the passband results in the following graph.

Results

The results are presented as graphs. For each test, the results are in five graphs. These five graphs show:

The baseband signal
The demodulator output
The demodulator output with post demodulation lowpass filtering
The demodulator output with the passband signal clipped at 10% of its real amplitude
The above with post demodulation lowpass filtering

There are four interesting SSTV lines in each of the three test cases. Links to the pages containing the graphs for each of the these lines follow:

Conclusions

Clipping of the FM SSTV waveform does degrade the baseband representation. Compare this unclipped case with this clipped case.
Lowpass filtering does not compensate for the degradation caused by clipping. Compare this case before and after lowpass filtering.
If frequencies generated by clipping which would be aliased into the SSTV passband are not filtered out prior to sampling, severe degradation results. See this example from test 9.
Baseband slew rates, when viewed through the SSTV pass bandwidth, that produce an apparent discontinuity in the baseband signal exhibit the Gibbs Phenomenon when demodulated with digital filters. Compare this case of a 3000 Hz per millisecond slew rate with this case of a 1000 Hz per millisecond slew rate on the white to sync transition.

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