Audio-Data-Analysis-Using-the-Fast-Fourier-Transform/music_esp_python.py at main · tiffanymillerr/Audio-Data-Analysis-Using-the-Fast-Fourier-Transform · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
#Tiffany Miller and Jordan Hoppenheim

from IPython.display import Audio
import numpy as np
import matplotlib.pyplot as plt

"""
Original file is located at
    https://colab.research.google.com/drive/1aXHxvy00I3OzWUz7qYytXJ3E9JM7FgY1

Generating, playing, plotting, analyzing a simple sound

The following assumes that a sound file "piano.wav" is saved on the Google Drive, in the "Colab Notebooks" directory.
"""

from google.colab import drive
drive.mount('/content/drive')

wav_piano = "/content/drive/My Drive/piano.wav"
Audio(wav_piano)

samplerate, data = wavfile.read(wav_piano)
print(f"sample rate = {samplerate}")
print(f"number of channels = 1")
n_datapoints = data.shape[0]
print(f"{n_datapoints} data points")
length_sec = n_datapoints / samplerate
print("length = {:2.3f} seconds".format(length_sec))

time = np.linspace(0., length_sec, data.shape[0])
plt.plot(time, data[:], label="mono channel")
plt.legend()
plt.xlabel("Time [s]")
plt.ylabel("Amplitude")
plt.show()

print(data[:])

plt.plot(data[int(0.2*n_datapoints):int(0.21*n_datapoints)], label="Left channel")
plt.show()

yf = np.fft.fft(data[:])
N = signal.shape[0]

fig, ax = plt.subplots()
ax.plot(np.abs(yf[:N//2]))
plt.show()

yf = np.fft.fft(data[:])
N = signal.shape[0]

fig, ax = plt.subplots()
plt.xlim([465, 500])
ax.plot(np.abs(yf[:N//2]))
plt.show()

yf = np.fft.fft(data[:])
N = signal.shape[0]

fig, ax = plt.subplots()
plt.xlim([940, 960])
ax.plot(np.abs(yf[:N//2]))
plt.show()

yf = np.fft.fft(data[:])
N = signal.shape[0]

fig, ax = plt.subplots()
plt.xlim([2380, 2395])
ax.plot(np.abs(yf[:N//2]))
plt.show()

yf = np.fft.fft(data[:])
N = signal.shape[0]

fig, ax = plt.subplots()
plt.xlim([1410, 1430])
ax.plot(np.abs(yf[:N//2]))
plt.show()

yf = np.fft.fft(data[:])
N = signal.shape[0]

fig, ax = plt.subplots()
plt.xlim([1890, 1910])
ax.plot(np.abs(yf[:N//2]))
plt.show()

"""Now we convert all the 7 peaks from frequency to time domaine. Then we combine all time domain component frequencies to get the orginal Piano"""

import numpy as np
f1 = 470.0              # in Hertz
f2 = 942.0
f3 = 2388.0
f4 = 1417.8
f5 = 1898.0           # in Hertz
sample_rate = 44100      # in Hertz
duration = 1            # in seconds
times = np.linspace(0, duration, duration*sample_rate)
signal1 = np.sin(2*np.pi*f1*times)

fig, ax = plt.subplots()
ax.plot(signal1[:200])
Audio(data=signal1, rate=sample_rate)

signal2 = 0.2*np.sin(2*np.pi*f2*times)
fig, ax = plt.subplots()
ax.plot(signal2[:200])
Audio(data=signal2, rate=sample_rate)

signal3 = 0.17*np.sin(2*np.pi*f3*times)
fig, ax = plt.subplots()
ax.plot(signal3[:200])
Audio(data=signal3, rate=sample_rate)

signal4 = 0.1*np.sin(2*np.pi*f4*times)
fig, ax = plt.subplots()
ax.plot(signal4[:200])
Audio(data=signal2, rate=sample_rate)

signal5 = 0.05*np.sin(2*np.pi*f5*times)
fig, ax = plt.subplots()
ax.plot(signal5[:200])
Audio(data=signal5, rate=sample_rate)

signal = signal1 + signal2 + signal3 + signal4 + signal5
fig, ax = plt.subplots()
ax.plot(signal[:1000])
Audio(data=signal, rate=sample_rate)

"""### Some simple transforms that should be understood / verified by hand calculation"""

np.fft.fft(np.array([1,0,0,0]))

np.fft.fft(np.array([0,1,0,0]))

np.fft.fft(np.array([0,0,1,0]))

np.fft.fft(np.array([0,0,0,1]))

np.fft.ifft(np.array([1,0,0,0]))

np.fft.ifft(np.array([0,1,0,0]))

np.fft.ifft(np.array([0,0,1,0]))

np.fft.ifft(np.array([0,0,0,1]))

trans = np.fft.fft(np.array([1,2,3,4]))
trans

np.fft.ifft(trans)