Analyzing Audio Files.ipynb

Kernel: Python 3 (system-wide)

Analyzing Audio Files

Using Discrete Fourier-like and Haar-like Transforms

import numpy as np
import IPython
from scipy.io import wavfile
import matplotlib.pyplot as plt
import wave
import os

Functions

def cutoff(y,h):
    return np.array([el if abs(el) > h else 0 for el in y])

def normalize(vec):
    if (vec == 0).all():
        raise ValueError('Not possilbe to normalize.')
    return vec / np.sqrt(sum(vec**2))

def haar_matrix(N):
    AT = np.zeros((2**N, 2**N))
    row = 0
    for e in range(1,N+2):
        s = 2**e
        col = 0
        while col < 2**N:
            AT[row][col:int(col+s/2)] = 1
            AT[row][int(col+s/2):int(col+s)] = -1
            row += 1
            col += s
    return np.array([normalize(row) for row in AT]).transpose()

haar_matrix(2)

array([[ 0.70710678,  0.        ,  0.5       ,  0.5       ],
       [-0.70710678,  0.        ,  0.5       ,  0.5       ],
       [ 0.        ,  0.70710678, -0.5       ,  0.5       ],
       [ 0.        , -0.70710678, -0.5       ,  0.5       ]])

def fourier_matrix(N):
    A = np.array([[1]])
    size = 1
    while size < 2**N:
        same = np.vstack([A,A]).transpose()
        flip = np.vstack([A,-1*A]).transpose()
        A = np.vstack([same,flip]).transpose()
        size = len(A)
    return A / np.sqrt(2**N)

fourier_matrix(2)

array([[ 0.5,  0.5,  0.5,  0.5],
       [ 0.5, -0.5,  0.5, -0.5],
       [ 0.5,  0.5, -0.5, -0.5],
       [ 0.5, -0.5, -0.5,  0.5]])

Using the functions

N = 10

fs, data = wavfile.read('440+367.wav')

x = data[230_000:230_000 + 2**N].transpose()[0]

sampleRate = 44100.0 # hertz
obj = wave.open('input.wav','w')
obj.setnchannels(1) # mono
obj.setsampwidth(2)
obj.setframerate(sampleRate)
for i in range(len(x)):
    obj.writeframesraw(x[i])
obj.close()

IPython.display.Audio("input.wav")

fig, ax = plt.subplots(figsize=(20,10))
ax.plot(x,'k');

pre = fourier_matrix(N).transpose() @ x

max(pre)

70871.03125

y = fourier_matrix(N) @ cutoff(pre, 4000)

sampleRate = 44100.0 # hertz
obj = wave.open('output.wav','w')
obj.setnchannels(1) # mono
obj.setsampwidth(2)
obj.setframerate(sampleRate)
for i in range(len(y)):
    obj.writeframesraw(y[i])
obj.close()

IPython.display.Audio("output.wav")

fig, ax = plt.subplots(figsize=(20,10))
ax.plot(y,'r');
ax.plot(x,'k');