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Online-SeminarPsychoakustik 2 – Transiente Vorgänge,tonale Komponenten und Modulation
Andreas Langmann
Unrestricted @ Siemens AG 2018
Modulations MetrikenHilbert Envelope & Modulation TheoryFluctuation Strength and Roughness
Tonale MetrikenTonalityTone to NoiseProminence Ratio
Transiente MetrikenTime varying Loudness N10KurtosisWavelets
Transiente MetrikenTime varying Loudness N10KurtosisWavelets
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• Event less than 1 second in duration, usually in milliseconds• Impulsive, changing amplitude rapidly• Traditional FFT techniques are not always effective in analyzing• Types of signals: keyboard clicks, injector ticks, piston slap, door slam, other human actuated sounds
Clicks, Clunks and Pings! What is a Transient?
Loudness N10
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N10 Loudness
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N10 Loudness
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N10 Loudness
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N10 Loudness
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N10 Loudness
Kurtosis
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C L
A S
S E
S
Kurtosis - Histogram
4
32
1
time
ampl
itude
155
2
1 2 3 4
# sa
mpl
es
C L A S S E S
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C L
A S
SE S
Histogram: Square Wave
4
32
1
time
ampl
itude
800
8
1 2 3 4
# sa
mpl
es
C L A S S E S
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C L
A S
S E
S
Histogram: Impact
4
32
1
time
ampl
itude
0100
1
1 2 3 4
# sa
mpl
es
C L A S S E S
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C L
A S
S E
S
Histogram: Gaussian Random
4
32
1
time
ampl
itude
4119
5
1 2 3 4
# sa
mpl
es
C L A S S E S
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Distribution
1 2 3 4
# sa
mpl
es
Square Wave
1 2 3 4
Gaussian Random
1 2 3 4
Impact
Kurtosis (k) is a unitless parameterthat measures the relative sharpnessor flatness of a distribution for a signalrelative to a normal or Gaussian one.
Unrestricted © Siemens AG 2018Page 18 Siemens PLM Software
Kurtosis
=0<0 >0
1 2 3 4
# sa
mpl
es
Square Wave
1 2 3 4
Gaussian Random
1 2 3 4
Impact
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Kurtosis
• Equal 0 -> Normal Distribution, "mesokurtic.“; example signal: Guassian Random
• Negative (“<0”) – Wide Distribution, "platykurtic“; example signal: Square/Sine Wave
• Positive (“>0”) – Narrow Distribution, "leptokurtic“; example signal: Impact
Time-Frequency Analysis: Wavelets
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13.5 Hz, 5 Volts
5 seconds
Time-Frequency Analysis: Wavelets
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0
10
20
1 32 54
In a perfect world, this is our frequency spectrum vs. time
13.5 Hz
time
Freq
Time-Frequency Analysis: Wavelets
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time
Perform FFT
T=0.5 sec
T=1/(Df)
Df = 2 Hz
Freq
0
10
20
1 32 4
Leakage in frequency domain due to Df, amplitude reduced
5
Time-Frequency Analysis: Wavelets
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Perform FFT
Df = 0.5 Hz
T=1/(Df)
T= 2 sec0
10
20
1 32 4
Leakage in time domain due to T, incorrect signal
determination
5 time
Freq
Time-Frequency Analysis: Wavelets
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Traditional FFT methods do not work well on transient events:
Good Time Resolution Bad Frequency
Good Frequency Resolution Bad Time
Solution: Wavelets Alternative Time-Frequency Methods
Not FFT based (per se)
Generate large amount of information over small time duration (I.e., analyze only milliseconds worth of data)
Time-Frequency Analysis: Wavelets
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Traditional FFT WaveletTime
Freq.
2 Hz
8 Hz
Time
Freq.
8 Hz
2 Hz
Time-Frequency Analysis: Wavelets
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FFT Wavelet
Tonale MetrikenTonalityTone to NoiseProminence Ratio
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Tonal Examples
Tonal noise issues characterized by:
Distinct audible peaks at discrete frequencies Opposite of broadband
Turbocharger Mosquito
Hz
dB
Gear WhineVuvuzela
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TONAL METRICS
Tonality Tone-to-Noise Prominence Ratio
DIN 45681 provides an iterative method to detect tones by
comparing the levels of each spectral line
1 Tonality Unit (t. u.) has the tonality of a 1 kHz sine tone
@ 60dB
ECMA-74 and ISO 7779 describe the calculation
Levels of the prominent discrete tones are
compared to the noise level in the same critical
band
ECMA-74 and ISO 7779 describe the calculation
Average SPL of the critical band centered around the tone is
higher than surrounding critical bands
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TONALITY
Tonality
DIN 45681 provides an iterative method to detect tones by
comparing the levels of each spectral line
1 Tonality Unit (t. u.) has the tonality of a 1 kHz sine tone
@ 60dB
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Tonality Calculation
Pure tones produce a tonality value of 1.0
Pure random noise produces a tonality value of 0.0
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TONE-TO-NOISE
Tone-to-Noise
ECMA-74 and ISO 7779 describe the calculation
Levels of the prominent discrete tones are
compared to the noise level in the same critical
band
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Critical Bands
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PROMINENCE RATIO
Prominence Ratio
ECMA-74 and ISO 7779 describe the calculation
Average SPL of the critical band centered around the tone is
higher than surrounding critical bands
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Tonal Metrics
15000.001500.00 Hz
100.00
10.00
dB(A
)Pa
5390.63 10374.22 11114.91
93.82
37.49
49.39
Spectrum brand_A (A)
5390.63 PR Prominent Prominence Ratio 10374.22 11114.91 RMS93.82 Yes 13.69 dB@ 5390.63 Hz 37.49 49.39 70.66 dB(A)
Curve
15000.001500.00 Hz
100.00
10.00
dB(A
)Pa
8390.63Spectrum brand_A (A)
8390.63 PR Prominent Prominence Ratio69.89 No 1.19 dB@ 8390.63 Hz
Curve
Modulations MetrikenHilbert Envelope & Modulation TheoryFluctuation Strength and Roughness
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MODULATION METRICS
Sounds which vary in amplitude “slowly” over time• Electric Motor “warble”• Exhaust/Intake “Growl”• Aircraft Turbo Props• Cooling fan and engine
running at same speed
Phase shift between signals causes modulation in amplitude – these can be often perceived as
annoying
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Modulation Theory
What does the sum of a 400 Hz sine wave and 405 Hz sine wave look like?
What do you hear?
400 Hz
405 Hz
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400 Hz
405 Hz
400+405 Hz
Modulation Theory
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5 Modulations per Second
400 Hz
405 Hz
400+405 Hz
Modulation Theory
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No 5 Hz in FFT!
Only 400 and 405 Hz.
Modulation Theory
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0.61 0.65s
-0.10
0.12
Rea
lV
4:HighPass500:None5:Envelope_of_HighPass:None
• Envelope done by Hilbert Transform
• Hilbert Transform separates slowly varying envelope from rapidly varying signal
Modulation Theory
Fluctuation Strengthand Roughness
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Roughness and Fluctuation Strength
Let’s take two sweeping sine tones over 10 secs: 10 Hz to 100 Hz 11 Hz to 110 Hz
1 Hz!
0 seconds 10
110
Hz
0
What is initial modulation
frequency?
What is the end modulation
frequency at 10s?
10 Hz!
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Engine Harmonics
20 Hz
600 6000
600
Hz
0
200 Hz
40 Hz
60 Hz
400 Hz
600 Hz
2nd order
4th order
6th order
RPM10 Hz
30 Hz
50 Hz100 Hz
300 Hz
500 Hz 5th order
3th order
1st order
15 Hz
150 Hz
!
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ROUGHNESS and FLUCTUATION STRENGTH
Fluctuation Strength focuses
on slower modulations,
between 0 and 20 Hz, max at 4Hz
Roughnessfocuses on faster
modulations, between 20 and
300 Hz, max at 70 Hz
1 vacil is
fluctuation strength
produced by a 1000 Hz tone of 60 dB which is 100%
amplitude modulated at 4Hz
1 asper is roughness
produced by a 1000 Hz tone of 60 dB which is 100%
amplitude modulated at 70 Hz
Andreas LangmannPreSales Solution Consultant
Siemens PLMSimulation & Testing Solutions
Thank you