【Basics】Voice Signal Processing in MATLAB: Implementing Sampling, Encoding, and Decoding of Voice Signals

# 2.1 Principles of Voice Signal Sampling

Voice signals are continuously varying analog signals, and to convert them into digital signals that computers can process, they must be sampled and encoded. Sampling refers to the discretization of analog signals at certain time intervals, converting continuous signals into a series of discrete sample values.

### 2.1.1 Sampling Theorem

The sampling theorem states that to avoid aliasing (where high-frequency signals masquerade as low-frequency signals), the sampling frequency must be at least twice the highest frequency of the signal. For voice signals, whose highest frequency is about 4 kHz, the sampling frequency should be at least 8 kHz.

### 2.1.2 Selection of Sampling Frequency

The choice of sampling frequency affects both the quality of the voice signal and the file size. The higher the sampling frequency, the better the quality of the voice signal, but the larger the file size. Generally, a sampling frequency of 8 kHz is sufficient for telephone-quality voice signals; for high-fidelity voice signals, the sampling frequency should be 44.1 kHz or higher.

# 2. Voice Signal Sampling and Encoding

### 2.1 Principles of Voice Signal Sampling

#### 2.1.1 Sampling Theorem

The sampling theorem is the most fundamental theorem in voice signal sampling. It states that: in order to reconstruct a continuous signal without distortion, the sampling frequency must be at least twice the highest frequency of the signal.

#### 2.1.2 Selection of Sampling Frequency

The choice of sampling frequency depends on the frequency spectrum of the voice signal. Typically, the frequency spectrum of human voice signals is between 0-4 kHz, and therefore, to meet the requirements of the sampling theorem, the sampling frequency is usually chosen as 8 kHz.

### 2.2 Methods of Voi***

***mon methods of voice signal encoding include:

#### 2.2.1 PCM Encoding

PCM (Pulse Code Modulation) encoding is a lossless encoding method that quantizes analog voice signals into a series of discrete digital values. The quality of PCM encoding depends on the number of quantization bits; the higher the number of bits, the better the encoding quality.

% PCM encoding
[speech_signal, fs] = audioread('speech.wav'); % Read voice signal
num_bits = 16; % Quantization bits
encoded_signal = audioread('encoded_speech.wav'); % Encoded voice signal

% Line-by-line interpretation
% The audioread() function reads the voice signal, fs is the sampling frequency.
% num_bits is the number of quantization bits, the larger the value, the better the encoding quality.
% encoded_signal is the encoded voice signal.

#### 2.2.2 ADPCM Encoding

ADPCM (Adaptive Differential Pulse Code Modulation) encoding is a lossy encoding method that reduces data volume by predicting and encoding the difference of the signal. The quality of ADPCM encoding depends on the order of the predictor; the higher the order, the better the encoding quality.

% ADPCM encoding
[speech_signal, fs] = audioread('speech.wav'); % Read voice signal
order = 4; % Order of the predictor
encoded_signal = adpcm(speech_signal, order); % Encoded voice signal

% Line-by-line interpretation
% The adpcm() function performs ADPCM encoding, order is the order of the predictor.
% encoded_signal is the encoded voice signal.

#### 2.2.3 LPC Encoding

LPC (Linear Predictive Coding) encoding is a lossy encoding method that reduces data volume by predicting the linear combination of the signal. The quality of LPC encoding depends on the order of prediction and the prediction coefficients; the higher the order and the more accurate the prediction coefficients, the better the encoding quality.

% LPC encoding
[speech_signal, fs] = audioread('speech.wav'); % Read voice signal
order = 10; % Order of prediction
[encoded_signal, prediction_coefficients] = lpc(speech_signal, order); % Encoded voice signal and prediction coefficients

% Line-by-line interpretation
% The lpc() functio