THE CHARACTERISTICS OF SOUNDS ANALYSIS AND SYNTHESIS OF SOUNDS Study aid for learning of Communication Acoustics VIHIA 000 2017. szeptember 27., Budapest Fülöp Augusztinovicz professor BME Dept. of Networked Systems and Services fulop@hit.bme.hu
Classification of sounds According to origin speech music noise On the basis of temporal variation sinusoidal periodic transient (but still deterministic) irregular, random complex
Sinusoidal process A mechanical example: the swing Just one single frequency!
How are non-sinusoidal sounds generated? Fundamental tone of a square wave Wave Sound
Generation of non-sinusoidal vibration The first three components Wave Sound
Generation of non-sinusoidal vibration The first four components Wave Sound
Generation of non-sinusoidal vibration The first ten components Wave Sound
Components in the frequency domain The first five components: spectrum of the square wave
Synthesis of a square wave
Another example: the sawtooth wave The fundamental
Another example: the sawtooth wave The first two components Wave Sound
Another example: the sawtooth wave The first five components Wave Sound
Another example: the sawtooth wave
Frequency spectrum of the sawtooth wave Note: same frequencies, but faster decrease of amplitudes
Harmonics Harmonics: multiples of the fundamental frequency f, 2 f, 3 f, n f 0 0 0 0 Musical notions: octave, third-octave
Generation of self-sustaining waves One-dimensional propagation and reflection (along a rigid tube) 0 Particle displacement L x
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L Reversal of phase, because displ. must be zero
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L Reversal of phase, because displ. must be zero
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
Generation of self-sustaining waves One-dimensional propagation and reflection x Particle displacement L
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,... 0 0 0 tube with one closed and one open end : f, 3 f, 5 f,... 0 0 0
A practical, very simple example: the pan s pipes v p Z = 0 (p = 0) Z = (v = 0) L = λ / 4 f = c / 4L
Model of a 1-D waveguide Hang és tér kölcsönhatásai Augusztinovicz Fülöp, Hálózati Rendszerek és Szolgáltatások Tsz. Budapesti Műszaki és Gazdaságtudományi Egyetem 32
Buildup of resonance in a closed waveguide Hang és tér kölcsönhatásai Augusztinovicz Fülöp, Hálózati Rendszerek és Szolgáltatások Tsz. Budapesti Műszaki és Gazdaságtudományi Egyetem 33
Intonation of organ pipes
Intonation (aka voicing) of organ pipes
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
Operation of the chimney flute Bolyai János Matematikai Társulat Küldöttgyűlése 2010. 04. 17. 37
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) https://www.youtube.com/watc h?v=j-zczjxsxnw The real problem is not just resonance: it is aerodynamic flutter
From sinusoids to transients
Relationship of frequency and time domain Temporal variation Frequency content This is the Heisenberg uncertainty principle of signal theory!
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 (1768 1830) 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
Harmonic content > tone/timbre Comparison of the sound of a flute and a violin https://www.youtube.com/watch?v=c5o16fl0gqm Előadó Neve Előadás címe 42 BME Hálózati Rendszerek és Szolgáltatások Tanszék
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
Comparison of male and female voice by thirdoctave band analysis 60 55 50 45 40 35 30 25 20 férfi hang női hang 15 10 20Hz 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
Standard octave and third-octave bands
Critical bands Critical Ban d Frequency (Hz) Critical Frequency (Hz) Ban Low High Width d Low High Width 0 0 100 100 13 2000 2320 320 1 100 200 100 14 2320 2700 380 2 200 300 100 15 2700 3150 450 3 300 400 100 16 3150 3700 550 4 400 510 110 17 3700 4400 700 5 510 630 120 18 4400 5300 900 6 630 770 140 19 5300 6400 1100 7 770 920 150 20 6400 7700 1300 8 920 1080 160 21 7700 9500 1800 9 1080 1270 190 22 9500 12000 2500 10 1270 1480 210 23 12000 15500 3500 11 1480 1720 240 24 15500 22050 6550 12 1720 2000 280
Practical examples of frequency analysis Előadás címe 47 Előadó Neve BME Hálózati Rendszerek és Szolgáltatások Tanszék