Basic Frequency Analysis of Sound

Contents:Frequency and WavelengthFrequency AnalysisPerception of Sound

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Perception of Sound

Frequency Range of Different Sound Sources

[Hz]1 10 100 1000 10 000Frequency

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[ ]

Audible Range

1 10 100 1000 10 000 [Hz]Frequency

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1 10 100 1000 10 000 [ ]

Wavelength

Wavelength, [m]

Speed of sound, c = 344 m/s

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Wavelength and Frequency

=cff

W l th [ ]20 10 5 2 1 0.2 0.1 0.05

Wavelength, [m]

10 20 50 100 200 500 1 k 2 k 5 k 10 k

Frequency, f [Hz]

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q y, [ ]

Diffraction of Soundb >

bb

E lExample:b = 1 m = 0.344 m ( f = 1 kHz)

Example :b = 0.1 m = 0.344 m ( f = 1 kHz)

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( )

Diffusion of Soundb >

b b

Example:b = 0.5 m = 0 344 m ( f = 1 kHz)

Example :b = 0.1 m = 0 344 m ( f = 1 kHz)

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0.344 m ( f 1 kHz) 0.344 m ( f 1 kHz)

Reflection of Sound

Source

SourceSource

Imaginary Source

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Imaginary Source

Basic Frequency Analysis of Sound

Contents:Frequency and WavelengthFrequency AnalysisPerception of Sound

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Perception of Sound

Why Make a Frequency Analysis

CB C

AmplitudeD E

Amplitude

A Time

AB C

D E

DE Sound

Time

Frequency

D

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Waveforms and Frequencies

p Lp

time

Frequencyp L

time

p Lp

pFrequencyLp

time

Frequency

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Typical Sound and Noise Signals

p Lp

time

Frequencyp L

time

p Lp

pFrequencyLp

time

Frequency

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Filters

Lpp

Frequency

Time

RMSPeak

pFrequency

Lp

FastSlow

Impulse

PeakTime

FrequencyImpulse

87.2

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Bandpass Filters and BandwidthB

0

Bandwidth = f fIdeal filter Bandwidth = f2 f1Centre Frequency = f0

Frequency

Ripple

f1 f0 f2=Area Area

0

- 3 dBPractical filter anddefinition of

Ripple

Practical filter anddefinition of

Frequency Frequency

definition of 3 dB Bandwidth

definition of Noise Bandwidth

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Frequency Frequencyf1 f0 f2 f1 f0 f2

Filter Types

Constant Bandwidth Constant Percentage Bandwidth (CPB)or Relative Bandwidth

y fB = x Hz B = y% =

y f0100

0 40 8020 60 20010050 70 150LinearFrequency

LogarithmicFrequency

B = 31,6 HzB = 10 Hz

B = 3,16 Hz

B = 1 octaveB = 1/3 octave

B = 3%

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, B 3%

Filter Types and Frequency Scales

B = 400 Hz B = 400 Hz B = 400 HzL

0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10kFrequency[Hz]0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10k

Linear Frequency Axis[Hz]

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

2 4 8 16 31.5 63 125 250 500 1k 2k 4k 16k8kFrequency[Hz]

Logarithmic Frequency Axis1

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Logarithmic Frequency Axis

Piano keys are arranged logarithmically!!Piano keys are arranged logarithmically!!

1/1 and 1/3 Octave Filters

B = 1/1 OctaveL

1/1 Octave

f f2 12=

B f= 0 7 70%0.f = 708 f = 1410

Frequency[H ]f1 = 708

f0 = 1000f2 = 1410 [Hz]

L

f f f2 3 1 12 125= = .

B = 1/3 OctaveL

1/3 Octave

Frequency[Hz]f1 = 891

f0 = 1000f2 = 1120

B f= 0 23 23%0.

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0

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

L B = 1/1 Octave

500 1000 2000Frequency[Hz]500 1000 2000

L

[Hz]

B = 1/3 OctaveL B = 1/3 Octave

800 1000 1250Frequency[Hz]

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Third-octave and Octave PassbandBand No. Nominal Centre

Frequency HzThird-octavePassband Hz

OctavePassband Hz

123

1.251.62

1.12 1.411.41 1.781 78 2 24 1 41 2 823

456

22.53.15

4

1.78 2.242.24 2.822.82 3.553.55 4.47

1.41 2.82

2.82 5.62

27282930

5006308001000

447 562562 708708 891891 1120

355 708

780 14103132

12501600

1120 14101410 1780

40 10 K 8910 11200414243

1.25 K16 K20 K

11.2 14.114.1 17.8 K17.8 22.4 K

11.2 22.4 K

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Linear vs Logarithmic Frequency Scales120 Hz 50 Hz

AcousticLevel

200 400 600 800 1K 1,2K 1,4K 1,6K 1,8K 2K HzLinearFrequency0

A tiAcousticLevel

20 50 100 200 500 1K 2K 5K 10K 20KLogarithmicFrequency

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20 50 100 200 500 1K 2K 5K 10K 20K Frequency

Selecting Bandwidth

AcousticLevel

Filterwidth

Frequency Spectrum

e e

AcousticFrequencyFrequency

Level

FrequencyFrequency

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FrequencyFrequency

The Spectrogram

/ OL

1/1 Octave

1/3 O t1/3 Octave

Frequency[Hz]

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Frequency Analysis Techniques

Analog Filter Sets Typically used in less costly CPB Serial Analysis

Digital Filter Analysis FFT most common, yields constant bandwidth analysis may or may

not be real time(*)Di it l Filt A l i CPB l i l l l ti (*) Digital Filter Analysis CPB analysis, nearly always real time(*)

FFT converted to CPB be aware of standards requirements before using

Both Simultaneously as in PULSE system Both Simultaneously as in PULSE systemOthers

* Real Time Analysis all frequencies analyzed all the time without any data loss

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Most important in Frequency Analysis

B = bandwidthT = time

BT 1

(often called the Uncertainty Principle)

Note: applies to both analog and digital filtering

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Note: applies to both analog and digital filtering

Basic Frequency Analysis of Sound

Contents:Frequency and WavelengthFrequency AnalysisPerception of Sound

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Perception of Sound

Sound Frequencies

Infra Audio Ultra

0.02 0.2 2 20 200 2000 20.000 200K HzFrequency

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Auditory Field

140dB

120Threshold of Pain

120

100

80vel

Limit of Damage Risk

80

60

Pre

ssur

e Le

v

Speech

Music

40

20Soun

d P

Threshold

0

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

in Quiet

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Frequency [Hz]

Equal Loudness Contours for Pure Tones

120 120130

Soundpressure

100

80 8090

100110

level, Lp(dB re 20 Pa)

80

6050

607080

40

20 20

304050

Phon010

20 Hz 100 Hz 1 kHz 10 kHz

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20 Hz 100 Hz 1 kHz 10 kHzFrequency

970379

Perception of Noise

Change in Sound Level (dB)

Change in Perceived Loudness

1-3

5

Just perceptible

Noticeable difference

10

15

Twice (or 1/2) as loud

Large change

20 Four times (or 1/4) as loud

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Lp40 dB Equal Loudness Contours and A-Weight

40

20

40

p(dB)40 dB Equal

Loudness Contour normalized to 0 20

0

normalized to 0 dB at 1kHz

20 Hz 100 1 kHz 10 kHzLp(dB)

0

-2040

A-weighting

40 dB Equal Loudness Contour inverted and compared

ith-40

20 Hz 100 1 kHz 10 kHz

A weightingwith A-weighting

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20 Hz 100 1 kHz 10 kHz

Frequency Weighting Curves

Lp[dB]

D

Li

0

CD

Lin.

-20A

B

D AB + C

-40

60

10 100 1 k 10 kFrequency[Hz]

-60

20 k2 k 5 k200 50020 50

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Calibration and Weighting!

Lp[dB] L 8 6dB

0

[dB] L = 8.6dB

-20

-40A-weighting

10 100 1 k 10 kFrequency[Hz]

-60

20 k2 k 5 k200 50020 50

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Use of Frequency Weighting

RMSPeak

Weighting

FastSlow

Impulse

87.2

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Serial Analysis

321

RMS

321 n

FastSlow

RMSPeak

SlowImpulse

87.2

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Parallel Analysis

RMS

321 n

FastSlow

RMSPeak

SlowImpulse

87.2

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The Sound Level Analyzer

dB 1/3 Octave Analysis

RMS

Weighting1/1, 1/3 oct80

100

FastSlow

RMSPeak

40

60

SlowImpulse

87.2125 250 500 1k 2k 4k 8k L A

20

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The Spectrogram and Overall levels

L[dB]

1/1 Octave

1/3 Octave

Frequency[Hz]L [dB(A)] [Hz]LA [dB(A)]

LB [dB(B)]LC [dB(C)]LD [dB(D)]L [dB]

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LLin. [dB]

Topic Summary

Basic introduction to audible frequency range and q y gwavelength of soundDiffraction, reflection and diffusion of soundFrequency analysis using FFT and Digital filtersq y y g gFundamental concepts for 1/1 and 1/3 octave filtersHuman perception of sound and background for A,B,C and D-weightingg gSignal flow and analysis in Sound Level Meters

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