Speech signal processing - Fundamentals (I): basic acoustic knowledge

One 、 acoustic wave

1、 Basic concepts

Sound is produced by the vibration of an object .

When tuning fork vibrates , Excite the surrounding air particles to vibrate , Generate a pressure fluctuation superimposed on the atmospheric pressure . Because air is compressible , Under the interaction of particles , Constantly alternating compression and expansion , And gradually spread out .

Sound waves do not travel by the movement of matter , But the transmission of energy . Particles do not spread forward with sound waves , It vibrates only near the original equilibrium position , The vibration of neighboring particles is affected by the interaction between particles , To spread energy around , Form fluctuations .

Sound waves can travel in an elastic medium , Cannot propagate in a vacuum .

Sound generation ： When an object vibrates , Will cause fluctuations in the surrounding air , Cause the distance between air particles to change , This causes a change in air pressure , Then through the eardrum to reflect the air pressure into the human brain .

acoustic wave ： From a physical point of view , Sound is a mechanical wave , It is produced by the vibration of an object , The vibration of an object makes the surrounding medium （ air ） Produce fluctuations . The waves that travel in the air are longitudinal waves .

Sound waves are also divided into periodic and aperiodic sound waves , The simplest periodic sound wave is a single frequency sound wave , Also called pure tone . It is a fixed frequency generated by simple harmonic vibration 、 Sound waves that vary sinusoidally .

$A_0$： Vibration amplitude ;
$f=\frac{1}{T}$： Number of vibrations per second ,T The time required to complete a vibration cycle , It's called a period ;
$\theta$： Initial phase .

The frequency of sound waves that can be felt by the human ear is from 20Hz~20KHz.

2、 Physical quantity of sound wave

2.1 Sound pressure

Sound pressure is the increase in pressure caused by the presence of sound waves , Unit is Pa. But generally speaking, the sound pressure is taken as the root mean square value , It is called effective sound pressure , So in fact, it is always positive .

2.2 Sound power

Sound power refers to the unit time , Sound waves pass through a specified area perpendicular to the direction of propagation . In noise monitoring , Sound power refers to the total sound power of the sound source , Unit is W.

2.3 A strong voice

Sound intensity refers to the sound intensity per unit time , Sound energy per unit area perpendicular to the propagation direction , Unit is W/S. It is called the characteristic impedance of air to sound wave .

Two 、 Sound pressure level

The audible sound pressure amplitude fluctuation range of human ear is [ The formula ], The fluctuation range of the sound pressure amplitude is very large , The ratio of the two has reached [ The formula ].
Common symbols for sound pressure level SPL To express , But there are other symbols , Such as LP, L, LdB, L（dB） or L（dBA） The form such as ,A Express A Calculation right . In the field of acoustics ,dB It is often used to characterize sound pressure level SPL (Sound Pressure Level） Size .
The response of the human ear to sound intensity is not linear , It's logarithmically proportional , So that the unit of logarithm can be used to represent the proportion of changes in human hearing , therefore , In logarithm dB The sound pressure level expressed in form came into being . Decibel is the unit of sound pressure level .

Decibel （dB） Defined as the logarithmic ratio of two values , These two values are the measured value and the reference value （ Also known as the reference value ）, There are two definitions ：

Power ratio ：[ The formula ]

Amplitude ratio ：[ The formula ]

According to the fluctuation range of the audible sound pressure amplitude of the human ear ：

The reference value of sound pressure is [ The formula ], This value indicates that the human ear is 1000 Hz Average audible threshold at , Or the human ear 1000Hz Average minimum perceived sound pressure fluctuation at .
Every time the sound pressure is doubled , The sound level increases 6dB.

What is? -3dB

Power ratio : [ The formula ]
Amplitude ratio : [ The formula ]

-3dB Also called half power point or cut-off frequency point . At this time, the power is half of the normal power , The sound pressure is normal 0.707.

The audible sound of the human ear has a certain frequency range （20-20K Hz） And a certain sound pressure level range （0-120dB）, The human ear is not equally sensitive to all frequencies . The most sensitive frequency band of normal human ear is 3000Hz To 6000Hz, Usually , The sound perception ability of low frequency band and high frequency band is not as good as that of medium frequency band .
It is generally necessary to check the sound pressure level heard , Correction by gain factor . The most used is A Calculation right . dBA It refers to the sound A Calculation right . Usually yes A The result of weighting , Unit of use dBA or dB (A） To express .A Weighting corresponds to 40 Square ISO response curve ,B,C Corresponding 70,100 Square equivocal curve .

3、 ... and 、 The compounding of sound

When there are two or more sound sources in space , At this time, the sound wave emitted by each sound source propagates in space without changing its propagation law due to the existence of other sound waves . But the wave at a certain position in space is the superposition of the vibration excited by each sound wave at that point , This phenomenon is called superposition of sound waves .

Sound wave superposition

When two sound waves are superimposed , There are several special cases ：

• Same amplitude and frequency , The propagation direction is the same , Opposite phase . When two sound waves are superimposed , Will offset each other , The amplitude is zero . Achieve the purpose of silencing
  
  Same amplitude , The propagation direction is the same , Similar frequency . When sound waves are superimposed, so-called “ pat ” The phenomenon .

When the frequency difference between two sound waves is in different frequency range , Will show different modulation characteristics . If the frequency difference between the two is less than 20Hz, There will be obvious amplitude fluctuation , This is what the beat phenomenon shows ; When the frequency difference is greater than 20HZ, And below 300Hz when , Can feel the obvious rough characteristics ; When the frequency difference is greater than 300HZ when , You can feel two distinct pure tones .

Fundamental wave
Take a standard sine wave as a reference , It is called fundamental wave .

harmonic
Also called overtone , Harmonics are integers higher than the frequency of the fundamental wave Multiple wave .
The superposition of fundamental and harmonic waves constitutes the sound composition .

Monophonic
Sound waves, especially when a single instrument plays a single sound （ Harmonic superposition ）, The frequency of its fundamental wave is called pitch .

The harmonics superimposed by single tones of different instruments are different in frequency and amplitude , Therefore, the timbre of musical instruments varies greatly .

Four 、 Four elements of sound

loudness （loudness)

It is the subjective feeling of the human ear about the size of the sound , The unit is song （Sone） Hefang （Phon）. Also known as intensity

Amplitude dependent
Logarithmically proportional to sound intensity .
The sound frequency is related to
![[ The isoacoustic curve .png]] Low frequency sound needs a higher sound pressure level to have the same loudness as high-frequency sound .
Loudness in addition to the harmonic pressure level 、 Frequency dependent external , And the duration of the signal . For a duration less than 200ms Pure tone signal , People will feel louder and louder as time goes on , Last longer than 200 ms The rear loudness tends to be stable .

tone （pitch)
It is people's subjective feeling about tone or pitch , The unit is beauty （Me), Also called pitch .

Determined by frequency ;
Tone is also related to sound intensity .
The tone is different from the frequency

Length of sound

Sound duration

timbre （Timbre)
Different timbres are caused by different frequency components and amplitudes of different sounds . Also called sound quality .

The lowest frequency of sine wave is the fundamental wave
A sine wave whose frequency is higher than the fundamental wave is called a harmonic

Different frequency components make up different timbres .

The human ear is sensitive to different intensities 、 The auditory range of sounds of different frequencies is called the sound range .

Within the range of the human ear , The subjective feeling of sound auditory psychology mainly includes loudness 、 pitch 、 Timbre and masking effect 、 Positioning, etc .

loudness 、 pitch 、 timbre 、 Length can be used subjectively to describe having amplitude 、 Any complex sound with three physical quantities of frequency and phase , So it is also called sound “ Four elements ”, They are the basis of psychoacoustics .

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Reference material ：
Voice signal processing （ One ）： Basic acoustic knowledge