A NEW ACCURATE METHOD OF HARMONIC-TO-NOISE
RATIO EXTRACTION
Ricardo J. T. de Sousa
School of Engineering , University of Porto, Rua Roberto Frias, Porto, Portugal
Keywords: Voice quality, Voice diagnosis, Harmonic-to-noise ratio, Hoarseness, Roughness.
Abstract: In this paper, an accurate method that estimates the HNR from sustained vowels based on harmonic
structure modeling is proposed. Basically, the proposed algorithm creates an accurate harmonic structure
where each harmonic is parameterized by frequency, magnitude and phase. The harmonic structure is then
synthesized and assumed as the harmonic component of the speech signal. The noise component can be
estimated by subtracting the harmonic component from the speech signal. The proposed algorithm was
compared to others HNR extraction algorithms based on spectral, cepstral and time domain methods, and
using different performance measures.
1 INTRODUCTION
1.1 Speech Assessment
In the audition tests which are include in speech
assessment, perceptive parameters such as
hoarseness, breathiness and roughness are evaluated
in order to characterize the physiological changes of
the vocal folds. In general, these physiological
changes are indicative of the presence of structures
such polyps, nodules and laryngeal cancer. In order
to quantify the hoarseness and roughness
phenomena in pathological voices, non-invasive
noise measures such as Normalised Noise Energy
(NNE) (Kasuya et al., 1986), Glottal to Noise
Excitation (GNE) (Michaelis et al, 1997), Harmonic
to Noise Ratio (HNR) (Yumoto and Gould, 1982)
were developed and integrated in voice quality
diagnosis.
The HNR measure contains information of both
harmonic and noise components and is sensitive to
several kinds of periodicities such jitter and shimmer
(Murphy and Akande, 2006). This measure is
defined as the ratio of harmonic component energy
and noise component energy (Yumoto and Gould,
1982).
1.2 Existing HNR Extraction Methods
In this paper, three algorithms based on time,
spectral and cepstral techniques are reviewed in
order to compare the performance of the proposed
algorithm to the existing HNR algorithms. Each
algorithm is a representative example of different
approaches to the estimation of important quality
parameter of the voice signal. Several techniques
such voice models based algorithms and adaptive
techniques were found in this research.
As an example of time based method, the
Boersma’s algorithm (Boersma, 1993) is based on
the second maximum of normalized autocorrelation
function detection, which is used in the following
equation (1).
()
()
,
r1
r
log.10HNR
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
τ−
τ
=
(1)
where
(
)
τ
'
r is the second local maximum of the
normalized autocorrelation and
τ
is the computed
by a pitch detector.
Spectral methods consider that the harmonic
component information is concentrated in the
spectral peaks and the noise is concentrated in the
valleys. The method separates the spectrum of the
voice signal into two regions (harmonic regions and
noise regions). Yegnanararayana (Yegnanararayana
et al, 1998) algorithm is an example of spectral
based method. The cepstral approach considers that
the harmonic information is concentrated in the
rahrmonics peaks (mainly in the first one) and the
noise information is concentrated in low quefrencies.
Most of cepstral algorithms perform cepstral
351
J. T. de Sousa R. (2009).
A NEW ACCURATE METHOD OF HARMONIC-TO-NOISE RATIO EXTRACTION.
In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing, pages 351-356
DOI: 10.5220/0001552903510356
Copyright
c
 SciTePress

segmentation with short-pass or comb lifters
carefully dimensioned. In general, these methods
yield an estimation of the spectral baseline of the
noise, from where the HNR value can be computed.
Qi (Qi and Hillman, 1997) algorithm is an example
of this method.
2 PROPOSED METHOD
2.1 HNR Extraction Method
The proposed HNR method consists of harmonic
and noise component estimation. Initially, the signal
is segmented into frames and a sine window with the
following equation (2) is applied.
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
+
π
=
2
1
n
N
sin)n(h
, 1Nn0 −≤≤
(2)
The harmonic component is then estimated from
the Odd Discrete Fourier Transform (ODFT)
(Ferreira, 1998) of the signal by extracting the
frequency, magnitude and phase of each harmonic.
In the ODFT domain, the parameters of the
harmonic structure are easily measured and are not
much affected by noise. These parameters are used
to synthesize the harmonic structure in ODFT
domain. The harmonic component is subtracted from
the complete signal which yields the noise
component estimation, as is shown in the Figure 1.
Figure 1: Schematic diagram of harmonic and noise
component estimation.
Finally, the HNR value of each frame is
calculated from these two components using the
equation (3).
)k(R
)k(H
log.10=HNR
2/N
1=k
2
2/N
1=k
2
(3)
2.2 Extraction of Harmonic Spectral
Parameters
Each harmonic is modeled (Ferreira, 2001) by a
sinusoid according to equation (4):
⎥
⎦
⎤
⎢
⎣
⎡
ϕ+Δ+
π
= n)(
N
2
sin.A)n(x ll
(4)
where A is the sinusoid amplitude, N is the window
length,
l and Δ l are respectively the integer part and
the fractional part of the DFT bin which correspond
the sine frequency. The bin fractional part represents
the distance between the
l bin and the true value of
frequency. The algorithm computes the ODFT of the
voice signal and next the local maxima are found by
a peak picking algorithm. The maxima bins are the
initials values which correspond to the integer part
of the true frequency bin. The harmonic parameters
are computed using the equations below (Ferreira,
2001), following the order of presentation.
()
()
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎛
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
−
+
π
=Δ
G/1
O
O
1X
1X
21
3
arctan
3
l
l
l
(5)
)
N
1
1.(.
2
1
1.)(X
O
+Δπ−
⎟
⎠
⎞
⎜
⎝
⎛
π
−π+∠=ϕ ll
(6)
F
O
)1.2(
6
cos.2
3
.
N
)(X.4
A
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
−Δ
π
=
l
l
(7)
where Xo is the ODFT, G and F are calibration
parameters adjusted experimentally.
2.3 Harmonic Component Synthesis
The harmonic structure is estimated by performing a
synthesis of each sinusoid parameters extracted from
the ODFT representation of each frame of the signal
(Ferreira, 2001) considering the windowing effect.
In order to compute the sinusoid spectrum, the
frequency response of a sine window without the
frequency modulation implications (frequency shift)
was calculated as shown in the equations which
represents the spectrum phase (8) and magnitude (9)
of h(n).
BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing
352

2
)N1(
)(H
−ω−
=ω∠
(8)
cos sin
11
22
()
11
2
sin sin
22
N
N
HA
NN
ωπ
ω
ππ
ω
ω
=×+
⎛⎞ ⎛⎞
−+
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
(9)
The magnitude of the spectrum can be calculated
for each k bin, carefully replacing ω by the
following values.
()
5,0
N
2
−Δ
π
=ω l , l
=
k
(10)
()
5,0
N
2
+Δ
π
=ω l
, 1k −= l
(11)
() 5,1
N
2
−Δ
π
=ω
l , 1k +
=
l
(12)
()
k5,0
N
2
−Δ−
π
=ω l , 1k1 −≤≤ l
(13)
() k5,0
N
2
+−Δ
π
=ω
l ,
2/Nk2 ≤≤+l
(14)
where A is the sinusoid spectral amplitude, N is
the window length and Δ
l is the fractional
component of the DFT bin. The phase of the
spectrum is computed using the following equations:
ϕ=∠ )k(S
,
l=k
(15)
⎟
⎠
⎞
⎜
⎝
⎛
−+ϕ=∠
N
1
1)k(S
, 1k1 −≤
≤
l
(16)
⎟
⎠
⎞
⎜
⎝
⎛
−−ϕ=∠
N
1
1)k(S
,
2/Nk2 ≤≤
+
l
,
(17)
where S(k) is the sinusoid spectrum and φ is the
estimated phase. Finally, all sinusoid spectra are
summed up yielding the synthetic harmonic
structure.
3 ALGORITHM TESTS
The proposed method was tested in the Matlab
environment with synthesized voice sounds in order
to characterize their accuracy and behaviour when
submitted to an acoustic diversity. The algorithm
also was submitted to real voices in order to
characterize the behaviour under real conditions. For
both experiments, the algorithm was calibrated so
that they could measure with less error as possible.
An analysis window length of 2048 points has been
used.
3.1 Tests with Synthesized Voices
Test with synthesized voice sounds allow
establishing a target (theoretical value) which can be
used to compare to the measured value from the
algorithm, yielding performance parameters for the
algorithm evaluation. In this regard, a synthesized
voice signal is generated with known harmonic and
noise component and fundamental frequency. The
synthesized voice signal is received by the
algorithm which measures and returns a HNR value
for each frame. Finally, the theoretical and measured
values are compared resulting the algorithm
performance measures scores.
3.1.1 Synthesis of Voice Sounds
The synthesis module creates the test voice signals
with known features according to a source-filter
model configuration to simulate some acoustic
events which are aimed to be measured. This source-
filter model simulates a real voice in stationary
conditions. Looking at Figure 3, the harmonic
component of the glottal impulse g
h
(n) is generated
initially by creating a unitary pulse train i(n) signal
with a specific fundamental frequency.
Next, this signal is applied to a filter, whose
impulse response is an LF model (Fant et al, 1985)
glottal impulse waveform. Basically, the noise
component of the glottal impulse consists of white
gaussian noise g
r
(n) with certain energy (Levison,
2005). These two signals are summed up, yielding as
a result the complete glottal impulse signal g(n). The
glottal impulse components are applied to the filter
of the vocal tract and lip radiation so that the speech
signal s(n) and its harmonic s
h
(n) and noise s
r
(n)
component can be produced. The theoretical HNR
value was adjusted through the energy of the noise
component and the fundamental frequency (F0)
trough the pulse generator. The vocal tract filter
consisted of an all-pole IIR filter which yields
formants at 664, 1027 and 2617 Hz simulating the
/a/ phoneme. The lip radiation was modelled by a
first order difference operator R(z)=1-0.99z
-1
. Voice
specialists use /a/ phoneme as stimulus in order to
A NEW ACCURATE METHOD OF HARMONIC-TO-NOISE RATIO EXTRACTION
353

perform their perceptive assessment due to the fact
that the associated vocal tract presents a
configuration with less constrictions and
obstructions. Synthesized voice sounds that simulate
a female voice (F0=200 Hz) and male voice
(F0=100 Hz) with several degree of hoarseness (5
dB, 10 dB, 15 dB, 20 dB, 25 dB) were used. These
voice sounds were synthesized at sampling rate of
16 kHz.
Figure 3: Production of the synthesized signals.
3.1.2 Comparison of Measured and
Theoretical HNR Values
Both measured and theoretical HNR values are
compared by the analysis module in order to
compute the performance scores. Figure 4 shows an
example of theoretical and estimated HNR values
comparison, for each frame. The more these curves
are close the more the algorithms are effective.
Basically, the performance measures quantify the
difference between these sequences of HNR values.
In the experiments, the average of error (18) was
considered as a suitable performance measure for the
overall evaluation of the algorithms. This measure
compares the mean value of theoretical HNR values
and the mean value of the measured HNR values.
0 50 100 150
6
7
8
9
10
11
12
13
Frame Index
HNR(dB)
Figure 4: Theoretical (slashed line) and estimated (solid
line) HNR.
[]
∑
=
−=
f
N
1i
measuredltheoretica
f
)i(HNR)i(HNR
N
1
E
(18)
where N
f
is the number of frames, i is the frame
index, and HNR
theoretical
are HNR
measured
the
theoretical and measured HNR value, expressed in
dBs.
3.2 Tests with Real Voices
From a pathological voice sounds data base, six
voice sounds of three male and three female were
firstly selected among 17 voice patients (7 male, 10
female). These sounds were collected from speech
therapy sessions regarding patients who have a
certain level of hoarseness. For each gender, three
levels of perceived hoarseness voice were defined
(lowest, middle and highest levels of noise). This
selection was made considering three voice sounds
with very distinct perceptive amount of noise. Six
non-voice specialists have evaluated the selected
voices with the same loudness, and have agreed in
regard to noise level order. With very distinct noise
levels it is possible to guarantee that most people
would establish the same noise level order. These
voice sounds were recorded at sampling rate of
44100 Hz, with 16bit/sample accuracy and pre-
processed so that the loudness could be the same.
4 RESULTS
4.1 Tests with Synthesized Voices
Results
In this section, the results of HNR extraction
algorithms with synthesized voices are presented on
two tables showing the average error of the main
existing methods (time, spectral and cepstral
approaches) and the proposed method. The results of
the algorithms performance were evaluated
according to the error average level, the variation of
average error in function of F0 and theoretical HNR
value, and the general trend to underestimate or
overestimate the HNR value. Mean of absolute value
(MA), mean value (M) and standard deviation (SD)
of the errors average were calculated to support this
evaluation.
Analysing the Table 1 to 4 according to the
absolute MA of the average error, it can be
concluded that the proposed method presents low
error level for sounds with F0=200 Hz (MA=0,21).
However, the time based method presents low error
level for sounds with F0=100 Hz (MA=0,11). In
fact, the time based method shows major errors for
high values of F0 due to detection faults of the
second maximum of the normalized autocorrelation.
The proposed algorithm is more effective to provide
HNR estimative for higher values of F0, detecting
the harmonic structure.
BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing
354

Table 1: Comparison of average error (dB) for the
different HNR methods and F0=100 Hz.
Theoretical
HNR (dB)
Time
based
Spectral
based
Cepstral
based
Proposed
method
5 0,19 -0,61 -1,15 0,37
10 0,12 -0,79 -0,63 -0,27
15 0,09 -0,67 -0,20 -0,40
20 0,07 -0,05 0,27 -0,27
25 0,06 0,50 0,82 0,27
Table 2: Mean of absolute value (MA), average (M) and
standard deviation (SD) of the average of errors for
F0=100Hz.
Time
based
Spectral
based
Cepstral
based
Proposed
method
MA 0,11 0,52 0,61 0,31
M 0,11 -0,32 -0,18 -0,06
SD 0,05 0,54 0,77 0,35
Table 3: Comparison of average error (dB) for the
different HNR methods and F0= 200 Hz.
Theoretical
HNR (dB)
Time
based
Spectral
based
Cepstral
based
Proposed
method
5 0,80 -0,9 -2,45 0,12
10 0,65 -0,31 -1,87 -0,16
15 0,61 -0,34 -1,48 0,17
20 0,59 0,16 -1,12 -0,22
25 0,59 0,71 -0,71 0,40
Table 4: Mean of absolute value (MA), average (M) and
standard deviation (SD) of the average of errors for
F0=200Hz.
Time
based
Spectral
based
Cepstral
based
Proposed
method
MA 0,65 0,49 1,53 0,21
M 0,65 0,60 -1,53 0,08
SD 0,09 0,49 0,67 0,25
Examining the average error variation in function
of F0, the spectral method presents little difference
between MA for 100 Hz and 200 Hz of F0. This
means that the spectral has the same efficiency to
detect the harmonics in female and male voices.
However it yields higher error than the proposed
method.
The analysis of variation of average error
according to theoretical HNR value reveals better
results for time-based method using both 100 Hz and
200Hz of F0. The autocorrelation is less vulnerable
to the noise. The proposed algorithm yields some
faults in the high frequency harmonics, which are
particularly abundant in male voices. Although the
proposed algorithm presents the second lower
variation (SD=0,35 for F0=100Hz and SD=0,24 for
F0=200Hz ) under our test conditions.
The M of the proposed algorithm for both F0,
lead to the conclusion that this algorithm has a low
tendency to underestimate or overestimate. The
other algorithms present a higher deviation in regard
to the exact value, which in certain cases, are
considerable, such the cepstral for 200 Hz of F0
(M=-1,53). This fact is caused by the non-fitting of
the estimated noise base line. Regarding the
proposed algorithm, an eventual deviation can be
originated by the non-detection or a fake detection
of some harmonics.
4.2 Tests with Real Voices Results
The measured HNR values are presented on two
tables where they can be compared. The proximity
of the HNR values returned by the tested algorithms
for each voice sound was verified.
Table 5: Comparison of the HNR methods measures (dB)
of female voice sounds.
Method
Real voice sounds
Voice
sound 1
Voice
Sound 2
Voice
Sound 3
Time based 10,06 12,54 17,62
Spectral based 11,15 12,11 14,72
Cepstral based 10,48 13,71 18,40
Proposed method 9,53 12,16 14,39
Looking at the Tables 5 and 6, the values of
measured HNR are very similar except in the cases
of higher HNR in the female voices. The differences
between HNR values which were produced by each
algorithms for the same voice are expected
considering the error that were estimated in the tests
with synthesized voices.
Table 6: Comparison of the HNR methods measures (dB)
of male voice sounds.
Method
Real voice sounds
Voice
Sound 1
Voice
Sound 2
Voice
Sound 3
Time based 9,19 10,66 18,32
Spectral based 9,72 11,03 17,82
Cepstral based 9,52 10,76 19,75
Proposed method 9,61 10,43 18,88
The proposed algorithm yielded results that
present the same order as the perceptual order
(lowest, middle, highest) for female and male
voices.
A NEW ACCURATE METHOD OF HARMONIC-TO-NOISE RATIO EXTRACTION
355

5 CONCLUSIONS
From the test with synthesized voices, it can be
concluded that the proposed algorithm presents a fair
level of accuracy, in particular for female voices
which is very important feature in a diagnosis scene.
The algorithm doesn’t have significant tendency to
underestimated or overestimate. This feature means
that there is no need to calibrate or compensate the
estimated HNR value. In some cases, calibration
may not be effective due to the acoustic diversity of
human voices. In spite of presenting the second best
values regarding the variation of the errors according
to F0 and theoretical HNR variation, it can be
concluded that the measurement performed by the
proposed algorithm is not substantially affected by
the F0 and the noise level. This means that the
proposed algorithm measures the female and male
voices and several hoarseness levels with
approximately the same accuracy.
From the tests with real voices, the proposed
algorithm showed coherent HNR values,
approximately similar to the HNR values of other
algorithms. The harmonic plus noise model assumes
good approximation of the harmonic and noise
components which are present in pathological
voices. Moreover, the results show that there is a
correspondence between the artifacts that were
associated to harmonic component and to noise
component in each signal representation.
ACKNOWLEDGEMENTS
This work was developed in a doctoral program
supported by the Portuguese Foundation for Science
and Technology under the reference
SFRH/BD/24811/2005.
REFERENCES
Levison, S. E., 2005. Mathematical Models for Speech
Technology, John Wiley & Sons Ltd, The Atrium,
Southern Gate, Chichester,West Sussex PO19 8SQ,
England.
Yumoto, E., and Gould, W., 1982. Harmonics-to-noise
ratio as an index of the degree of hoarseness, The
Journal Acoustic Society of America. 71(6):1544-
1550.
Ferreira ,Aníbal J. S., 1998.An Odd-DFT based approach
to time-scale expansion of audio signals. IEEE
Transactions on Speech and Audio Processing,
7(4):441–453.
Ferreira ,Aníbal J. S., 2001.Accurate estimation in the
ODFT domain of the frequency, phase and magnitude
of stationary sinusoids. In IEEE Workshop on
Applications of Signal Processing to Audio and
Acoustics, pages 47–50. IEEE.
Yegnanarayana, B., d’Alessandro, C., Darsinos, V. 1998.
An iterative algorithm for decomposition of speech
signals into periodic and aperiodic components.
Speech and Audio Processing, IEEE Transactions
6(1): 1-11.
Qi, Y., and Hillman, R. E., 1997. Temporal and spectral
estimations of harmonics-to-noise ratio in human
voice signals. The Journal of the Acoustical Society of
America 102(1): 537-543.
Boersma, P., 1993.Accurate short-term analysis of the
fundamental frequency and the harmonics-to-noise
ratio of a sampled sound. In Proceedings of the
Institute of Phonetic Sciences 17, 97-110.
Murphy, P. J. and. Akande, O., 2006. Noise estimation in
voice signals using short-term cepstral analysis, The
Journal of the Acoustical Society of America. 121
(3):1679-1690.
Michaelis ,D., Gramss, T., Strube H.W., 1997. Glottal-to-
Noise Excitation Ratio a New Measure for Describing
Pathological Voices. Acustica-Acta Acustica 83,700-
706
Fant, G., Liljencrants, J. and Lin, Q., 1985. A four
parameter model of glottal flow. STL/QPSR 4/1985,
French Swidish Symposium 1,1-13
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