QUANTIFYING THE EFFECTS OF LOSSY DIGITAL AUDIO
COMPRESSION ALGORITHMS ON ELECTRIC NETWORK
FREQUENCY SIGNALS IN FORENSIC ANALYSIS
by
Harrison Allen Archer
B.S., University of Colorado Denver 2010
A thesis submitted to the
University of Colorado Denver
in partial fulfillment
of the requirements for the degree of
Master's of Science
National Center for Media Forensics
College of Arts and Media
2011
201
by Harrison Allen Archer
All rights reserved.
This thesis for the Master's of Science
degree by
Harrison Allen Archer
has been approved by
Catalin Grigoras
Lome F. Bregitzer
t
Date
Archer, Harrison Allen (M.S., Media Forensics)
Quantifying the Effects of Lossy Digital Audio Compression Algorithms on
Electric Network Frequency Signals in Forensics Analysis
Thesis directed by Associate Professor Catalin Grigoras
ABSTRACT
In forensic analysis, the electric network frequency can often be used to determine
the time and date that an audio recording was created. Many forensic scientists
working with media question the quality and validity of audio evidence that was
created by or has been converted to lossy compressed audio formats. The
following work outlines a study designed to quantify the effects of lossy
compression algorithms on electric network frequency signals. It shows that no
forensic analysis based on the electric network frequency should be disregarded in
legal proceedings solely for the reason that the audio file had been converted to
any of the ten algorithms tested in this study.
This abstract accurately represents the content of the candidate's thesis. I
recommend its publication.
Signed
Catalin Grigoras
DEDICATION
I dedicate this thesis to my parents, Paul Archer and Lecia Barker, as well as Zak
Archer, Joe and Lainey Archer, Amy Archer, and Bill Aspray. Without the
guidance and support of my family, this would not have been possible.
ACKNOWLEDGMENT
I would like to give special thanks to Catalin Grigoras for his guidance and
support during the process of my graduate education and throughout the creation
of this thesis. I would also like to thank Jeffrey M. Smith for his instruction and
Lome F. Bregitzer for his participation on my committee.
TABLE OF CONTENTS
List of Figures...............................................viii
Chapter
1. Introduction..................................................1
2. Lossy Compression Formats....................................4
3. Methodology..................................................7
3.1 Processes...................................................7
3.2 Formulas....................................................9
4. Results.....................................................10
4.1 Correlation Coefficients...................................10
4.1.1 Correlation Coefficients for First Control................13
4.2 Mean Quadratic Differences.................................33
4.2.1 Mean Quadratic Differences for First Control..............35
5. Second Control..............................................44
vii
TABLE OF CONTENTS (Cont.)
6. Third Control.............................................65
7. Visual Analysis...........................................86
8. Discussion................................................91
Works Cited..................................................94
viii
LIST OF FIGURES
Figure
1.1 ENF Interlaboratory Results.....................................1
4.1 Correlation Coefficients.......................................15
4.2 Correlation Coefficients (Top 8)...............................16
4.3 Correlation Coefficients With Mean Subtraction.................17
4.4 Correlation Coefficients With Mean Subtraction
(Top 8)........................................................18
4.5 Correlation Coefficients With Mean Subtraction
(Top 2)........................................................19
4.6 Mean Values Of Correlation Coefficients........................20
4.7 Mean Values Of Correlation Coefficients (Top 8)................21
4.8 Standard Deviation Of Correlation Coefficients.................22
4.9 Mean Values Of Correlation Coefficients With
Mean Subtraction...............................................23
4.10 Mean Values Of Correlation Coefficients With
Mean Subtraction (Top 8).......................................24
4.11 Mean Values Of Correlation Coefficients With
Mean Subtraction (Top 2).....................................25
4.12 Standard Deviation Of Correlation Coefficients With
Mean Subtraction.............................................26
4.13 Correlation Coefficients Against First Control...............27
IX
LIST OF FIGURES (Cont.)
4.14 Mean Values Of Correlation Coefficients Against
First Control................................................28
4.15 Standard Deviation Of Correlation Coefficients Against
First Control................................................29
4.16 Correlation Coefficients With Mean Subtraction Against
First Control................................................30
4.17 Mean Values Of Correlation Coefficients With Mean
Subtraction Against First Control............................31
4.18 Standard Deviation Of Correlation Coefficients With
Mean Subtraction Against First Control.......................32
4.19 Mean Quadratic Differences...................................36
4.20 Mean Quadratic Differences (Top 8)...........................37
4.21 Mean Quadratic Differences (Top 2)...........................38
4.22 Mean Values Of Mean Quadratic Differences....................39
4.23 Standard Deviation Of Mean Quadratic Differences.............40
4.24 Mean Quadratic Differences Against First Control.............41
4.25 Mean Values Of Mean Quadratic Differences
Against First Control........................................42
4.26 Standard Deviation Of Mean Quadratic Differences
Against First Control........................................43
5.1 Correlation Coefficients With Mean Subtraction Between
All ALaw Recordings.........................................45
x
LIST OF FIGURES (Cont.)
5.2 Mean Quadratic Differences Between All ALaw
Recordings..................................................46
5.3 Correlation Coefficients With Mean Subtraction Between
All DVIADPCM Recordings................................47
5.4 Mean Quadratic Differences Between All DVI ADPCM
Recordings..................................................48
5.5 Correlation Coefficients With Mean Subtraction Between
All MP3 With Constant Bit Rate Recordings...................49
5.6 Mean Quadratic Differences Between All MP3
With Constant Bit Rate Recordings...........................50
5.7 Correlation Coefficients With Mean Subtraction
Between All High Quality MP3 With
Variable BitRate Recordings................................51
5.8 Mean Quadratic Differences Between All High Quality
MP3 With Variable BitRate Recordings.......................52
5.9 Correlation Coefficients With Mean Subtraction
Between All Low Quality MP3 With
Variable BitRate Recordings................................53
5.10 Mean Quadratic Differences Between All Low Quality
MP3 With Variable BitRate Recordings.......................54
5.11 Correlation Coefficients With Mean Subtraction Between
All Microsoft ADPCM Recordings..............................55
5.12 Mean Quadratic Differences Between All
Microsoft ADPCM Recordings.................................56
5.13 Correlation Coefficients With Mean Subtraction Between
All MuLaw Recordings.......................................57
XI
LIST OF FIGURES (Cont.)
5.14 Mean Quadratic Differences Between All
MuLaw Recordings..............................................58
5.15 Correlation Coefficients With Mean Subtraction
Between All High Quality WMA With Constant
BitRate Recordings............................................59
5.16 Mean Quadratic Differences Between
All High Quality WMA With Constant
BitRate Recordings............................................60
5.17 Correlation Coefficients With Mean Subtraction Between
All Low Quality WMA With Constant BitRate
Recordings.....................................................61
5.18 Mean Quadratic Differences Between All Low
Quality WMA With Constant BitRate Recordings..................62
5.19 Correlation Coefficients With Mean Subtraction Between
All WMA With Variable BitRate Recordings......................63
5.20 Mean Quadratic Differences Between All
WMA With Variable BitRate Recordings..........................64
6.1 ALaw CC Intravariability V. Intervariability...................66
6.2 ALaw MQD Intravariability V. Intervariability..................67
6.3 DVIADPCM CC Intravariability V. Intervariability................68
6.4 DVI ADPCM MQD Intravariability V. Intervariability..............69
6.5 MP3 With Constant BitRate CC Intravariability
V. Intervariability......................................70
6.6 MP3 With Constant BitRate MQD Intravariability
V. Intervariability......................................71
xii
LIST OF FIGURES (Cont.)
6.7 High Quality MP3 With Variable BitRate CC
Intravariability V. Intervariability........................72
6.8 High Quality MP3 With Variable BitRate MQD
Intravariability V. Intervariability........................73
6.9 Low Quality MP3 With Variable BitRate CC
Intravariability V. Intervariability........................74
6.10 Low Quality MP3 With Variable BitRate MQD
Intravariability V. Intervariability........................75
6.11 Microsoft ADPCM CC Intravariability V.
Intervariability..........................................76
6.12 Microsoft ADPCM MQD Intravariability V.
Intervariability..........................................77
6.13 MuLaw CC Intravariability V. Intervariability....................78
6.14 MuLaw MQD Intravariability V. Intervariability...................79
6.15 High Quality WMA With Constant BitRate
CC Intravariability V. Intervariability.....................80
6.16 High Quality WMA With Constant BitRate
MQD Intravariability V. Intervariability....................81
6.17 Low Quality WMA With Constant BitRate CC
Intravariability V. Intervariability........................82
6.18 Low Quality WMA With Constant BitRate MQD
Intravariability V. Intervariability........................83
6.19 WMA With Variable BitRate CC Intravariability
V. Intervariability.........................................84
xiii
LIST OF FIGURES (Cont.)
6.20 WMA With Variable BitRate MQD Intravariability
V. Intervariability.....................................85
7.1 Visual Analysis For ALaw And MuLaw..........................87
7.2 Visual Analysis For ADPCM Formats.............................88
7.3 Visual Analysis For MP3 Recordings............................89
7.4 Visual Analysis For WMA Recordings.............................90
XIV
1. Introduction
Alternating current electricity is used to power the vast majority of the world. In
most countries, the frequency of the electric current is either 50 or 60 Hz. In the
United States, 60 Hz is used. In an ideal situation, the frequency would remain
constant at precisely 60 Hz. However, based on the consumption of electricity
across a power grid, the frequency constantly varies randomly within 0.6 Hz [1].
There are three power grids in the United States (Eastern, Western, and Texas),
each of which has a different variation. Across any power grid, the electric
network frequency (ENF) is almost the same including the variations [1][2][3].
The following figure shows the nearly identical variations in ENF across a power
grid in Europe.
N
X
X
UJ
X
iu
N*
X
Ui
time [sec]
(a)
(b)
(c)
Figure 1.1 ENF Interlaboratory Results, (a) Bucharest, (b) Amsterdam, (c) Madrid. Courtesy,
Grigoras [1],
1
Widespread use of portable audio recorders in consumer and law enforcement
settings has caused a dramatic increase in the amount of digital audio evidence
used in legal proceedings. The ENF is often captured by devices used to record
audio signals, whether the signal is transmitted through sound pressure waves, by
electromagnetic fields, or directly induced by the power supply of a recording
device. Electromagnetic fields are present, however faint they may be, in most
locations where power is distributed throughout a building. A recording device
may pick up ENF through these fields whether it is a battery operated device or if
it is powered from the power grid. This does not mean with certainty that the
ENF signal will be present in every audio file produced under the above
circumstances nor that the signal will necessarily be pronounced enough to
perform an analysis.
For forensic purposes, because the variations in the ENF are random, they can be
used to determine the exact time that an audio file was made by matching the
variations of a forensic recording with a period of time in an ENF database. For
that reason, databases of the exact ENF are now being recorded in various
locations around the world. Verifying a claimed time and date of recording with
the use of ENF analysis is one of many criterions used in the authentication of a
digital audio recording, though the ENF analysis alone is not adequate evidence
of authenticity. According to the Audio Engineering Society Standard AES27
1996 (r2007), an authentic audio recording is defined as "a recording made
simultaneously with the acoustic events it purports to have recorded, and in a
manner fully and completely consistent with the method of recording claimed by
the party who produced the recording; a recording free from unexplained artifacts,
alterations, additions, deletions, or edits" [6].
Methods of using ENF analysis to authenticate a forensic audio recording have
been presented by Sanders [2], Grigoras [1], and Cooper [4]. Methods of
analyzing ENF include a frequency against time analysis involving visual
examinations of spectrograms, frequency domain analysis in which the frequency
with the maximum magnitude for each unit of time is used to produce a series of
ENF values, and a time domain analysis in which zero crossings of a band passed
signal are used to determine the ENF.
Unfortunately, many forensic recordings are not made with the highest quality
equipment and audio formats. Many forensic recordings are now being made
with the use of lossy digital compression algorithms which reduce the amount of
data used to store the audio file. In many areas of audio forensics, recordings
2
made with the use of lossy compression have a questioned quality and validity.
The effects of lossy compression on ENF signals in analog recordings has been
studied by Morjaria [5] using the frequency against time analysis method in which
visual analysis of spectrograms is used. The results showed that, for most
compression formats, the analog signal recorded was not significantly altered by
the compression algorithm to the point that a visual analysis of the ENF would no
longer be possible. Moijaria had concluded that MP3 did not maintain the ENF
signal, that the ENF signal was "destroyed," and that a visual ENF analysis was
not possible after conversion to MP3. These conclusions conflict with the results
of this study which shows that MP3 algorithms do not have a seriously
detrimental effect on ENF signals.
The purpose of the following study is to quantify the effects of lossy compression
on ENF signals which were recorded digitally. The method used to examine the
audio files is a frequency domain analysis and statistical examination of the
differences between the ENF signals. The result will be to show that no forensic
analysis based on the electric network frequency should be disregarded in legal
proceedings solely for the reason that the audio file had been converted to any of
the ten algorithms tested in this study. This study used the western power grid of
the United States. The original uncompressed audio files were recorded as part of
the National Center for Media Forensics' ENF database. This database, located in
Denver, Colorado, is consistent with recommendations set forth by Grigoras et al.
[7].
3
2. Lossy Compression Formats
The ten compression algorithms that were tested in this experiment were Alaw,
mulaw, DVI ADPCM, Microsoft ADPCM, high quality MP3 with variable bit
rate, low quality MP3 with variable bitrate, MP3 with constant bitrate, high
quality Windows Media Audio (WMA) with constant bitrate, low quality WMA
with constant bitrate, and WMA with variable bitrate.
The original uncompressed pulse code modulation (PCM) audio files of the ENF
used for this experiment had a sample rate of 8 kHz and a 16 bit depth.
Therefore, the bitrate of these original audio files was 128 kilobits per second
(kbps). They are saved with .WAV file extensions.
Alaw and mulaw (or plaw) are standard compression algorithms used in
telecommunications. Mulaw is used mainly in North America and Japan; Alaw
is more prevalent in the rest of the world and is the standard in Europe. They are
companding algorithms which decrease the dynamic range of the audio file. A
law has a slightly lower dynamic range than mulaw. These algorithms are used
because linear digital encoding is inefficient with speech signals. By reducing the
dynamic range and increasing the signal to noise ratio, the efficiency of coding is
improved and quantization error is reduced. The result is a smaller number of bits
used to transmit an intelligible speech signal. The companding component of
these algorithms can be applied in the analog domain by using an amplifier with
nonlinear gain. If telecommunications are transmitted between an Alaw
network and a mulaw network, the Alaw algorithm is used. Both are saved
with .WAV file extensions. Various files with .WAV file extensions are
differentiated by the header data. Alaw and mulaw are also used in some .AU
audio file formats created by Sun Microsystems (other encodings are also used in
the .AU format including PCM and ADPCM). A typical 8 kHz Alaw or mulaw
audio file is reduced to 8bits and has a bitrate of 64 kbps. Audio files converted
to these formats result in files 50% the size of the original PCM audio file.
Two variations of adaptive differential pulse code modulation (ADPCM) were
tested: Microsoft ADCPM and DVI ADPCM. These two algorithms both save
the data with a .WAV file extension. ADPCM algorithms allow for a varied
quantization level. The goal of the varied quantization level is to use a smaller
bandwidth to achieve similar signal to noise ratios as larger bandwidths. When
encoding from PCM, ADPCM calculates the differences between samples and
stores those values while making predictions about the final audio file. Upon
4
decoding, the prediction is combined with the quantized differences to create a
reconstructed signal. With lower sample rates, distortion in high frequencies of
ADPCM audio files becomes audible, but this is not a problem with 44.1 kHz or
higher sample rates. In telephony, ADPCM is sometimes combined with the A
law or mulaw algorithms to create 4 bit ADPCM samples from the Alaw or mu
law samples. ADPCM is also used in Voice over IP communications. A typical
Microsoft ADPCM audio file uses only 4 bits per sample and has a bitrate of 32
kbps. The Microsoft ADPCM algorithm used in this experiment was multiple
pass and had a large block size. The result was a compression ratio of 3.91:1 and
a bitrate of roughly 32.7 kbps. The DVI ADPCM algorithm used exactly 4 bits
per sample and had a bitrate of 32 kbps. Audio files converted to Microsoft
ADPCM resulted in files that were approximately 21% the size of the original
PCM audio files and audio files converted to DVI ADPCM yield files
approximately 19% the size of the original PCM audio files.
MPEG2 Audio Layer 3, or MP3, is a compression algorithm designed by the
Moving Picture Experts Group as part of the MPEG1 and MPEG2 standards.
MP3 is arguably the most common form of lossy audio compression in the world.
MP3 algorithms work by using psychoacoustic properties, reducing the accuracy
of portions of the signal that are deemed less relevant. High frequencies, for
example, are nearly eliminated because they are out of the range of most humans'
hearing. This is called perceptual encoding. Psychoacoustic models are provided
in the MPEG1 standard, but precise specifications for the encoder are not
included. Those implementing the standard were to create their own encoders to
meet the psychoacoustic models. There are now a wide variety of MP3 encoders
available. For this experiment, an MP3 PRO algorithm was used which uses a
small amount of extra data other MP3 algorithms don't use to help in
reconstructing higher frequencies and can therefore use smaller overall bitrates
that achieve comparable quality as algorithms with higher bitrates. The audio
files are saved in a .MP3 file. Three settings of this algorithm were tested. The
first was a constant bitrate version in which the same bitrate is used for the
entire audio file. The compression ratio was 16:1 and the bitrate was
approximately 8 kbps. Audio files converted with this algorithm yield files
approximately 6% the size of the original PCM audio file. Two MP3 settings
with variable bitrate were used: the highest and lowest quality settings for
variable bitrate MP3. With variable bitrate encoding, more complex signals are
encoded with a higher bitrate than less complex signals. The highest quality
setting had a bitrate that ranges from 75120 kbps. ENF audio files converted
with this highest quality setting yielded files approximately 9% the size of the
5
original audio files. The lowest quality setting had a bitrate that ranged from 40
50 kbps. ENF audio files converted with this lowest quality setting yielded files
approximately 6% the size of the original PCM audio files.
Windows Media Audio, or WMA, is a lossy audio compression algorithm
designed by the Microsoft Corporation. There are four variations of WMA
codecs. The first is the original WMA compression algorithm known simply as
WMA which was first created in 1999 though it has been revised since that time.
WMA operates on similar principles as MP3 in that it uses perceptual encoding
and psychoacoustics to determine which components of the audio content are less
relevant for human hearing. It also can be applied with both constant bitrate and
variable bitrate. The second is WMA Pro, which supports multichannel audio
and higher resolution audio. A lossless version of WMA was created to compress
audio data without losing audio quality. And the fourth codec is WMA Voice,
which was created to accurately capture human speech. Version 9.2 of the
original WMA codec was used for this experiment. The audio files are saved
with a .WMA file extension. Three settings of this algorithm were tested in this
experiment. The variable bitrate setting resulted in files approximately 7% the
size of the original PCM audio file and the lowest quality constant bitrate setting
which used 5 kbps also resulted in files approximately 7% the size of the original
PCM audio file. The highest quality constant bitrate setting used 8 kbps and
resulted in files approximately 6.5% the size of the original PCM audio file.
6
3. Methodology
3.1 Processes
The goal of the following process was to create ENF audio files which would be
identical to the original files other than that they were processed with a lossy
compression algorithm. These compressed files could then be compared to the
original to determine the effect that the lossy compression algorithms had on the
ENF signal. One hundred test samples were used for each of ten compression
algorithms. To ensure that the test samples were unique, one hundred different
hours of ENF audio files were used from five different months.
Audio files of the ENF were used from the ENF database at the National Center
for Media Forensics in Denver, Colorado. The database operates by reducing the
voltage of the electric current and recording it directly as an audio signal. The
original audio files were each one day in length. Each of these one day audio files
was then converted and saved with the ten different lossy compression algorithms
referred to in the previous section using Adobe Audition. Any additional audio
samples added to the start of an audio file by the compression algorithm were
removed to ensure that the compressed audio files' ENF signal was in phase with
the original files' ENF signal. Additional audio samples would throw off later
statistical calculations.
The twentyfour hour compressed and uncompressed audio files were divided into
hours. Twenty hours were used from each of five days, the first day of each of
five consecutive months. The result was 1,100 audio files: ten compressed audio
files of different formats for each of one hundred hours and the original one
hundred uncompressed hours.
The audio files were then prepared for an ENF analysis; they were downsampled
from their original sampling frequency of 8 kHz to 360 Hz and a bandpass filter
was applied from 55 Hz to 65 Hz (100% amplitude at 60 Hz, linearly reduced to
0% amplitude at 55 Hz and 65 Hz). This band pass filter ensured that the only
information examined was the ENF signal. For each of the 1,100 audio files, the
ENF was then calculated at one second intervals using the average frequency with
the maximum magnitude for each second and the frequencies were then saved as
a vector (a series of values: one ENF value per second) in a text format. During
this process, figures were produced representing the frequency variations of ENF
over time. (These figures allow for a visual analysis of the ENF to be conducted.)
7
Finally, calculations were made to find the statistical differences between the ENF
vectors of compressed audio files against the vector for the original audio files.
These calculations included mean quadratic differences and correlation
coefficients between the original and compressed audio files. The correlation
coefficients were also computed with mean subtraction (mean subtraction refers
to the average value of a frequency vector being subtracted from every value in
that vector before a correlation coefficient calculation is made; this allows for
subtle differences between the vectors to be made more apparent). Higher
correlation coefficients show a higher degree of similarity to the original
uncompressed audio file, whereas lower mean quadratic differences show a
higher degree of similarity to the original uncompressed audio file. A correlation
coefficient value of one (1) is the maximum value for a correlation coefficient and
shows that the two vectors are identical. A mean quadratic difference value of
zero (0) is the minimum value for a mean quadratic difference and shows that the
two vectors are identical. The mean values and standard deviations of the
correlation coefficients (with and without mean subtraction) and mean quadratic
differences were also calculated for each format. The mean value calculations
allow for an algorithm's overall degradation of the ENF to be generalized,
whereas the standard deviation calculations show the range of effects that an
algorithm can have on the ENF signal.
Calculations were also made to find the statistical difference between the
compressed formats and three controls. The first control used was to compare the
PCM audio files vector with the previous hours PCM frequency vector. The
second control was to calculate the correlation coefficients with mean subtraction
and mean quadratic differences between all audio files of a compressed format
and all the other audio files of that format. The third control was to calculate the
correlation coefficients with mean subtraction and mean quadratic differences
between all the audio files of a compressed format and every other hours PCM
audio file. The purpose of the three controls is to show that it would be extremely
unlikely to produce high correlation coefficients or low mean quadratic
differences when comparing any two hours' PCM vectors, any two hours'
compressed vectors, or any compressed hour with any other hour's PCM vector.
If the controls did not show that matching hours produce higher correlation
coefficients or lower mean quadratic differences than nonmatching hours, then
the study would not be relevant.
8
3.2 Formulas
The formula for correlation coefficients (CC), shown here with mean subtraction,
is as follows where x and y are vectors being compared against each other and xm
and ym are the mean values of the vectors:
The formula for mean quadratic difference (MQD) is as follows where x and y are
vectors being compared against each other:
To find the mean values (p) of all correlation coefficients or mean quadratic
differences for an algorithm where x is a vector containing all the values of either
correlation coefficients or mean quadratic differences, the following formula was
used:
To find the standard deviation (c) of all correlation coefficients or mean quadratic
differences for an algorithm where p is the mean of all values for either
correlation coefficients or mean quadratic differences and x is a vector containing
all the values of either correlation coefficients or mean quadratic differences, the
following formula was used:
Ik=i(*fc xm)(yk ym)
VÂ£fc=i(*fc ~ xm)2 Vlk=i(Yk ~ ym)2
k=N
XiLiOi m)2
a =
N
9
4. Results
4.1 Correlation Coefficients
The highest correlation coefficients belong to the Alaw and mulaw algorithms
[Figures 4.1, 4.2]. The Alaw algorithm held the single highest mean value of
correlation coefficients: 0.999999999982075 [Figures 4.6 and 4.7], but the
difference between the mean values for Alaw correlation coefficients and mulaw
correlation coefficients was negligible (a difference in mean values of
approximately 1.399 x 1013). The Alaw and mulaw algorithms also produced
the lowest standard deviation in correlation coefficients [Figure 4.8]. The
standard deviation of correlation coefficients was roughly 4.8915 x 10~12 for A
law and 5.1664 x 1012 for mulaw. The Alaw algorithm produced a slightly
lower standard deviation of correlation coefficients; again, the difference in
standard deviations between the two algorithms was negligible. These two
algorithms represent the extreme highs in correlation coefficients, and therefore
cause the least signal degradation.
The Alaw and mulaw algorithms were followed by the Microsoft ADPCM
algorithm, which held the third highest mean value of correlation coefficients:
0.999999999901071 [Figures 4.6 and 4.7] but had the seventh highest standard
deviation of correlation coefficients: roughly 5.6584 x 1011 [Figure 4.8] (the
highest quality WMA algorithm with constant bitrate and all three MP3
algorithms produced less varied results).
The high quality WMA algorithm with constant bitrate produced the fourth
highest average values for correlation coefficients (0.999999999852890) [Figures
4.6 and 4.7], and the sixth lowest standard deviation of correlation^coefficients
(roughly 4.0223 x 1011) [Figure 4.8].
The DVI ADPCM algorithm had the fifth highest mean value of correlation
coefficients (0.999999999844249) [Figures 4.6 and 4.7], though it held the eighth
highest standard deviation of correlation coefficients (roughly 9.7664 x 1011)
[Figure 4.8]; it produced more varied results than algorithms with lower average
correlation coefficients, much like the Microsoft ADPCM algorithm.
The high quality MP3 algorithm with variable bitrate held the sixth highest mean
value of correlation coefficients (0.999999999752317) and the third lowest
10
standard deviation of correlation coefficients (roughly 2.4344 x 1011), followed
by the low quality MP3 algorithm with variable bitrate which held the seventh
highest mean value of correlation coefficients (0.999999999741477) and the
fourth lowest standard deviation of correlation coefficients (roughly 2.8767 x
1011) [Figures 4.6, 4.7, and 4.8]. The MP3 algorithm with constant bitrate held
the eighth highest mean value of correlation coefficients (0.999999999617195)
and the fifth lowest standard deviation of correlation coefficients (roughly
3.4487 x 1011) [Figures 4.6, 4.7, and 4.8].
Two WMA algorithms produced the two lowest average correlation coefficients
[Figure 4.1]. The WMA algorithm with variable bitrate held the second lowest
mean value of correlation coefficients (0.999999997216846) but also produced
the highest standard deviation of correlation coefficients (roughly 3.6725 x
10_1), whereas the low quality WMA algorithm with constant bitrate held the
lowest mean value of correlation coefficients (0.999999997216107) and the
second highest standard deviation (roughly 3.6706 x 1010). For both mean
values of correlation coefficients and standard deviation of correlation
coefficients, the difference between the WMA algorithm with variable bitrate
and the low quality WMA algorithm with constant bitrate was negligible (a
difference in mean values of approximately 7.389 x 1013 and a difference in
standard deviations of approximately 1.348 x 10~19). These two algorithms
represent the extreme lows in correlation coefficients, and therefore cause the
most signal degradation.
When the correlation coefficients were calculated with mean subtraction [Figures
4.3, 4.4, and 4.5], though the compression algorithms' rank remain in the same
order for mean values of correlation coefficients [Figures 4.9, 4.10, and 4.11], the
standard deviations of correlation coefficients rearrange dramatically [Figure
4.12]. The highest quality WMA algorithm with constant bitrate moves up from
sixth to the third lowest standard deviation of correlation coefficients, the
Microsoft ADPCM algorithm moves up from seventh to the fourth lowest
standard deviation of correlation coefficients, the highest quality MP3 algorithm
with variable bitrate moves down from third to the fifth lowest standard deviation
of correlation coefficients, the lowest quality MP3 algorithm with variable bitrate
moves down from fourth to the sixth lowest standard deviation of correlation
coefficients, the DVI ADPCM algorithm moves up from eighth to the seventh
lowest standard deviation of correlation coefficients, and the MP3 algorithm with
11
constant bitrate moves down from fifth to the eighth lowest standard deviation of
correlation coefficients.
12
4.1.1 Correlation Coefficients for First Control
Calculating correlation coefficients for the first control [Figure 4.13], the PCM
vector being tested against the previous hours PCM vector, resulted in much
lower values than any of the compression algorithms produced when compared
against the same hours PCM vector and a much higher standard deviation of
correlation coefficients [Figures 4.13, 4.14, and 4.15]. These differences are far
clearer when the correlation coefficient is applied to the first control with mean
subtraction [Figures 4.16, 4.17, and 4.18]. For the compression algorithms being
tested against the same hours PCM vector, mean values of correlation
coefficients with mean subtraction ranged from the Alaw algorithm yielding a
0.999497714578915 to the lowest quality WMA algorithm with constant bitrate
yielding a 0.928355315643604; a range of only 0.071142398935315. The mean
value of correlation coefficients with mean subtraction for the first control was
0.108186984019554. Here, the range from the mean value of correlation
coefficients with mean subtraction for the lowest quality WMA algorithm with
constant bitrate to the mean value of the control was a larger
0.820168331624050, and the range from the mean value of correlation
coefficients for Alaw to the mean value of the control was an even larger
0.891310730559361. The highest standard deviation for the correlation
coefficients with mean subtraction of the tested algorithms against the same
hours PCM audio file was 0.033566 (lowest quality WMA algorithm with
constant bitrate) and the lowest was 0.000300 (Alaw). The standard deviation
of the correlation coefficients with mean subtraction for the first control was
0.222028. The lowest values for the correlation coefficients calculated with mean
subtraction for the control were approximately 0.49.
13
For all of the following plots, including mean quadratic difference plots in Section
4.2, the xaxis is a list of algorithms in alphabetical order defined here:
Figures Legend and Abbreviations:
1: Alaw (AL)
2: DVIADPCM (DVI)
3: MP3 with Constant BitRate (MP3C)
4: Highest Quality MP3 with Variable BitRate (MP3H)
5: Lowest Quality MP3 with Variable BitRate (MP3L)
6: Microsoft ADPCM (MSA)
7: mulaw (ML)
8: Highest Quality WMA with Constant BitRate (WMAH)
9: Lowest Quality WMA with Constant BitRate (WMAL)
10: WMA with Variable BitRate (WMAV)
11: First Control: Previous Hours PCM Vector (CPCM)
14
Correlation Coefficients
1
0 999999995
*
*
r
) r
_L
AL DVI MP3C MP3H MP3L MSA ML
Figure 4.1 Correlation Coefficients
WMAH WMAL WMAV
Correlation Coefficients
1 i
0.99999999945
_i__________i_________i_________i_________i_________i_________i__________i_________i_________i__
AL DVI MP3C MP3 If MP3L MSA ML WMAH WMAL WMAV
Figure 4.2 Correlation Coefficients (Top 8)
Correlation Coefficients
0.86
AL
t t
t t
1 *
$ *
* f
4 k
__j_________i_________i_________i_________i_________i_________i_________i________i__
DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.3 Correlation Coefficients With Mean Subtraction
Correlation Coefficients
I
1
0 995
*
*
*
*
*
t
t
*
0.975 
*
*
*
+
*
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.4 Correlation Coefficients With Mean Subtraction (Top 8)
1.
* * * *
i
AL DVI W3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.5 Correlation Coefficients With Mean Subtraction (Top 2)
Correlation Coefficients
1
0.999999997
AL DVI MP3C MP3H MP3L MSA ML WMAH
Figure 4.6 Mean Values Of Correlation Coefficients
WMAL WMAV
Correlation Coefficients
1
*
Â¥
*
i..............................................:............................................h...............................................t.............................................................................................t
*
099999999966
AL
___I_
DVI
____I_________i_________I__________i_________i__________i_________i__________i__
MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.7 Mean Values Of Correlation Coefficients (Top 8)
Standard Deviation
4
*
JL
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.8 Standard Deviation Of Correlation Coefficients
Correlation Coefficients
1
0 90 
0 95 
0 94
AL DVI W3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.9 Mean Values Of Correlation Coefficients With Mean Subtraction
Correlation Coefficients
0.990
* *
*
*
0.992
v *
\
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.10 Mean Values Of Correlation Coefficients With Mean Subtraction (Top 8)
Correlation Coefficients
0.9995
0 9995
0.9995
0.9995
0.9995
0.9995
AL
DVI MP3C MP3II MP3L MSA ML WMAH WAT AT. WMAV
Figure 4.11 Mean Values Of Correlation Coefficients With Mean Subtraction (Top 2)
Standard Deviation
0.036
.jfc_____________________________________________________________^_________________________________
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.12 Standard Deviation Of Correlation Coefficients With Mean Subtraction
Correlation Coefficients
1 r*.............+................*...............+...............*...............*...............*..............*
1 ! ? 
t

1
i
i
#
*.
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV CPCM
Figure 4.13 Correlation Coefficients Against First Control
Correlation Coefficients
'i+
0 99999996
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.14 Mean Values Of Correlation Coefficients Against First Control
CPCM
Standard Deviation
Correlation Coefficients
1 4
0
0.5f~
___L
AL
*.......*......i.......*.......4.......f.......i
I________I_________I________I_________I________I_________I________I_________I__
DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.16 Correlation Coefficients With Mean Subtraction Against First Control
I
*
*
..*..
CPCM
Correlation Coefficients
'rt
O.B
0.6
0.4
\
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV CPCM
Figure 4.17 Mean Values Of Correlation Coefficients With Mean Subtraction Against First Control
Standard Deviation
0.25
02
i..................................................................:........................................................................\...............................................................................................................................................v.....................................................................\...............................................................................................................................................\.........................................................................
0.15
0 1
L
i
0.05
t t
^^^^^^^^_________________j_
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV CPCA
Figure 4.18 Standard Deviation Of Correlation Coefficients With Mean Subtraction Against First Control
4.2 Mean Quadratic Differences
The lowest mean quadratic differences again belonged to the Alaw and mulaw
algorithms [Figures 4.19, 4.20, and 4.21], Though the difference in average
values for mean quadratic differences between the two algorithms was trivial, the
lower value was held by the Alaw algorithm. (Average values of mean quadratic
differences were roughly 5.9303 x 10~6 for Alaw and 5.9471 x 106 for mu
law [Figure 4.22].) Much like the correlation coefficients, the mean quadratic
differences also showed that the Alaw algorithm typically causes the least ENF
signal degradation. It should be noted that the mulaw algorithm held mean
quadratic difference values both higher and lower than the range of values for the
Alaw algorithm, therefore having a higher standard deviation meaning that its
effect on the ENF signal is slightly less predictable than that of the Alaw
algorithm. The standard deviation of mean quadratic differences was roughly
8.4485 x 107 for Alaw and 8.9148 x 10~7 for mulaw [Figure 4.23]. These
two algorithms represent the extreme lows in mean quadratic differences, and
therefore cause the least signal degradation.
The Alaw and mulaw algorithms were followed by the Microsoft ADPCM
algorithm, which held the third lowest average mean quadratic differences
(1.3248 x 105) [Figure 4.22] and the ninth highest standard deviation of mean
quadratic differences (4.7653 x 106) [Figure 4.23]. Also like the correlation
coefficients, though its average value for mean quadratic differences was low,
showing less average signal degradation, it produced a much higher standard
deviation of mean quadratic differences and therefore had a less predictable effect
on the ENF signal than other algorithms which had higher mean quadratic
differences. The DVI ADPCM algorithm had the fourth lowest average value for
mean quadratic differences (1.6406 x 105) [Figure 4.22] but had the single
highest standard deviation of mean quadratic differences (6.5584 x 106) [Figure
4.23]. This differs from the correlation coefficients where the highest quality
WMA algorithm with constant bitrate held the fourth highest correlation
coefficients though the difference between average values for mean quadratic
differences is negligible between the DVI ADPCM algorithm and the highest
quality WMA algorithm with constant bitrate (a difference of 5.9126 x 107).
The DVI ADPCM algorithm produced mean quadratic difference values much
higher and much lower than the range of values for the highest quality WMA
algorithm with constant bitrate, which had a far lower standard deviation of mean
quadratic differences. The highest quality WMA algorithm with constant bitrate
33
then held the fifth lowest average value of mean quadratic differences (1.6998 x
105) [Figure 4.22] and the sixth lowest standard deviation of mean quadratic
differences (2.3569 x 106) [Figure 4.23].
The highest quality MP3 algorithm with variable bitrate held the sixth lowest
average value of mean quadratic differences (2.2238 x 105) [Figure 4.22] and
the third lowest standard deviation of mean quadratic differences (1.0802 x
106) [Figure 4.23], followed by the lowest quality MP3 with variable bitrate
which held the seventh lowest average value of mean quadratic differences
(2.2711 x 105) [Figure 4.22] and the fifth lowest standard deviation of mean
quadratic differences (1.2662 x 106) [Figure 4.23]. The MP3 algorithm with
constant bitrate had the eighth lowest average value of mean quadratic
differences (2.7652 x 105) [Figure 4.22] and the fourth lowest standard
deviation of mean quadratic differences (1.2515 x 106) [Figure 4.23]. Much
like the data from the correlation coefficient calculations, the MP3 algorithms had
low standard deviations of mean quadratic differences and therefore had a more
predictable effect on the ENF signal than some of the algorithms with lower
average values of mean quadratic differences.
The two WMA algorithms which produced the extreme lows for correlation
coefficients also produced the extreme highs for mean quadratic differences. The
WMA algorithm with variable bitrate produced the second highest average value
of mean quadratic differences (7.4501 x 105) [Figure 4.22] and the third
highest standard deviation of mean quadratic differences (4.5878 x 106) [Figure
4.23]. The lowest quality WMA algorithm with constant bitrate held the highest
average value for mean quadratic differences (7.4512 x 105) [Figure 4.22] and
the fourth lowest standard deviation of mean quadratic differences (4.5860 x
106) [Figure 4.23]. Much like the correlation coefficients, between these two
WMA algorithms, the algorithm with the higher average value of mean quadratic
differences and therefore less signal degradation produced the higher standard
deviation of mean quadratic differences and was therefore less predictable. Also,
as was the case for the correlation coefficients, the difference between these two
algorithms in both average value of mean quadratic differences and in standard
deviation of mean quadratic differences was trivial.
34
4.2.1 Mean Quadratic Differences for First Control
Calculating mean quadratic differences for the first control, the PCM vector being
tested against the previous hours PCM vector, resulted in much higher values than
any of the compression algorithms produced when compared against the same
hours PCM vector and a much higher standard deviation of mean quadratic
differences [Figures 4.24, 4.25, and 4.26],
35
Mean Quadratic Difference
lx) t* cn CT)
g
o
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.19 Mean Quadratic Differences
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.20 Mean Quadratic Difference (Top 8)
Mean Quadratic Difference
9
0
x 10'#
4 4
e ^ l t j S 4 *
i t 4 4 $ i 4  i K 4 t $
: 4 4 4 4 .. .... .4 4 4 4 4 4 4 4 4 4 4
4 4 4 s 4 * * ) 4 ( 4 f 4 It. ....4
f 3 t
\ \
\
_J_________I________L_________I_________I________I_________I_________I________I_________I__
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.21 Mean Quadratic Difference (Top 2)
Mean Quadratic Difference
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.22 Mean Values Of Mean Quadratic Differences
Standard Deviation
x 10
7 i
3
*
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV
Figure 4.23 Standard Deviation Of Mean Quadratic Differences
Mean Quadratic Difference
Mean Quadratic Difference
x 10
3 5 
2.5 
15
0 5
*
_L
*
*
_i_
*
AL DVI MP3C MP3H MP3L MSA ML WMAII WMAL WMAV
Figure 4.25 Mean Values Of Mean Quadratic Differences Against First Control
CPCM
Standard Deviation
* to
0.6
0.5
04
Jl.
JL
t
_L
Jl
*
t
_L
AL DVI MP3C MP3H MP3L MSA ML WMAH WMAL WMAV CPCM
Figure 4.26 Standard Deviation Of Mean Quadratic Differences Against First Control
5. Second Control
The second control, to calculate the statistical differences between all the
recordings of a compressed format and all the other recordings of that format,
returned very low correlation coefficients and high mean quadratic differences.
This shows that any two recordings of a compressed format will not create high
correlation coefficients or low mean quadratic differences.
44
40
T
U1
o
1.02 0.015 001 0.005 0 0.005 0.01 0.015 0.02
Correlation Coefficient
Figure 5.1 Correlation Coefficients With Mean Subtraction Between All ALaw Recordings
25
20
15
GO
O
C
s
o
o
0,0
5
0
in1~r~1111
23456789 10
Mean Quadratic Difference 104
Figure 5.2 Mean Quadratic Differences Between All ALaw Recordings
1.02 0.015 0.01 0.005 0 0.005 0.01 0.015 0.02
Correlation Coefficient
Figure 5.3 Correlation Coefficients With Mean Subtraction Between All DVIADPCM Recordings
25
20
15
10
5
0
Mean Quadratic Difference
Figure 5.4 Mean Quadratic Differences Between All DVIADPCM Recordings
x 10
35
4*
ID
30
0.02
0015 0.01 0 005 0 0.005 0.01 0015
Correlation Coefficient
Figure 5.5 Correlation Coefficients With Mean Subtraction Between All
MP3 With Constant BitRate Recordings
0.02
1..........1...........I.~~....."T...........1
Figure 5.6 Mean Quadratic Differences Between All MP3 With Constant BitRate Recordings
35
j.02 0.015 0.01 0.005 0 0.005 0.01 0.015 0.02
Correlation Coefficient
Figure 5.7 Correlation Coefficients With Mean Subtraction Between All High Quality
MP3 With Variable BitRate Recordings
Ul
NJ
Mean Quadratic Difference
Figure 5.8 Mean Quadratic Differences Between All High Quality MP3 With
Variable BitRate Recordings
40
35
30
25
20
15
10
5
fti
T
1
0.015 0.01 0.005 0 0.005 0.01 0.015 0.1
Correlation Coefficient
Figure 5.9 Correlation Coefficients With Mean Subtraction Between All Low Quality
MP3 With Variable BitRate Recordings
Mean Quadratic Difference
Figure 5.10 Mean Quadratic Differences Between All Low Quality MP3
With Variable BitRate Recordings
40
35
30
25
rfl
4>
c
d>
Â§ 20
5
o
O
15
10
5
$
43.015 0 01 0 0n* 0 0.005 0.01 0.015 0
Correlation Coefficient
Figure 5,11 Correlation Coefficients With Mean Subtraction Between All Microsoft ADPCM Recordings
25
20
15
10
5
0
i i r~~r~r111 i
23456789 10
Mean Quadratic Difference > io4
Figure 5.12 Mean Quadratic Differences Between All Microsoft ADPCM Recordings
40
35
30
25
Xfl
O
O
e
6
g 20
O
o
o
15
10
5
0
0.(
n
0.015 0.01 0.005 0 0.005 0.01 0.015 0
Correlation Coefficient
Figure 5.13 Correlation Coefficients With Mean Subtraction Between All MuLaw Recordings
U1
00
l...................................................I.................................................I ........................................... ! I
Figure 5.14 Mean Quadratic Differences Between All MuLaw Recordings
1.02 *0 015 0 01 0.005 0 0.005 0.01 0 015 0 02
Correlation Coefficient
Figure 5.15 Correlation Coefficients With Mean Subtraction Between All High Quality
WMA With Constant BitRate Recordings
25
T
Mean Quadratic Difference
Figure 5.16 Mean Quadratic Differences Between All High Qualtiy WMA With
Constant BitRate Recordings
Occurrences
Correlation Coefficient
Figure 5.17 Correlation Coefficients With Mean Subtraction Between All Low Quality
WMA With Constant BitRate Recordings
Occurrences
Mean Quadratic Difference
Figure 5.18 Mean Quadratic Differences Between All Low Quality WMA
With Constant BitRate Recordings
Correlation Coefficient
Figure 5.19 Correlation Coefficients With Mean Subtraction Between All
WMA With Variable BitRate Recordings
cn
Mean Quadratic Difference
Figure 5.20 Mean Quadratic Differences Between All WMA With Constant BitRate Recordings
6. Third Control
The third control was to calculate for each compressed format the statistical
differences between every hours compressed audio file frequency vector and
every hours PCM audio file frequency vector. All compressed audio files of a
format were compared to all PCM audio files. It returned very low correlation
coefficients and very high mean quadratic differences when a compressed
formats vector was not compared with the corresponding PCM hours vector.
When the vectors were compared with the corresponding PCM hours vector, the
results returned were as reported in the preceding sections on correlation
coefficients and mean quadratic differences. These results have been plotted in
histograms to illustrate the wide gap between correlation coefficients and mean
quadratic differences for matching hours and nonmatching hours. This shows
that an audio file of a compressed format will not produce high correlation
coefficients or low mean quadratic differences when compared with another
hours PCM frequency vector. Intravariablity refers to a compressed audio file
being compared with the corresponding hour's PCM vector; whereas
itervariability refers to a compressed audio file being compared with any audio
file that did not come from the same hour.
65
BO
70
BO
50
VI
o
o
C
i>
H 40
3
o
a
o
30
20
10
0
I
0 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Mean Quadratic Difference *10
Figure 6.2 ALaw MQD Intravariability V. Intervariability
CT>
KD
1.2 03 0.4 0.5 0.6 0.7 0.8
Mean Quadratic Difference
Figure 6.4 DVIADPCM MQD Intravariability V. Intervariability
0.4 05 0.6
Mean Quadratic Difference
Figure 6.6 MP3 With Constant BitRate MQD Intravariability V. Intervariability
70
60
50
U40
G
i
O
O
O30
20
10
0
0.1 0.2 0.3 0.4 0.5 0.6 07 0.8 0.9
Mean Quadratic Difference
Figure 6.8 High Quality MP3 With Variable BitRate MQD Intravariability V. Intervariability
Figure 6.9 Low Quality MP3 With Variable BitRate CC Intravariability V. Intervariability
60
50
40
30
20
10
0
n
0.1 0.2 0.3 0.4 0.5 0.6 07 0.6 0.9 1
Mean Quadratic Difference o3
Figure 6.10 Low Quality MP3 With Variable BitRate MQD Intravariability V. Intervariability
cn
1000
Xfl
8 m
0
o
o
O500
400
"[......... I
I I I T
J_________L
"T............T'
J_________I________I_________L
~T
J_________l
0.1 0.2 03 0.4 0.5 0.6 0.7 0.0 09 1 1.1
Correlation Coefficient
Figure 6.11 Microsoft ADPCM CC Intravariability V. Intervariability
60
50
40
0>
o
a
a>
Â§ 30
o
o
o
20
10
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Mean Quadratic Difference * >3
Figure 6.12 Microsoft ADPCM MQD Intravariability V. Intervariability
1400
T
1200
"nI
00
xfi
a
a
i
o
o
o
8.2
1
0.1 0
0.1 0 2 0 3 0.4 0.5 0 6 0.7 0 8 0.9 1 1 1 1 2
Correlation Coefficient
Figure 6.13 MuLaw CC Intravariability V. Intervariability
80
70
60
50
40
30
20
10
0
r_1pjr
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 09 1
Mean Quadratic Difference *10 3
Figure 6.14 MuLaw MQD Intravariability V. Intervariability
Figure 6.15 High Quality WMA With Constant BitRate CC Intrvariability V. Intervariability
60
50
Mean Quadratic Difference
Figure 6.16 High Quality WMA With Constant BitRate MQD Intravariability V. Intervariability
1400
1
00
ro
g 800
C
(D
i
o
o
o 600
400
200
_L
_L
02
0.1
0.1
0.3
0.5
Correlation Coefficient
Figure 6.17 Low Quality WMA With Constant BitRate CC Intravariability V. Intervariability
Occurrences
UOO
T
T
1
oo
P>
Vi
C
(U
i
O
O
0.1
0 1
02
03
0.8
09
Correlation Coefficient
Figure 6.19 WMA With Variable BitRate CC Intravariability V. Intervariability
60
T
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 8
Mean Quadratic Difference
Figure 6.20 WMA With Constant BitRate MQD Intravariability V. Intervariability
7. Visual Analysis
It is clear in the following figures that the ENF signal is maintained well
enough by all the algorithms tested to complete a visual analysis with the
procedure described in the methodology. A close look at most of the figures
will reveal slight differences between the original PCM recording and the
compressed formats. The differences are most obvious in the two WMA
algorithms which produced the lowest correlation coefficients and the highest
mean quadratic differences. Though they did not yield the greatest numbers, a
visual analysis can still be successfully executed.
86
