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.

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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

Langmann.Andreas@siemens.com

Thank you