Basic Frequency Analysis BA766911

8/11/2019 Basic Frequency Analysis BA766911

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As can be seen, the range of perception of sound for humans - at amaximum for young people - goes from 20 to 20000 Hz.

With age, the human perception of the highest frequencies decreasesgradually. When exposed to excessive noise levels, hearing can bedamaged, causing reduced sensitivity for hearing low sound levels. Thedamage can also be restricted to distinct frequency ranges.

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1 10 100 1000 10 000 [Hz]

Frequency

Audible Range


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Wavelength,[m]

Speed of sound, c = 344 m/s

Wavelength

A sound signal from a loudspeaker mounted at one end of a tube willproduce a sound wave that propagates forward at a speed of 344 m/s.

If the signal is a single sine signal the sound wave will consist of a number ofpressure maxima and minima all separated by one wavelength.


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b

Diffraction of Sound

Example:

b = 1 m

= 0.344 m ( f = 1 kHz)

Example :

b = 0.1 m

= 0.344 m ( f = 1 kHz)

b

b

>>

Objects placed in a sound field may cause diffraction.

But the size of the obstruction should be compared to the wavelength of thesound field to estimate the amount of diffraction.

If the obstruction is smaller than the wavelength, the obstruction is negible.

If the obstruction is larger than the wavelength, the effect is noticeable as ashadowing effect.


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Example:

b = 0.5 m

= 0.344 m ( f = 1 kHz)

b b

Example :

b = 0.1 m

= 0.344 m ( f = 1 kHz)

b

Diffusion of Sound

Diffusion occurs when sound passes through holes in e.g. a wall.

If the holes are small compared to the wavelength of the sound, the soundpassing will re-radiate in an omnidirectional pattern similar to the originalsound source.

When the hole has larger dimensions than the wavelength of the sound, thesound will pass through with negligible disturbance.


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When sound hits obstructions large in size compared to its wavelength,reflections take place.

If the obstruction has very little absorption, all the reflected sound will haveequal energy compared to the incoming sound. This is one of the importantdesign principles used when constructing reverberant rooms.

If almost all reflected energy is lost due to high absorption in the reflectingsurfaces, the situation is close to what is found in an anechoic room.

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Imaginary Source

Source

SourceSource

Reflection of Sound


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Basic Frequency Analysis of Sound

Contents:l Frequency and Wavelength

l Frequency Analysis

l Perception of Sound


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p Lp

time

Frequency

time

time

p

p

Lp

FrequencyLp

Frequency

Waveforms and Frequencies

Three examples of the relationship between the waveform of a signal in thetime domain compared to its spectrum in the frequency domain.

In the top figure a sine wave of large amplitude and wavelength is showingup as a single frequency with a high level at a low frequency.

In the middle figure a low amplitude signal with small wavelength is seen toshow up in the frequency domain as a high frequency with a low level.

At the bottom figure it is shown how a sum of the two signals above also inthe frequency domain shows up as a sum.


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p Lp

time

Frequency

time

time

p

p

Lp

FrequencyLp

Frequency

Typical Sound and Noise Signals

Most natural sound signals are complex in shape. The primary result of afrequency analysis is to show that the signal is composed of a number ofdiscrete frequencies at individual levels present simultaneously.

The number of discrete frequencies displayed is a function of the accuracy ofthe frequency analysis which normally can be defined by the user.


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To analyze a sound signal, frequency filters or a bank of filters are used. Ifthe bandwidths of these filters are small a highly accuracy analysis isachieved.

The signal flow chart shown illustrates the elements in a simple sound levelmeter.

On top is a microphone for signal pick up. Then a gain amplification stagefollowed by a single frequency filter - here shown as an ideal filter. In thefollowing we will look at real filters. After filtering follows a rectifier with thestandardised time constants Fast, Slow and Impulse and the signal level isfinally converted to dB and shown on the display.

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Fast

SlowImpulse

87.2

RMSPeakTime

p

Frequency

Lp

Frequency

Lp

Time

p

Filters


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B

0

0

- 3 dB

Frequency Frequency

Frequency

Ideal filter

Practical filter and

definition of3 dB Bandwidth

Ripple

f1 f0 f2

f1 f0 f2

=

Bandwidth = f2 f1

Centre Frequency = f0

f1 f0 f2

Practical filter and

definition ofNoise Bandwidth

Area Area

Bandpass Filters and Bandwidth

Ideal filters are only a mathematical abstraction. In real life, filters do nothave a flat top and and vertical sides. The departure from the idealised flattop is described as an amount of ripple. The bandwidth of the filter is

described as the difference between the frequencies where the level hasdropped 3 dB in level corresponding to 0.707 in absolute measures.

It is useful to define a Noise Bandwidth for a filter. This corresponds to anideal filter of the same level as the real filter, but with its bandwidth (NoiseBandwidth) set to leave the two filters with the same area.


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The two most used filter banks are:

Filters that have the same bandwidth e.g. 400 Hz and displayed using alinear frequency scale. This is what normally is a result of a (FFT) FastFourier Transform analysis. Constant bandwidth filters are mainly used inconnection with analysis of vibration signals.

Filters which all have the same constantpercentagebandwidth (CPB filters)e.g.1/1 octave, are normally displayed on a logarithmic frequency scale.Sometimes these filters are also called relative bandwidth filters. Analysiswith CPB filters (and logarithmic scales) is almost always used in connectionwith acoustic measurements, because it gives a fairly close approximation tohow the human ear responds.

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0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10k

B = 400 Hz

Linear Frequency Axis

(primarily used in vibration analysis)

2 4 8 16 31.5 63 125 250 500 1k 2k 4k 16k8k

Frequency

[Hz]

Logarithmic Frequency Axis(primarily used in acoustic analysis)

B = 400 Hz B = 400 Hz

B = 1/1 Octave B = 1/1 Octave B = 1/1 Octave

Frequency

[Hz]

L

L

1

Filter Types and Frequency Scales


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One advantage of constant percentage bandwidth filters are that e.g. twoneighbouring filters combine to one filter with flat top, but with double thewidth.

Three 1/3 octave filters combine to equal one 1/1 octave filter.

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500 1000 2000

800 1000 1250

L

L

Frequency

[Hz]

Frequency

[Hz]

B = 1/1 Octave

B = 1/3 Octave

3 1/3 Oct. = 1/1 Oct.


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Band No. Nominal CentreFrequency Hz

Third-octavePassband Hz

OctavePassband Hz

123456

1.251.62

2.53.15

4

1.12 1.411.41 1.781.78 2.242.24 2.822.82 3.553.55 4.47

1.41 2.82

2.82 5.62

272829303132

500630800

100012501600

447 562562 708708 891

891 11201120 14101410 1780

355 708

780 1410

40414243

10 K1.25 K16 K20 K

8910 1120011.2 14.1

14.1 17.8 K17.8 22.4 K

11.2 22.4 K

Third-octave and Octave Passband

List of Band No., Nominal Centre Frequency, Third-octave Passband andOctave Passband.


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A detailed signal with many frequency components show up with a filtershape as the dotted curve when subjected to an octave analysis. The solidcurve shows the increased resolution with more details when a 1/3 octave

analysis is used.

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L

Frequency

[Hz]

1/1 Octave

1/3 Octave

The Spectrogram


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Only the sounds in the frequency range from 20 to 20000 Hz can beperceived by the human ear and auditory system.

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Infra Audio Ultra

0.02 0.2 2 20 200 2000 20.000 200K Hz

Frequency

Sound Frequencies


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This display of the auditory field illustrates the limits of the human auditorysystem.

The solid line denotes, as a lower limit, the threshold in quiet for a pure toneto be just audible.

The upper dashed line represents the threshold of pain. However if the Limitof Damage Risk is exceeded for a longer time, permanent hearing loss mayoccur. This could lead to an increase in the threshold of hearing as illustratedby the dashed curve in the lower right-hand corner.

Normal speech and music have levels in the shaded areas, while higherlevels require electronic amplification.

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140

dB120

100

80

60

40

20

0

20 50 100 200 500 1k 2k 5k 10k 20 kFrequency [Hz]

Sound

Pressure

Level

Thresholdin Quiet

Limit of Damage Risk

Threshold of Pain

Speech

Music

Auditory Field


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Here are shown the normal equal loudness contours for pure tones. Thedashed curve indicates the normal binaural minimum audible field.

Note the very non-linear characteristics of the human perception. Almost 80dB more SPL is needed at 20 Hz to give the same perceived loudness as at3-4 kHz.

This observation together with frequency masking - limitations in the earscapability to discriminate closely spaced frequencies at low sound levels inthe presence of higher sounds - is the foundation for the calculation of theloudness of stationary signals.

Loudness of non-stationary signals also needs to take the temporal maskingof the human perception into account.

A correct calculation of these loudness values is crucial for all the followingmetrics calculations such as Sharpness, Fluctuation Strength andRoughness.

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Sound

pressure

level, Lp(dB re 20 Pa)

120

100

80

60

40

20

Phon0

10

20

30

40

50

60

70

80

90

100

110

120

130

20 Hz 100 Hz 1 kHz 10 kHzFrequency

970379

Equal Loudness Contours for Pure Tones


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Top figure is the equal loudness contour for 40 dB at 1 kHz.

The popular A-weighting at the bottom is shown in comparison to theinverted 40 dB equal loudness contour.

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40

20

0

20 Hz 100 1 kHz 10 kHz

40

0

-20

-40

20 Hz 100 1 kHz 10 kHz

40

Lp(dB)

Lp

(dB)

A-weighting

l 40 dB EqualLoudnessContournormalized to 0dB at 1kHz

l 40 dB EqualLoudnessContour inverted

and comparedwith

A-weighting

40 dB Equal Loudness Contours and A-Weight


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The A-weighting, B-weighting and C-weighting curves follow approximatelythe 40, 70 and 100 dB equal loudness curves respectively.

D-weighting follows a special curve which gives extra emphasis to thefrequencies in the range 1 kHz to 10 kHz. This is normally used for aircraftnoise measurements.

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0

-20

-40

10 100 1 k 10 k

Lp

[dB]

A

B

CD

AB + C

D

Lin.

Frequency

[Hz]

-60

20 k2 k 5 k200 50020 50

Frequency Weighting Curves


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0

-20

-40

10 100 1 k 10 k

Lp

[dB]

A-weighting

Frequency

[Hz]

-60

20 k2 k 5 k200 50020 50

L= 8.6dB

Calibration and Weighting!

Please be careful when calibrating a system with a weighting filter switchedin.

Using a pistonphone which has a calibration frequency of 250 Hz you get 8.6dB less signal reading than using a sound level calibrator with a testfrequency of 1000 Hz if an A weighting filter is switched in.


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All sound level meters have built in A-weighting, and some have also otherslike B and C-weighting.

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Fast

SlowImpulse

87.2

RMSPeak

Weighting

Use of Frequency Weighting


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For more detailed frequency analysis sound level meters can have a serialfilter bank of 1/1 octave and maybe also 1/3 octave bandwidths. As only onefilter is active at a time the analysis time is long and requires the sound field

to be stationary. The advantage is a lower price.

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Fast

SlowImpulse

RMSPeak

87.2

321 n

Serial Analysis


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A sound level meter with a parallel filter bank is the most expensive, but thefastest in operation and does not require the signal to be stationary.

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Fast

SlowImpulse

RMSPeak

87.2

321 n

Parallel Analysis


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The most advanced sound level meters act more like an ordinary soundanalyzer having both a parallel filter bank and a selection of weighting filters.

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Fast

SlowImpulse

87.2

RMSPeak

Weighting1/1, 1/3 oct

125 250 500 1k 2k 4k 8k LA20

40

60

80

100

dB 1/3 Octave Analysis

The Sound Level Analyzer


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The advanced sound level meters often feature comprehensive displaysshowing all the analysis results from both the parallel analysis filters and theweighting curves simultaneously.

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L[dB]

Frequency

[Hz]

1/1 Octave

1/3 Octave

LA[dB(A)]LB[dB(B)]

LC[dB(C)]

LD[dB(D)]

LLin.[dB]

The Spectrogram and Overall levels


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Conclusion

Headlines of Basic Frequency Analysis of Sound

l Basic introduction to audible frequency range andwavelength of sound

l Diffraction, reflection and diffusion of sound

l Frequency analysis using FFT and Digital filters

l Fundamental concepts for 1/1 and 1/3 octave filters

l Human perception of sound and background for A,B,C

and D-weightingl Signal flow and analysis in Sound Level Meters


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Literature for Further Reading

l Acoustic Noise Measurements

Brel & Kjr (BT 0010-12)

l Noise Control - Principles and Practice

Brel & Kjr (188-81)

Basic Frequency Analysis BA766911

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