SM 5 BSZ - Very narrow waterfall graphs for VLF experimenting with Linrad.
(Mar 21 2004)

Millihertz waterfal graphs with Linrad

Figure 1 below shows a simulation of a VLF experiment with Linrad. The screen dump is done with Linrad-01.15 as one of the tests to verify that Linrad still runs properly on elderly computers.

The computer is a Pentium 133 MHz with 24 megabytes of RAM. The amount of memory really used by Linrad is about 6 megabytes. The signal is the audio output from a TS-520 tuned to 7 MHz. An audio signal generator running at 1 kHz was placed on top of the TS-520 to provide a narrowband signal. The TS-520 itself does not by far have the stability to make anything visible at resolutions well below 1 Hz.

Fig 1. Simulated VLF spectrum with high resolution.

The sampling speed used for figure 1 is 22050 Hz. It is obvious from figure 1 that a sampling speed of 7 kHz would be fully adequate. The total CPU load is 44%, half of it is the wideband spectrum, the rest is output processing. The processing parameters are shown in table 1.

First FFT bandwidth (Hz) [5]
First FFT window (power of sin) [2]
First forward FFT version [2]
First FFT storage time (s) [4]
First FFT amplitude [1000]
Enable second FFT [0]
First mixer bandwidth reduction in powers of 2 [10]
First mixer no of channels [1]
Baseband storage time (s) [800]
Table 1. Parameters used for figure 1

Figure 1 demonstrates that the Pentium processor 133 has much more processor power than needed for decoding very slow Morse code with millihertz waterfall graphs. The hardware required would have to have adequate frequency stability but since Linrad can sample at rather high rates there is no need for narrow analog filters.

The sampling speed in the wide spectrum is 11025 Hz in complex format (analytic time function). In the baseband, the sampling rate is 210 = 1024 times lower. The transform size in the baseband is 212 = 4096 which means that the input to one transform spans a time of 380.4 seconds. With a sine squared window and 50% overlapping transforms this means that the lines of the waterfall are produced at a rate of 18.9 lines/hour. The baseband waterfall in figure 1 spans a total time of more than 7 hours.

The audio signal generator, an Oltronix RCO-6K, has drifted from 999.2 Hz to 999.9 Hz over the 7 hours. An RC oscillator can not be expected to be particularly stable, so the FM noise on the signal is not unexpected.

When actually using Linrad for VLF, one would zoom the wide waterfall to cover a few hundred Hz or less to allow fine tuning of the position of the baseband.