Characterizing the Audio Signal: Transforming to Frequency Domain

Characterizing an audio signal involves converting the time domain signal into frequency domain, and understanding its frequency components, by. This is an important step because it gives a lot of information about the signal. You can use a mathematical tool like Fourier Transform to perform this transformation.

Example

The following example shows, step-by-step, how to characterize the signal, using Python, which is stored in a file. Note that here we are using Fourier Transform mathematical tool to convert it into frequency domain.

Import the necessary packages, as shown here:

import numpy as np

import matplotlib.pyplot as plt
from scipy.io import wavfile

Now, read the stored audio file. It will return two values: the sampling frequency and the the audio signal. Provide the path of the audio file where it is stored as shown in the command here:

frequency_sampling, audio_signal = wavfile.read("/Users/admin/sample.wav")

In this step, we will display the parameters like sampling frequency of the audio signal, data type of signal and its duration, using the commands given below:

print('\nSignal shape:', audio_signal.shape)
print('Signal Datatype:', audio_signal.dtype)
print('Signal duration:', round(audio_signal.shape[0] / float(frequency_sampling), 2), 'seconds')

In this step, we need to normalize the signal, as shown in the following command:

audio_signal = audio_signal / np.power(2, 15)

This step involves extracting the length and half length of the signal. Use the following commands for this purpose:

length_signal = len(audio_signal)
half_length = np.ceil((length_signal + 1) / 2.0).astype(np.int)

Now, we need to apply mathematics tools for transforming into frequency domain. Here we are using the Fourier Transform.

signal_frequency = np.fft.fft(audio_signal)

Now, do the normalization of frequency domain signal and square it:

signal_frequency = abs(signal_frequency[0:half_length]) / length_signal
signal_frequency **= 2

Next, extract the length and half length of the frequency transformed signal:

len_fts = len(signal_frequency)

Note that the Fourier transformed signal must be adjusted for even as well as odd case.
if length_signal % 2:

signal_frequency[1:len_fts] *= 2
else:
signal_frequency[1:len_fts-1] *= 2

Now, extract the power in decibal(dB):

signal_power = 10 * np.log10(signal_frequency)

Adjust the frequency in kHz for X-axis:

x_axis = np.arange(0, len_half, 1) * (frequency_sampling / length_signal) / 1000.0

Now, visualize the characterization of signal as follows:

plt.figure()
plt.plot(x_axis, signal_power, color='black')
plt.xlabel('Frequency (kHz)')
plt.ylabel('Signal power (dB)')
plt.show()

You can observe the output graph of the above code as shown in the image below:

In the next post we are going to generate a monotone signal using a Python program.