【Practical Exercise】Audio Signal Processing Implementation Using MATLAB

# 2.1 Audio Signal Representation and Analysis

### 2.1.1 Time Domain and Frequency Domain Analysis

Audio signals are typically represented as functions of amplitude varying with time in the time domain. Time domain analysis focuses on the changes in the signal over time, allowing for the visual observation of waveform characteristics.

Frequency domain analysis transforms signals from the time domain to the frequency domain, represented as functions of amplitude or power varying with frequency. Frequency domain analysis can reveal the frequency components contained in the signal, aiding in the identification and extraction of useful information.

### 2.1.2 Fourier Transform and Short-Time Fourier Transform

The Fourier transform is a mathematical tool for converting time-domain signals into frequency domain representations. It decomposes the signal into a series of sine waves, each with a specific frequency and amplitude.

The Short-Time Fourier Transform (STFT) is an extension of the Fourier transform, which divides the signal into overlapping time windows and performs a Fourier transform on each window. The STFT provides a time-frequency representation, displaying both the time-domain and frequency-domain information of the signal simultaneously.

# 2. MATLAB Audio Signal Processing Basics

### 2.1 Audio Signal Representation and Analysis

#### 2.1.1 Time Domain and Frequency Domain Analysis

An audio signal is a function of time and can be represented as a waveform. Time domain analysis refers to the direct study of the changes in the audio signal along the time axis. It can reveal information about the signal's amplitude, frequency, and phase.

#### 2.1.2 Fourier Transform and Short-Time Fourier Transform

The Fourier transform is a mathematical tool that decomposes a time-domain signal into a superposition of sine waves. It can reveal the frequency components of the signal. However, the Fourier transform is not suitable for non-stationary signals because its results are static.

The Short-Time Fourier Transform (STFT) is an improvement over the Fourier transform, dividing the signal into short time windows and then performing a Fourier transform on each window. This yields a time-frequency representation, revealing the changes in the signal over time and frequency.

### 2.2 Digital Signal Processing Basics

#### 2.2.1 Sampling Theorem and Quantization

The sampling theorem stipulates that to accurately reconstruct an analog signal, the sampling frequency must be at least twice the highest frequency of the signal. Quantization refers to the process of discretizing continuous analog signals into finite digital values.

#### 2.2.2 Filter Design and Application

A filter is a device that processes signals, selectively allowing or attenuating signals based on frequency. Filter design involves selecting the appropriate type and parameters of the filter to meet specific application requirements.

**Code Block:**

% Design a bandpass filter
Fs = 44100;           % Sampling frequency
Fpass1 = 1000;        % Lower passband frequency
Fpass2 = 2000;        % Upper passband frequency
Apass = 1;            % Passband gain
Astop = 60;           % Stopband attenuation
N = 100;              % Filter order

[b, a] = butter(N, [Fpass1 Fpass2]/(Fs/2), 'bandpass');

% Apply the filter
y = filter(b, a, x);

**Logical Analysis:**

* The `butter` function designs an Nth-order bandpass filter with a passband frequency range of [Fpass1, Fpass2], a passband gain of Apass, and a stopband attenuation of Astop.
* The `filter` function applies the filter to the input signal x, resulting in the filtered output signal y.

# 3. MATLAB Audio Signal Processing Practice

### 3.1 Audio Signal Reading, Writing, and Preprocessing

#### 3.1.1 File Formats and Read/Write Functions

MATLAB provides various functions for reading and writing audio files in different formats. The most commonly used functions are `audioread` and `audiowrite`. The `audioread` function reads audio files and returns a matrix containing the audio data. The `audiowrite` function writes audio data to a file.

% Read audio file
[y, Fs] = audioread('audio.wav');

% Write audio file
audiowrite('output.wav', y, Fs);

MATLAB supports various audio file formats, including WAV, AIFF, AU, and MP3. To view a list of supported file formats, the `audioformats` function can be used.

#### 3.1.2 Signal Preprocessing Techniques

Before processing audio signals, they typically need to undergo preprocessing. Preprocessing techniques include:

***Resampling:** Converting the sampling rate of the audio signal to another sampling rate.
***Normalization:** Normaliz