THE CHARACTERISTICS OF SOUNDS ANALYSIS AND SYNTHESIS OF SOUNDS

Átírás

1 THE CHARACTERISTICS OF SOUNDS ANALYSIS AND SYNTHESIS OF SOUNDS Study aid for learning of Communication Acoustics VIHIA szeptember 27., Budapest Fülöp Augusztinovicz professor BME Dept. of Networked Systems and Services

2 Classification of sounds According to origin speech music noise On the basis of temporal variation sinusoidal periodic transient (but still deterministic) irregular, random complex

3 Sinusoidal process A mechanical example: the swing Just one single frequency!

4 How are non-sinusoidal sounds generated? Fundamental tone of a square wave Wave Sound

5 Generation of non-sinusoidal vibration The first three components Wave Sound

6 Generation of non-sinusoidal vibration The first four components Wave Sound

7 Generation of non-sinusoidal vibration The first ten components Wave Sound

8 Components in the frequency domain The first five components: spectrum of the square wave

9 Synthesis of a square wave

10 Another example: the sawtooth wave The fundamental

11 Another example: the sawtooth wave The first two components Wave Sound

12 Another example: the sawtooth wave The first five components Wave Sound

13 Another example: the sawtooth wave

14 Frequency spectrum of the sawtooth wave Note: same frequencies, but faster decrease of amplitudes

15 Harmonics Harmonics: multiples of the fundamental frequency f, 2 f, 3 f, n f Musical notions: octave, third-octave

16 Generation of self-sustaining waves One-dimensional propagation and reflection (along a rigid tube) 0 Particle displacement L x

17 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

18 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

19 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

20 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

21 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

22 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L Reversal of phase, because displ. must be zero

23 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L Reversal of phase, because displ. must be zero

24 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

25 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

26 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

27 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

28 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

29 Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L

30 Relationship between L and f If the tube is closed on both ends: c 2L = λ = f f 0 c = 2L If one end is closed and the other is open: λ c 2L = = 2 2 f c f0 = 4L The same thing happens, if more periods of wave correspond to the length of tube: tube closed at both ends : f, 2 f, 3 f, tube with one closed and one open end : f, 3 f, 5 f,

31 A practical, very simple example: the pan s pipes v p Z = 0 (p = 0) Z = (v = 0) L = λ / 4 f = c / 4L

32 Model of a 1-D waveguide Hang és tér kölcsönhatásai Augusztinovicz Fülöp, Hálózati Rendszerek és Szolgáltatások Tsz. Budapesti Műszaki és Gazdaságtudományi Egyetem 32

33 Buildup of resonance in a closed waveguide Hang és tér kölcsönhatásai Augusztinovicz Fülöp, Hálózati Rendszerek és Szolgáltatások Tsz. Budapesti Műszaki és Gazdaságtudományi Egyetem 33

34 Intonation of organ pipes

35 Intonation (aka voicing) of organ pipes

36 This is how the organ pipes work Abbey of Montserrat and its organ builder Hang és tér kölcsönhatásai Augusztinovicz Fülöp, Hálózati Rendszerek és Szolgáltatások Tsz. Budapesti Műszaki és Gazdaságtudományi Egyetem 36

37 Operation of the chimney flute Bolyai János Matematikai Társulat Küldöttgyűlése

38 Formation of sounds in real-life systems The wave, propagating along a waveguide is reflected from both ends If the excitation appears in identical phase, amplification If he newly supplied energy is just enough to maintain the process: self-sustaining wave If it is too much: resonance A vey famous resonance: the collapse of the Tacoma bridge (US, November 7, 1940) h?v=j-zczjxsxnw The real problem is not just resonance: it is aerodynamic flutter

39 From sinusoids to transients

40 Relationship of frequency and time domain Temporal variation Frequency content This is the Heisenberg uncertainty principle of signal theory!

41 And backwards (t f): Fourier-analysis A periodic function x(t) of period T can be transformed into an infinite series of sinusoids of amplitude X: Xi i 1 T j2π t x( t T ) e 0 = T ( ) x t = i= X e i i j2π t T This is the Fourier-series (expansion) A nonperiodic function x(t) can be transformed into a continuous function, representing a continuous distribution X(f) of components in the frequency domain Joseph Fourier ( ) j2πft j2πft ( ) = ( ) ( ) = ( ) X f x t e dt x t X f e df This is the Fourier-integral Előadó Neve Előadás címe 41 BME Hálózati Rendszerek és Szolgáltatások Tanszék

42 Harmonic content > tone/timbre Comparison of the sound of a flute and a violin Előadó Neve Előadás címe 42 BME Hálózati Rendszerek és Szolgáltatások Tanszék

43 Frequency analysis - experimental Aim is to separate various frequency components by decomposing into bands of constant absolute bandwidth decomposing into bands of constant relative bandwidth Narrow-band frequency analysis is aimed at exact identification of tonal frequencies Standard octave or third-octave band analysis is aimed at modelling/imitating the human hearing system

44 Comparison of male and female voice by thirdoctave band analysis férfi hang női hang Hz 25Hz 31.5Hz 40Hz 50Hz 63Hz 80Hz 100Hz 125Hz 160Hz 200Hz 250Hz 315Hz 400Hz 500Hz 630Hz 800Hz 1kHz 1.25kHz 1.6kHz 2kHz 2.5kHz 3.15kHz 4kHz 5kHz 6.3kHz 8kHz 10kHz 12.5kHz 16kHz 20kHz Hangnyomásszint - db Frekvenciasáv - Hz

45 Standard octave and third-octave bands

46 Critical bands Critical Ban d Frequency (Hz) Critical Frequency (Hz) Ban Low High Width d Low High Width

47 Practical examples of frequency analysis Előadás címe 47 Előadó Neve BME Hálózati Rendszerek és Szolgáltatások Tanszék