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%matplotlib inline
import numpy, scipy, matplotlib.pyplot as plt, IPython.display as ipd
import librosa, librosa.display
plt.rcParams['figure.figsize'] = (14, 5)
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plt.style.use('seaborn-muted')
plt.rcParams['figure.figsize'] = (14, 5)
plt.rcParams['axes.grid'] = True
plt.rcParams['axes.spines.left'] = False
plt.rcParams['axes.spines.right'] = False
plt.rcParams['axes.spines.bottom'] = False
plt.rcParams['axes.spines.top'] = False
plt.rcParams['axes.xmargin'] = 0
plt.rcParams['axes.ymargin'] = 0
plt.rcParams['image.cmap'] = 'gray'
plt.rcParams['image.interpolation'] = None
The energy (Wikipedia; FMP, p. 66) of a signal corresponds to the total magntiude of the signal. For audio signals, that roughly corresponds to how loud the signal is. The energy in a signal is defined as
$$ \sum_n \left| x(n) \right|^2 $$The root-mean-square energy (RMSE) in a signal is defined as
$$ \sqrt{ \frac{1}{N} \sum_n \left| x(n) \right|^2 } $$Let's load a signal:
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x, sr = librosa.load('audio/simple_loop.wav')
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sr
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x.shape
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librosa.get_duration(x, sr)
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Listen to the signal:
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ipd.Audio(x, rate=sr)
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Plot the signal:
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librosa.display.waveplot(x, sr=sr)
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Compute the short-time energy using a list comprehension:
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hop_length = 256
frame_length = 512
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energy = numpy.array([
sum(abs(x[i:i+frame_length]**2))
for i in range(0, len(x), hop_length)
])
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energy.shape
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Compute the RMSE using librosa.feature.rmse:
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rmse = librosa.feature.rmse(x, frame_length=frame_length, hop_length=hop_length, center=True)
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rmse.shape
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rmse = rmse[0]
Plot both the energy and RMSE along with the waveform:
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frames = range(len(energy))
t = librosa.frames_to_time(frames, sr=sr, hop_length=hop_length)
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librosa.display.waveplot(x, sr=sr, alpha=0.4)
plt.plot(t, energy/energy.max(), 'r--') # normalized for visualization
plt.plot(t[:len(rmse)], rmse/rmse.max(), color='g') # normalized for visualization
plt.legend(('Energy', 'RMSE'))
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Write a function, strip, that removes leading silence from a signal. Make sure it works for a variety of signals recorded in different environments and with different signal-to-noise ratios (SNR).
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def strip(x, frame_length, hop_length):
# Compute RMSE.
rmse = librosa.feature.rmse(x, frame_length=frame_length, hop_length=hop_length, center=True)
# Identify the first frame index where RMSE exceeds a threshold.
thresh = 0.01
frame_index = 0
while rmse[0][frame_index] < thresh:
frame_index += 1
# Convert units of frames to samples.
start_sample_index = librosa.frames_to_samples(frame_index, hop_length=hop_length)
# Return the trimmed signal.
return x[start_sample_index:]
Let's see if it works.
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y = strip(x, frame_length, hop_length)
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ipd.Audio(y, rate=sr)
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librosa.display.waveplot(y, sr=sr)
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It worked!