Download presentation

Presentation is loading. Please wait.

Published byNia Adwell Modified over 2 years ago

1
Analysis of plucked sound signals using the Prony method Ye Lu 2011-12-15

2
Introduction Physical Modelling ----Digital Waveguide Synthesis ----Formant Synthesis ----Finite element Methods Plucked string instruments ----Karplus-Strong Algorithm

3
Prony Method developed by Gaspard Riche de Prony in 1795 extracts valuable information from a uniformly sampled signal and builds a series of damped complex exponentials or sinusoids

4
Prony Method

5
Fourier Series vs Prony Analysis Non-parametric -- Parametric undamped complex exponentials -- damped complex exponentials amplitude, phase and frequency -- amplitude, phase, frequency and damping coefficients

6
Karplus-Strong Algorithm [1] Karplus,K., and A. Strong. 1983. "Digital Synthesis of Plucked-String and Drum Timbres." Computer Music Journal 7(2) : 43-55. [2] Jaff, D., and J. Smith. 1983. "Extensions of the Karplus-Strong Plucked-String Algorithm." Computer Music Journal 7(2): 56-69

7
Implementation in Matlab x=(2*rand(Time,1)-1); for i=N+1:Time x(i)=0; end for i=1:N y(i)=x(i); end y(N+1)=x(1); for i=N+2:Time y(i)=x(i)+0.5*(y(i-N)+y(i-N-1)); end

8
Frequency Response

9
Modifications for the sound Decay Shortening Vibrato Glissandi

10
Mathematical formulations http://www.engr.uconn.edu/~sas03013/docs/PronyAnalysis.pdf

11
Mathematical formulations

12
Three Steps 1. Solve linear prediction model, which is constructed by the observed data set

13
Three steps 2. Find Roots of charactreristic polynomial formed from the linear prediction coefficients

14
Three steps 3. Solve the original set of linear equations to yield the estimates of the exponential amplitude and sinusoidal phase

15
Implementation in Matlab y=zeros(1,N); for i=1:N y(i)=x(800*i); end d=zeros(1,N/2); for i=1:N/2 d(i)=y(i+N/2); end D=zeros(N/2,N/2); for i=1:N/2 for j=N/2:-1:1 D(i,-j+N/2+1)=y(i+j-1); end a=pinv(D)*d'; muhat=roots([1,-a']); U=zeros(N,N/2); for i=1:N for j=1:N/2 U(i,j)=muhat(j,1)^(i-1); end C=pinv(U)*y';

16
F3+F4+F5

17
F1

18
F2

19
Using “prony” command in Matlab

20
Problems to be aware p less than N/2 Noise impacts the accuracy of the Prony pole estimation Noise can cause the damping factors to be too large

21
Conclusion Prony method extracts valuable information from a uniformly sampled signal and builds a series of damped complex exponentials or sinusoids Provide information of amplitude, phase, frequency and damping coefficients Very sensitive to the noise, and behave badly when noise presents

22
References [1] Karplus,K., and A. Strong. 1983. "Digital Synthesis of Plucked-String and Drum Timbres." Computer Music Journal 7(2) : 43-55. [2] Jaff, D., and J. Smith. 1983. "Extensions of the Karplus-Strong Plucked-String Algorithm." Computer Music Journal 7(2): 56-69 [3]http://www.engr.uconn.edu/~sas03013/do cs/PronyAnalysis.pdf [4] Kay and Maple, 1981, “Spectrum Analysis” Proceedings of the IEEE VOL, 69, No. 11: 1404- 1406

23
Thank you!

Similar presentations

Presentation is loading. Please wait....

OK

Automatic Control Theory-

Automatic Control Theory-

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on social contract theory rousseau Ppt on limits and continuity solutions Ppt on petroleum industry in india download Ppt on eye osmolarity Ppt on bond length of n2 Ppt on non agricultural activities in antigua Ppt on review of literature science Ppt on maths for class 2 Ppt on natural resources for class 8 Leadership ppt on accountability