├── matrix_pencil.m
├── README.md
└── PronyMethod.py


/matrix_pencil.m:
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 1 | function [answer] = matrix_pencil(x,p,Ts)
 2 | 
 3 | N=length(x);
 4 | Y=hankel(x(1:end-p),x(end-p:end));
 5 | 
 6 | Y1=Y(:,1:end-1);
 7 | Y2=Y(:,2:end);
 8 | 
 9 | l=eig(pinv(Y1)*Y2);
10 | 
11 | alfa=log(abs(l))/Ts;
12 | freq=atan2(imag(l),real(l))/(2*pi*Ts);
13 | 
14 | Z=zeros(N,p);
15 | for i = 1:length(l)
16 | Z(:,i)=transpose(l(i).^(0:N-1));
17 | end
18 | 
19 | rZ=real(Z);
20 | iZ=imag(Z);
21 | 
22 | rZ(isinf(rZ))=realmax*sign(rZ(isinf(rZ)));
23 | iZ(isinf(iZ))=realmax*sign(iZ(isinf(iZ)));
24 | 
25 | Z=rZ+1i*iZ;
26 | h=Z\x;
27 | Amp=abs(h);
28 | theta=atan2(imag(h),real(h));
29 | 
30 | answer=[Amp theta alfa freq];
31 | 
32 | end
33 | 
34 | 


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/README.md:
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 1 | # ReadMe
 2 | 这里有用矩阵束方法实现Prony方法的matlab和python代码，可用来分析时域信号。matlab代码来自参考文献，py代码的过程和功能和matlab代码一致。
 3 | 
 4 | 代码中的函数需要三个输入参数，分别是信号数组x\[n\]，分析阶数p（p阶意味着信号由p项指数项的线性组合表示）和采样时间。
 5 | 
 6 | 函数输出的是一个p×4矩阵，矩阵的列向量分别是振幅，初相位，衰减因子和频率。
 7 | 
 8 | -----------------------------------------------------------------------------------------------------------------------------------------
 9 | This repository includes matlab code and py code which implement Prony's method via Matrix Pencil Method.
10 | 
11 | A data sequence x\[n\] can be represented by the sum of p complex parameters (order p).The function requires three input parameters (x,p,Ts), which are data sequence x\[n\], p, and sampling period of signal x\[n\].
12 | 
13 | The output parameter of the function is a (p × 4) matrix whose column vectors are amplitude, initial phase, attenuation factor, and frequency.
14 | 
15 | Reference :
16 | Fernández Rodríguez, A., de Santiago Rodrigo, L., López Guillén, E. et al. Coding Prony’s method in MATLAB and applying it to biomedical signal filtering. BMC Bioinformatics 19, 451 (2018). https://doi.org/10.1186/s12859-018-2473-y
17 | 


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/PronyMethod.py:
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 1 | # -*- coding: utf-8 -*-
 2 | """
 3 | Created on Tue Jun 29 10:18:43 2021
 4 | 
 5 | @author: Tan Bingyang
 6 | """
 7 | 
 8 | import numpy as np
 9 | import math as mt
10 | import scipy.linalg as sl
11 | 
12 | 
13 | def MPM(phi,p,Ts):
14 |     
15 |     end=len(phi)-1
16 |     Y=sl.hankel(phi[:end-p],phi[end-p:])
17 |     Y1=Y[:,:-1]
18 |     Y2=Y[:,1:]
19 |     Y1p=np.linalg.pinv(Y1)
20 |     EV=np.linalg.eigvals(np.dot(Y1p, Y2))
21 |     EL=len(EV)
22 |     
23 | 
24 |     #Damping factor and frequency as Prony's method
25 |     alpha=np.empty([p])
26 |     frequency=np.empty([p])
27 |     for i in range(p):
28 |         alpha[i]=mt.log(abs(EV[i]))/Ts
29 |         frequency[i]=mt.atan2(EV[i].imag, EV[i].real)/(2*mt.pi*Ts)
30 |     
31 |     #complex residues (amplitudes and angle phases)as Prony's method
32 |     Z=np.zeros([EL,EL],dtype=complex)
33 |     rZ=np.empty([EL,EL])
34 |     iZ=np.empty([EL,EL])
35 |     for i in range(EL):
36 |         for j in range(EL):
37 |             Z[i,j]=EV[j]**i
38 |             rZ[i,j]=Z[i,j].real
39 |             iZ[i,j]=Z[i,j].imag
40 |     
41 |     h=np.linalg.solve(Z,phi[0:EL])
42 |     theta=np.empty([EL])
43 |     amp=abs(h)
44 |     for i in range(EL):
45 |         theta[i]=mt.atan2(h[i].imag, h[i].real)
46 | 
47 |     answer=np.c_[amp,theta,alpha,frequency]
48 |     return answer
49 | 
50 | 


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