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Digital-Signal-Processing_06_Quantization of Signals_Requantization of a Speech Signal

English

notebook

Signal Processing

EnglishnotebookSignal Processing

喇叭花

发布于 2023-08-02

推荐镜像 :digital-signal-processing:Digital-Signal-Processing-Lecture

推荐机型 :c2_m4_cpu

Quantization of Signals

Requantization of a Speech Signal

Requantization to 8 bit

Requantization to 6 bit

Requantization to 4 bit

Requantization to 2 bit

Quantization of Signals

🏃🏻 Getting Started Guide
This document can be executed directly on the Bohrium Notebook. To begin, click the Connect button located at the top of the interface, then select the digital-signal-processing:Digital-Signal-Processing-Lecture Image and choose your desired machine configuration to proceed.

📖 Source
This Notebook is from a famous Signal Processing Lecture. The notebooks constitute the lecture notes to the masters course Digital Signal Processing read by Sascha Spors, Institute of Communications Engineering, Universität Rostock.

This jupyter notebook is part of a collection of notebooks on various topics of Digital Signal Processing. Please direct questions and suggestions to Sascha.Spors@uni-rostock.de.

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Requantization of a Speech Signal

The following example illustrates the requantization of a speech signal. The signal was originally recorded with a wordlength of $w = 16$ bits. It is requantized by a uniform mid-tread quantizer to various wordlengths. The signal-to-noise ratio (SNR) after quantization is computed and a portion of the (quantized) signal is plotted. It is further possible to listen to the requantized signal and the quantization error. Note, the level of the quantization error has been normalized for better audability of the effects.

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[1]

import numpy as np

import matplotlib.pyplot as plt

import soundfile as sf

idx = 130000 # index to start plotting

def uniform_midtread_quantizer(x, w):

'''Uniform mid-tread quantizer with limiter.'''

# quantization step

Q = 1/(2**(w-1))

# limiter

x = np.copy(x)

idx = np.where(x <= -1)

x[idx] = -1

idx = np.where(x > 1 - Q)

x[idx] = 1 - Q

# linear uniform quantization

xQ = Q * np.floor(x/Q + 1/2)

return xQ

def evaluate_requantization(x, xQ):

'''Evaluate rquantization by plotting signals and computing SNR.'''

e = xQ - x

# SNR

SNR = 10*np.log10(np.var(x)/np.var(e))

print('SNR: {:2.1f} dB'.format(SNR))

# plot signals

plt.figure(figsize=(10, 4))

plt.plot(x[idx:idx+100], label=r'signal $x[k]$')

plt.plot(xQ[idx:idx+100], label=r'requantized signal $x_Q[k]$')

plt.plot(e[idx:idx+100], label=r'quantization error $e[k]$')

plt.xlabel(r'sample index $k$')

plt.grid()

plt.legend()

# normalize error

e = .2 * e / np.max(np.abs(e))

return e

# load speech sample

x, fs = sf.read('/digital-signal-processing-lecture/data/speech.wav')

# normalize sample

x = x/np.max(np.abs(x))

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Original Signal ../data/speech.wav

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Requantization to 8 bit

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[2]

xQ = uniform_midtread_quantizer(x, 8)

e = evaluate_requantization(x, xQ)

sf.write('speech_8bit.wav', xQ, fs)

sf.write('speech_8bit_error.wav', e, fs)

SNR: 34.0 dB

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Requantized Signal speech_8bit.wav

Quantization Error speech_8bit_error.wav

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Requantization to 6 bit

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[3]

xQ = uniform_midtread_quantizer(x, 6)

e = evaluate_requantization(x, xQ)

sf.write('speech_6bit.wav', xQ, fs)

sf.write('speech_6bit_error.wav', e, fs)

SNR: 22.9 dB

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Requantized Signal speech_6bit.wav

Quantization Error speech_6bit_error.wav

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Requantization to 4 bit

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[4]

xQ = uniform_midtread_quantizer(x, 4)

e = evaluate_requantization(x, xQ)

sf.write('speech_4bit.wav', xQ, fs)

sf.write('speech_4bit_error.wav', e, fs)

SNR: 11.7 dB

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Requantized Signal speech_4bit.wav

Quantization Error speech_4bit_error.wav

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Requantization to 2 bit

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[5]

xQ = uniform_midtread_quantizer(x, 2)

e = evaluate_requantization(x, xQ)

sf.write('speech_2bit.wav', xQ, fs)

sf.write('speech_2bit_error.wav', e, fs)

SNR: 2.4 dB

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Requantized Signal speech_2bit.wav

Quantization Error speech_2bit_error.wav

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Copyright

This notebook is provided as Open Educational Resource. Feel free to use the notebook for your own purposes. The text is licensed under Creative Commons Attribution 4.0, the code of the IPython examples under the MIT license. Please attribute the work as follows: Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples.

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English

notebook

Signal Processing

EnglishnotebookSignal Processing

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