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This module details the testing methods used to compare the three methods of encryption (frequency, phase, and echo) studied as part of the fall 2008 ELEC 301 class project.

Testing

Aural tests

As our primary objective was to make the changes inaudible, we tested all of our algorithms aurally.

We initially tested the algorithms on a 440 Hz tone to ensure that the algorithms were working as expected. (We did not test the FMAon the tone as doing so would have been silly because the tone only has a single frequency with no other frequencies to modify.)

We continued our aural testing with a suite of six songs from different genres: classical, hip-hop, oldies, pop, rock, and techno.We adjusted any thresholds and predefined constants to the point of aural imperceptibility. Working within these limits we were then able to modify theseconstants to maximize bitrate, accuracy, and noise resilience.

The following figure details the particular songs chosen and their overall frequency spectrums.

Frequency spectrums of test suite songs

Bitrates

Our test suite had a CD quality sampling frequency: 44100Hz, which amounts to 220500 samples for a 5 second long clip.Ideally with no noise it would be possible to use a segment length of 2 samples. This setup translates to 220500/2 = 110250 segments in 5 seconds and 110250/5 =22050bits/sec. I.e. at CD quality, we cannot get more than a 22Kbits/sec data rate.

In practice we found that Mat lab was unable to handle this amount of data. We were, however, able to successfully reach 4800segments, or 46 samples per segment. These values translate to 220500/46 = 4793 segments in 5 seconds and 958bits/sec. I.e. we reliably demonstrated a 1Kbit/secdata rate.

Power ratios

To measure how much we had changed each of the signals by encoding bits, we took a power ratio of the original signal to theoutput signal.

Formula for power ratio

Formula for Power Ratio

We found these ratios for two different input characters: ‘@’ and ‘w’. Because ‘@’ is encoded by 100 0000 in ASCII, thesepower ratios measure the minimum amount of change we make to our signals. Because ‘w’ is encoded by 111 0111 in ASCII, these power ratios measure themaximum amount of change we make to our signals.

Power Ratios
FMA PSA EA
@ w @ w @ w
classical 1.0052 1.0362 1.0056 1.0352 0.9992 0.9955
hip/hop 1.0079 1.0507 1.0068 1.0413 0.997 0.9818
oldies 1.0133 1.0747 1.0069 1.0425 0.9986 0.9897
pop 1.0115 1.0776 1.0063 1.0388 0.9975 0.9842
rock 1.0131 1.0628 1.0072 1.0419 0.9975 0.9888
techno 1.0155 1.0897 1.0077 1.0463 0.9951 0.9723

Table 1. Power Ratios for each algorithm encoding one 1 per seven bits (“@”) and one 0 per seven bits (“w”)

Chart of Power Ratios

The most important feature of these results is that all of our power ratios are very close to one, indicating that we have notchanged the signal very much.

We also see some variation across the different songs because which values are changed and by how much depends on the song; forexample, with the PSA, the delay causes us to drop samples at the end of the segment, and the power in the dropped samples depends on the song.

As expected, for ‘w’, the power ratio is further from one as more one-bits are encoded. Because adding an echo can be variouslyconstructive or deconstructive, the power ratio does not reflect the number of one-bits as much as FMA and PSA. This fact also explains why the power ratiosfor the EA are generally lower than those for the FMA and PSA.

Finally for FMA and PSA the power of the marked signal was lower than the power of the original signal. For the FMA, thisdecline in power was expected because we scaled frequencies down, thus, deceasing the power in the frequency spectrum, which, as Parseval’s Theoremtells us, corresponds to decreasing the power of the signal. For the PSA, this decline in power was also expected because the PSA delays the signal in varioussegments, dropping samples in the marked signal. The EA was the only case in which the marked signal had greater power than the original signal because theechoes in this case were more constructive than destructive.

Questions & Answers

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Source:  OpenStax, Elec 301 projects fall 2008. OpenStax CNX. Jan 22, 2009 Download for free at http://cnx.org/content/col10633/1.1
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