new_contents: # -*- coding: utf-8 -*-
  """
  Created on Sat Feb 27 22:01:37 2016
  
  @author: ORCHISAMA
  """
  
  #calculate LPC coefficients from sound file
  from __future__ import division
  import numpy as np
  import matplotlib.pyplot as plt
  
  
  def autocorr(x):
      n = len(x)
      variance = np.var(x)
      x = x - np.mean(x)
      r = np.correlate(x, x, mode = 'full')[-n:] #n numbers from last index (l-n to l)
      result = r/(variance*(np.arange(n, 0, -1)))
      return result
      
    
  def createSymmetricMatrix(acf,p):
      R = np.empty((p,p))
      for i in range(p):
          for j in range(p):
              R[i,j] = acf[np.abs(i-j)]
      return R
      
      
  def lpc(s,fs,p):
      
      #divide into segments of 25 ms with overlap of 10ms
      nSamples = np.int32(0.025*fs)
      overlap = np.int32(0.01*fs)
      nFrames = np.int32(np.ceil(len(s)/(nSamples-overlap)))
      
      #zero padding to make signal length long enough to have nFrames
      padding = ((nSamples-overlap)*nFrames) - len(s)
      if padding > 0:
          signal = np.append(s, np.zeros(padding))
      else:
          signal = s
      segment = np.empty((nSamples, nFrames))
      start = 0
      for i in range(nFrames):
          segment[:,i] = signal[start:start+nSamples]
          start = (nSamples-overlap)*i
      
      #calculate LPC with Yule-Walker    
      lpc_coeffs = np.empty((p, nFrames))
      for i in range(nFrames):
          acf = autocorr(segment[:,i])
  #        plt.figure(1)
  #        plt.plot(acf)
  #        plt.xlabel('lags')
  #        plt.ylabel('Autocorrelation coefficients')
  #        plt.axis([0, np.size(acf), -1, 1])
  #        plt.title('Autocorrelation function')
  #        break
          r = -acf[1:p+1].T
          R = createSymmetricMatrix(acf,p)
          lpc_coeffs[:,i] = np.dot(np.linalg.inv(R),r)
          lpc_coeffs[:,i] = lpc_coeffs[:,i]/np.max(np.abs(lpc_coeffs[:,i]))
               
      return lpc_coeffs
  
subject: Add program to calculate Linear Prediction Coefficients