Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Psychoacoustic impact assessment ofsmoothed AM/FM resonance signals

Antonio Goulart, Marcelo QueirozJoseph Timoney, Victor Lazzarini

Computer Music Research Group - IME/USP - BrazilSound and Digital Music Technology Group - NUIM - Ireland

antonio.goulart@usp.br

SMC - 2015/07/31

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Resonance

tendency of a system to vibrate sympathetically at a particularfrequency in response to energy induced at that frequency.

FOF, VOSIM, ModFM, Phase distortion

Analysis/resynthesis

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

TB-303

Resonance Env Mod Decay Label

60% max min A

60% max 60% B

max 75% 25% C

max 75% 75% D

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Waveform D

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

x(t) = a(t) cos (θ(t))

θ(t) = f (t), instantaneous frequency => fits locallya(t), instantaneous amplitude

various techniquesHilbert Transform

x(t) = x(t) ∗ 1

πt90◦ phase shift => analytic signal

z(t) = x(t) + j x(t) = |z(t)|e jθ(t)

resynthesis

y(t) = a(t) cos

(∫ t

−∞f (τ)dτ

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Decomposition - Waveform D - AM portion

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Decomposition - Waveform D - FM portion

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Boxcar windowHanning window20 and 100 samples longwindow w(t)

y(t) = (a ∗ w)(t) cos

(∫ t

−∞(f ∗ w)(τ)dτ

)

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Comparison - AM portion - Smoothing with Boxcar 20

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Comparison - FM portion - Smoothing with Boxcar 20

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Brightness

center of gravity of the spectrumrelated to the most prominent portion of a spectrum(specially with resonant sounds)usually the metric that presents larger variations

Br =

N∑k=1

kak

N∑k=1

ak

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Tristimulus

introduced as a timbre equivalent to the color attributes in vision

Tr1 =a1

N∑k=1

ak

Tr2 =(a2 + a3 + a4)

N∑k=1

ak

Tr3 =

N∑k=5

ak

N∑k=1

ak

related to the warmth (3.5)12 / 21

Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Tristimulus

Tr1 + Tr2 + Tr3 = 1close to origin => strong fundamentalclose to right corner => strong high partialsclose to up corner => strong mid-range partials

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Irregularity

jaggedness, ripples

Ir =

N∑k=1

(ak − ak+1)2

N∑k=1

a2k

, aN+1 = 0

square, clarinet => max irregularity => hollow soundimpulse train => zero irregularity => buzz

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Brightness

Waveform A and C - AM/FM smoothing

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Brightness

Waveform A - AM-only and FM-only smoothing

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Tristimulus

Waveform A and C - AM/FM smoothing

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Tristimulus

Waveform A - AM-only and FM-only smoothing

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Irregularity

Waveform A and C - AM/FM smoothing

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

Irregularity

Waveform A - AM-only and FM-only smoothing

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Introduction AM/FM analysis Smoothing/Resynthesis Psychoacoustic metrics Results Conclusions

brightness/tristimulus point of view, not effective to smoothsignals with strong resonance(although it certainly changes the sound)

tristimulus more affected by smoothing the FM component

irregularity more affected by smoothing the AM component

more irregular input => more similar perceptual outcome

interesting variations when processing modest and mildresonances

longer smoothers => less artifacts

Hanning smoothers => less artifacts

suite of AM/FM effects

Thanks a lot!antonio.goulart@usp.br

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