MATLAB Basics: Tips for Using the Signal Processing Toolbox

# 1. Overview of MATLAB Signal Processing Toolbox

The MATLAB Signal Processing Toolbox offers a comprehensive collection of functions and applications that empower engineers and researchers to design, analyze, and implement a variety of signal processing algorithms. This chapter will introduce the basic functionalities and usage of the toolbox, laying a solid foundation for more in-depth signal analysis and processing in subsequent chapters.

## 1.1 Role and Functions of MATLAB Signal Processing Toolbox

The MATLAB Signal Processing Toolbox is primarily used for analyzing and processing signals in the time and frequency domains, filtering, spectral analysis, and signal transformation processing. It includes the design and application of various digital filters, Fast Fourier Transforms (FFT), window functions, and wavelet transforms, providing methods for analyzing and processing signals.

## 1.2 Main Modules and Functional Features

The main modules in the signal processing toolbox include:

- Signal generation and import-export module: Supports the generation of common signals and the import-export of signal data.
- Spectral analysis module: Provides signal spectral analysis and window function design.
- Filter design module: Enables the design of various types of digital filters, including FIR and IIR.
- Time-domain analysis module: Contains functions for signal convolution and correlation analysis.
- Frequency-domain processing module: Supports FFT transforms and frequency-domain filter design.
- Wavelet transform module: Used for wavelet analysis of signals, offering various methods of wavelet transformations.

The MATLAB Signal Processing Toolbox also has the capability to interact with other MATLAB toolboxes, such as integrating with the Statistics and Machine Learning Toolbox for signal feature extraction and classification, or combining with the real-time processing module for real-time signal processing and analysis.

In the upcoming sections, we will delve into the applications and practical cases of these modules, helping you utilize MATLAB more effectively for signal processing tasks.

# 2. Basics of Signal Analysis and Processing

## 2.1 Theoretical Foundations of Signal Processing

### 2.1.1 Classification and Characteristics of Signals

Signals are ubiquitous in the natural world and engineering technology, carrying information as physical quantities through the propagation of time or space. In signal processing, we can classify signals into two main categories: analog signals and digital signals.

- **Analog signals**: These are continuous signals that can take any value, such as the output signals from temperature or pressure sensors.
- **Digital signals**: Signals that have undergone sampling and quantization processes, consisting of a series of discrete values, such as data processed by computers.

Signals possess various characteristics, such as amplitude, frequency, and phase, which determine the shape of the signal and the information it carries. For example, the frequency dictates the "tone" of the signal, while the phase affects the alignment of the signal waveform.

Signal processing generally needs to consider the following characteristics:

- **Periodicity**: Periodic signals repeat their shape, while non-periodic signals do not.
- **Energy and power**: Energy signals have finite energy over an infinite time span, whereas power signals have constant power at any given time.
- **Linearity and nonlinearity**: Linear signal processing satisfies the superposition principle, while nonlinear processing does not.

### 2.1.2 Fourier Transform and Its Application in Signal Processing

The Fourier Transform is a powerful tool for analyzing the frequency characteristics of signals, converting them from the time domain to the frequency domain. This conversion is crucial for understanding and processing signals, as many signal processing techniques are based on frequency domain analysis.

The core concept of the Fourier Transform is that any periodic signal can be composed of a series of sine waves (or complex exponential functions) with different frequencies, amplitudes, and phases. Therefore, periodic signals can be represented using Fourier series.

For non-periodic signals, the Fourier Transform provides a continuous frequency distribution, known as the Fourier Transform spectrum. The inverse Fourier Transform can reconstruct the original signal from the spectrum.

In MATLAB, we use the `fft` function to perform a Fast Fourier Transform, as shown below:

X = fft(x);

Here, `x` is the time-domain signal, and `X` is its corresponding frequency domain representation. The spectrum can be obtained using `abs(X)` for the amplitude spectrum and `angle(X)` for the phase spectrum.

The Fourier Transform is widely applied in filtering, signal compression, signal separation, and noise reduction. For example, in noise reduction, we can identify the noise frequency components in the signal, filter them out in the frequency domain, and then reconstruct a clean time-domain signal through the inverse transform.

## 2.2 Common Signal Processing Methods

### 2.2.1 Principles of Filter Design

Filters are indispensable components in signal processing, allowing signals with specific frequency ranges to pass through while suppressing others. The design and application of filters are crucial for noise removal, signal separation, and voice processing.

Depending on the filter response, they can be classified into several types:

- **Low-pass filter**: Allows low-frequency signals to pass through while blocking high-frequency signals.
- **High-pass filter**: Allows high-frequency signals to pass through while blocking low-frequency signals.
- **Band-pass filter**: Only allows signals within a specific frequency range to pass through.
- **Band-stop filter**: Blocks signals within a specific frequency range while allowing other frequencies to pass.

A key parameter in filter design is the cutoff frequency, which defines the frequency boundary for signal passage or blocking.

In MATLAB, built-in functions can be used to design filters, such as using the `butter` function to design a Butterworth filter:

[b, a] = butter(n, Wn);

Here, `n` is the filter order, `Wn` is the normalized cutoff frequency (ranging between 0 and 1), and `b` and `a` are the filter coefficients.

After designing a filter, the `filter` function can be used to process signals:

y = filter(b, a, x);

Here, `x` is the original signal, and `y` is the filtered signal.

### 2.2.2 Spectral Analysis of Signals and Window Functions

Spectral analysis is an essential means to understand the frequency content of a signal. In MATLAB, we can use the `fft` function to calculate the signal spectrum, but this usually requires the signal length to be a power of 2. If the signal length does not meet this condition, zero-padding is necessary.

Y = fft(x, length(x));

Window functions are used in signal processing to reduce spectral leakage, which occurs when the finite length of a signal causes its spectrum to extend beyond its actual frequency range. To mitigate this effect, window functions can be applied to the ends of the time-domain signal.

MATLAB offers various window functions, such as the Hamming window (`hamming`) and Hanning window (`hann`). An example of using a window function is shown below:

w = hamming(length(x));   % Using Hamming window
x_windowed = x .* w;      % Applying the window function
Y = fft(x_windowed);      % Calculating the spectrum of the windowed signal

While window functions can reduce spectral leakage, they also introduce side lobes, which are additional frequency components produced by the multiplication of the window function with the signal. The choice of an appropriate window function depends on the application requirements and signal characteristics.

## 2.3 Importing and Exporting Signals in MATLAB

### 2.3.1 Reading and Storing Data

MATLAB provides various methods for reading and storing signal data, including text files, binary files, and data files in specific formats. To read data, MATLAB offers functions such as `load`, `csvread`, `textscan`, etc., for processing different formats of data files.

For instance, if data is stored in CSV format, the following code can be used to read it:

data = csvread('data.csv');

After processing signals, it is sometimes necessary to store the results. Data storage can be accomplished using `save` or `csvwrite` functions. To save in CSV format, the operation would be as follows:

csvwrite('output.csv', data);

When dealing with large datasets, data preprocessing and formatting are often required for subsequent analysis. Preprocessing may include removing outliers, data normalization, etc.

### 2.3.2 Data Preprocessing and Formatting

After importing data, it often needs to be preprocessed. Preprocessing steps include:

- Removing noise: Using filters or other methods to remove noise from the data.
- Data cleaning: Handling missing values, outliers, etc.
- Data normalization: Scaling data to a specific range, typically [0,1] or [-1,1].
- Data standardization: Adjusting data so that the mean is 0 and the standard deviation is 1.

An example of data preprocessing in MATLAB is shown below:

% Assuming data is a matrix of data read from a CSV file
cleaned_data = data;   % Initialize the preprocessed data

% Remove outliers
mean_val = mean(data);
std_dev = std(data);
threshold = 3;
cleaned_data(abs(data - mean_val) > threshold * std_dev) = NaN;

% Data standardization
standardized_data = (data - mean_val) / std_dev;

% Replace NaN values with mean
cleaned_data(isnan(cleaned_data)) = mean(data(isnan(data)));

Preprocessed data usually needs to be converted into a format suitable for signal processing. For example, data may need to be segmented or converted to a specific sampling frequency. This step is crucial for ensuring the accuracy of signal analysis.

A table is an excellent way to present the comparison before and after signal preprocessing. Below is an example table comparing the original signal, the denoised signal, and the standardized signal:

| Original Signal | Denoised Signal | Standardized Signal |
|-----------------|-----------------|---------------------|
| [Original data sequence] | [Denoised data sequence] | [Standardized data sequence] |

With such a table, it is clear to see the changes in the signal before and after preprocessing.

In practical applications of signal processing, data preprocessing and formatting is an iterative process. Based on the analysis results, it may be necessary to return to this step to adjust the processing method to achieve the best analysis outcome.

In the next chapter, we will demonstrate how to use MATLAB for time-domain and frequency-domain signal analysis and processing, and how to apply the Fourier Transform to practical signal processing through specific examples. Through these practices, we will gain a deeper understanding of the power and flexibility of the signal processing toolbox.

# 3. Practicing with MATLAB Signal Processing Toolbox

## 3.1 Time-Domain Signal Analysis and Processing
### 3.1.1 Basic Operations of Time-Domain Signals
In MATLAB, time-domain signal processing is the foundation for analyzing and designing signal processing systems. Time-domain analysis focuses on the changes in signals over time, allowing us to observe the instantaneous characteristics of signals, such as amplitude, frequency, and phase changes over time.

Basic signal operations include signal generation, signal superposition, signal scaling, and signal phase shifting, which are crucial for time-domain analysis.

Taking MATLAB code as an example, the following shows how to generate a simple sine wave signal in MATLAB and perform basic operations:

% Generating a simple sine wave signal
Fs = 1000;           % Sampling frequency
t = 0:1/Fs:1-1/Fs;   % Time vector
f = 5;               % Signal frequency, 5 Hz
A = 0.7;             % Signal amplitude
y = A*sin(2*pi*f*t); % Sine wave signal

% Signal superposition
y2 = y + 0.5*sin(2*pi*10*t); % Superimposing another frequency signal

% Signal scaling
y_scaled = 2 * y; % Doubling the signal amplitude

% Signal phase shift
y_shifted = A*sin(2*pi*f*t + pi/4); % Phase shifting the signal by 45 degrees

In the above code, we first define the sampling frequency `Fs` and the time vector `t`, then create a sine wave signal `y` with a frequency of 5Hz and an amplitude of 0.7. We demonstrate signal superposition, scaling, and phase shifting by modifying `y`.

### 3.1.2 Signal Convolution and Correlation Analysis
Convolution and correlation are important tools in signal processing for analyzing signal and system characteristics. In MATLAB, convolution can be implemented using the `conv` function, while correlation analysis can be performed using the `xcorr` function.

Signal convolution can be used to analyze the response of a signal passing through a linear time-invariant (LTI) system. For example, if we have a signal `x` and a system's impulse response `h`, the output signal `y` can be calculated through convolution:

% Signal x and impulse response h
x = [1 2 3 4];
h = [1 0.5];

% Calculate convolution
y = conv(x, h);

% Plot the result
stem(y);
title('Convolution Result');

In correlation analysis, the correlation function can be used to measure the similarity between two signals or determine the occurrence time of one signal within another. Correlation analysis is very useful in signal detection and signal alignment applications.

% Signal x and signal to be detected d
d = [***];

% Calculate cross-correlation
[crossCorr, lags] = xcorr(x, d);

% Plot cross-correlation result
plot(lags, crossCorr);
title('Cross-Correlation Result');

Through the above two segments of code, we understand how to perform signal convolution and correlation analysis in MATLAB, which are indispensable parts of signal processing basics.

## 3.2 Frequency-Domain Signal Analysis and Processing
### 3.2.1 Using Fast Fourier Transform (FFT)
The Fast Fourier Transform (FFT) is a key technology in frequency-domain analysis, significantly reducing the computational load for spectral analysis. MATLAB provides the `fft` function to perform a fast Fourier transform, while the `ifft` function is used for its inverse transform.

FFT converts time-domain signals into the frequency domain, allowing the analysis of signal frequency components. Below is an example of using MATLAB's FFT function:

% Continuing with the previously defined signal y
N = length(y); % Signal length
Y = fft(y);     % Compute FFT

% Calculate one-sided spectrum
f = (0:N-1)*(Fs/N); % Frequency vector
P2 = abs(Y/N);       % Two-sided spectrum
P1 = P2(1:N/2+1);    % One-sided spectrum
P1(2:end-1) = 2*P1(2:end-1);

% Plot one-sided spectrum
plot(f, P1);
title('One-Sided Spectrum');
xlabel('Frequency (Hz)');
ylabel('Amplitude');

In this code, we first compute the FFT of signal `y`, then convert it to a one-sided spectrum. Finally, we use the `plot` function to draw the one-sided spectrum.

### 3.2.2 Design and Application of Frequency-Domain Filters
Frequency-domain filters are widely used in signal processing for noise removal and signal separation. In MATLAB, the `freqz` function can be used to design and analyze the frequency response of filters.

The `freqz` function can display the magnitude and phase response of a filter, while the `filter` function can perform filtering operations. Below is a simple example of filter design and application:

% Design a low-pass filter
[b, a] = butter(5, 0.1); % A 5th-order Butterworth filter with a cutoff frequency of 0.1*Fs/2

% Display the frequency response of the filter
freqz(b, a);

% Apply the filter to signal y
y_filtered = filter(b, a, y);

% Plot the signal before and after filtering
subplot(2,1,1);
plot(t, y);
title('Original Signal');
subplot(2,1,2);
plot(t, y_filtered);
title('Filtered Signal');

In this code, we first design a 5th-order Butterworth low-pass filter and use the `freqz` function to plot its frequency response. Then, we apply the designed filter to signal `y` and plot the signal before and after filtering.

## 3.3 Wavelet Transform and Signal Processing
### 3.3.1 Basic Concepts of Wavelet Transform
The wavelet transform is a time-frequency analysis tool that can analyze different parts of a signal using waveforms of varying scales. Wavelet transform is widely applied in signal denoising and feature extraction. MATLAB provides a powerful wavelet toolbox to support wavelet transforms.

The core concepts of wavelet transform include wavelet functions and scaling functions. Wavelet functions are used to capture changes in signals at specific times and scales, while scaling functions are used to approximate signals.

### 3.3.2 Application Examples of MATLAB Wavelet Toolbox
In MATLAB's wavelet toolbox, the `wavedec` function can be used for multi-level wavelet decomposition, the `waverec` function for reconstruction, and the `wfilters` function to obtain wavelet and scaling filter coefficients.

The following is an example code for wavelet transform:

% Wavelet decomposition
[C, L] = wavedec(y, 3, 'db1'); % Using db1 wavelet for 3-level decomposition

% Wavelet reconstruction
y_reconstructed = waverec(C, L, 'db1');

% Plot the original signal and the reconstructed signal
subplot(2,1,1);
plot(t, y);
title('Original Signal');
subplot(2,1,2);
plot(t, y_reconstructed);
title('Reconstructed Signal');

In this code, we use the `wavedec` function to perform a three-level wavelet decomposition on signal `y` and the `waverec` function for signal reconstruction. Finally, we plot the images of the original signal and the reconstructed signal.

The above examples demonstrate the powerful capabilities of MATLAB in wavelet transform processing, providing us with more detailed and flexible signal analysis methods. The combination of wavelet transform and signal processing makes the analysis and processing of complex signals more efficient and accurate.

# 4. Advanced Signal Processing Techniques

## 4.1 Adaptive Signal Processing

### 4.1.1 Principles of Adaptive Filter Operation
An adaptive filter is a special type of digital filter that can automatically adjust its parameters based on the statistical characteristics of the input signal to achieve optimal performance. Its core idea lies in continuously updating the filter's weight coefficients through algorithmic iterations to minimize the error signal. Adaptive filters are commonly used in scenarios such as signal denoising, echo cancellation, and system identification. In the design of adaptive filters, the Least Mean Squares (LMS) algorithm is one of the most common implementations.

### 4.1.2 Implementation of LMS Algorithm in MATLAB
In MATLAB, we can use built-in functions or custom functions to implement the LMS algorithm. The following is a simple example that demonstrates how to implement the LMS algorithm in MATLAB to adjust filter weights to reduce the error signal.

% Assuming d(n) is the desired signal, x(n) is the input signal, and mu is the step size parameter
mu = 0.01; % Initialize step size
N = 1000; % Length of input signal
w = zeros(1, N); % Initialize filter weight vector
x = randn(1, N); % Randomly generate input signal
d = filter([0.5, -0.5], 1, x); % Generate desired signal, a simple FIR filter response

% LMS algorithm iteration
for n = 1:N
     y = w' * x(:, n); % Filter output
     e = d(n) - y; % Error signal
     w = w + 2 * mu * e * x(:, n); % Update weight vector
end

In this simple example, we first initialize the filter weight vector `w`, then in each iteration, calculate the current weight filter output `y`. Next, we calculate the error signal `e` and use the LMS algorithm's weight update formula to update the weight vector `w`.

### 4.1.3 LMS Algorithm Parameter Analysis
When implementing the LMS algorithm, choosing an appropriate step size `mu` is crucial. If the step size is too small, the filter's convergence speed will be slow; if it is too large, it may cause the algorithm to diverge. Therefore, selecting an appropriate `mu` is necessary for achieving good adaptive filter performance.

## 4.2 Multirate Signal Processing

### 4.2.1 Techniques of Signal Oversampling and Undersampling
Multirate signal processing involves changing the sampling rate of a signal, including oversampling and undersampling. Oversampling adds sampling points and is commonly used in the early stages of digital signal processing system design; undersampling reduces sampling points, used to reduce the complexity of the processing system or decrease data volume. In MATLAB, the functions `upsample` and `downsample` can be used to implement signal oversampling and undersampling.

### 4.2.2 Multirate System Design and MATLAB Implementation
When designing a multirate system, one must first define the system specifications, including the desired input-output sampling rates, filter type, and the required transition band width. Then, select an appropriate filter design method, such as the window method or the frequency sampling method, and use MATLAB to calculate the filter coefficients. Finally, implement the filter to complete the signal's oversampling or undersampling.

% Example: Perform undersampling on a signal
N = 1000; % Length of input signal
x = randn(1, N); % Randomly generate input signal
r = 2; % Undersampling rate
y = downsample(x, r); % Execute undersampling operation

With the above code, we downsample the input signal `x` by a factor of `r=2`, and the result is stored in `y`.

### 4.2.3 Impact of Sampling Rate Conversion
When performing multirate signal processing, ***revent aliasing, an anti-aliasing filter is typically used before sampling. Additionally, undersampling involves removing high-frequency components, which may lead to signal distortion.

## 4.3 Signal Processing in Digital Communication

### 4.3.1 Digital Modulation and Demodulation Techniques
Digital modulat***mon modulation techniques include Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK), and Phase Shift Keying (PSK). Demodulation is the inverse process of modulation, decoding the received analog signal back into the original digital information.

In MATLAB, the Communications System Toolbox can be used to design and simulate various digital modulation and demodulation processes. The following is a simple example of performing QPSK modulation and demodulation using MATLAB.

% Generate a random bit sequence
data = randi([0 1], 1000, 1);

% QPSK modulation
hMod = comm.QPSKModulator;
modData = step(hMod, data);

% Through an AWGN channel
SNR = 20; % Signal-to-noise ratio
rxSig = awgn(modData, SNR, 'measured');

% QPSK demodulation
hDemod = comm.QPSKDemodulator;
demodData = step(hDemod, rxSig);

% Calculate the bit error rate
errorStats = errorRate(data, demodData);
disp(['Bit error rate is: ' num2str(errorStats(1))])

### 4.3.2 Application of Channel Coding and Decoding in MATLAB
Channel coding techniques are widely ***mon channel coding techniques include convolutional coding, Reed-Solomon coding, etc. Decoding is the inverse process of coding, using specific algorithms to decode the encoded signal to restore the original data.

In MATLAB, built-in functions and objects can be used to simulate the processes of channel coding and decoding. For example, the following code demonstrates how to use convolutional coding and the Viterbi decoding algorithm.

% Generate a random bit sequence
data = randi([0 1], 100, 1);

% Create a convolutional encoder using poly2trellis with constraint length and generator polynomials
trellis = poly2trellis(7, [171 133]);

% Create convolutional encoder and Viterbi decoder objects
hEnc = comm.ConvolutionalEncoder(trellis);
hDec = comm.ViterbiDecoder(trellis);

% Coding and decoding process
encodedData = step(hEnc, data);
decodedData = step(hDec, encodedData);

% Calculate the bit error rate
errorStats = errorRate(data, decodedData);
disp(['Bit error rate is: ' num2str(errorStats(1))])

With the above code, we can simulate the process of convolutional coding and its corresponding Viterbi decoding and calculate the bit error rate after channel coding and decoding.

# 5. Advanced Applications of Signal Processing Toolbox

## 5.1 Advanced Filter Design

### 5.1.1 Optimization Techniques in Filter Design

In practical applications, the performance of filters often needs to meet specific criteria, such as filter bandwidth, transition band width, and filter order. Optimization techniques play a crucial role at this stage, ensuring that the designed filters meet performance requirements while achieving a balance in resource consumption.

A key aspect of optimization techniques is determining the parameters of the filter, including the filter order and cutoff frequency. Generally, the higher the filter order, the closer its performance is to an ideal filter, but it also introduces more computational complexity and delay. Therefore, functions like `fir1` or `butter` in MATLAB can be used, and by setting their order parameters, a preliminary determination of the filter design can be made.

Further optimization involves balancing filter performance with implementation complexity. For example, when designing a low-pass filter, one needs to determine its cutoff frequency and consider side lobe attenuation and transition band width. MATLAB provides rich tools to support these parameter adjustments, such as using `firpm` or `remez` functions to design windowed filters that can be customized for side lobe attenuation according to needs.

### 5.1.2 High-Order Filter Design in MATLAB

The signal processing toolbox in MATLAB provides various methods for designing high-order filters. The following is an example code using the `butter` function to design a high-order Butterworth filter:

% Set the filter order and cutoff frequency
n = 6; % Filter order
Wn = [0.2 0.4]; % Normalized cutoff frequency

% Use the butter function to design low-pass and high-pass filters
[zb, pb, kb] = butter(n, Wn, 'low');
[zt, pt, kt] = butter(n, Wn, 'high');

% Plot the filter's frequency response
freqz(zb, kb);
title('Frequency response of low-pass filter');
figure;
freqz(zt, kt);
title('Frequency response of high-pass filter');

In the above code, the `butter` function designed a 6th-order low-pass filter and a 6th-order high-pass filter with cutoff frequencies of normalized frequencies 0.2 and 0.4. Using the `freqz` function, we can plot the frequency response of the filters to visually assess their performance.

## 5.2 Real-Time Signal Processing and Simulation

### 5.2.1 Real-Time Data Acquisition and Processing

When processing real-time signals, the rate of data acquisition and the efficiency of processing algorithms are critical. MATLAB provides tools and methods for real-time data acquisition and processing, making it possible to acquire signals from physical devices and analyze them. Real-time signal processing often involves interactions with the hardware interfaces of external devices.

MATLAB's Data Acquisition Toolbox can be used to acquire real-time data from various data acquisition devices. The following is a simplified example showing how to read data from an analog device:

% Create a data acquisition object
da = daq.createSession('ni');

% Add an analog input channel
da.addAnalogInputChannel('Dev1', 0, 'Voltage');

% Start real-time acquisition and record data
startForeground(da);

In this simple example, we create a data acquisition session for an NI device and add an analog input channel to it. After calling the `startForeground` function, MATLAB begins to acquire data in real-time and display it in the command window.

### 5.2.2 Interaction Between MATLAB and Hardware Interfaces

Interacting with hardware interfaces allows MATLAB to control external devices, execute real-time signal processing, and feed back the results to these devices. MATLAB provides interfaces for various hardware platforms, including Arduino and Raspberry Pi.

The following is a simple example of interacting with an Arduino interface using MATLAB:

% Create a connection to the Arduino device
a = arduino;

% Send a signal through the digital output port of the Arduino
a.DigitalWrite('D2', 1);
pause(2); % Pause for 2 seconds
a.DigitalWrite('D2', 0);

This code first establishes a connection to an Arduino board, then sends a high-level signal through digital port D2, which remains active for 2 seconds before being turned off.

## 5.3 Application of Signal Processing in Machine Learning

### 5.3.1 Feature Extraction and Signal Classification

An important application of machine learning in the field of signal processing is the automatic identification and classification of signals. This typically requires the extraction of meaningful features from the raw signal, which are then fed into a machine learning model for training and classification.

MATLAB provides a comprehensive machine learning toolbox, streamlining the process from feature extraction to model training. The following is a simple example demonstrating how to use MATLAB to extract signal features and train a Support Vector Machine (SVM) classifier:

% Assuming we have a signal feature matrix features and corresponding labels labels
% Use fitcsvm function to train an SVM classifier
SVMModel = fitcsvm(features, labels);

% Use the trained model for prediction
predictions = predict(SVMModel, newFeatures);

In this example, the `fitcsvm` function is used to train an SVM model, where `features` is a feature matrix, and `labels` is a vector containing the labels. Once the model is trained, the `predict` function can be used to classify new signal features.

### 5.3.2 Integration of Signal Processing with Deep Learning Frameworks

Deep learning is increasingly applied in signal processing, and MATLAB provides a series of deep learning models and pre-trained networks through the Deep Learning Toolbox, which can be used for complex signal analysis tasks.

To combine deep learning with signal processing, signals usually need to be converted into a format that deep networks can process, such as time-frequency spectrograms. Then, pre-trained networks or custom network architectures are used for classification or regression tasks.

The following is an example of using a pre-trained network for audio signal classification:

% Read audio file and convert to a feature spectrogram
[audioIn, fs] = audioread('audioFile.wav');
spectrogramInput = audioIn;
spectrogramInput = spectrogramInput / max(abs(spectrogramInput));

% Load a pre-trained audio network
net = audiorecnet;

% Perform prediction
label = classify(net, spectrogramInput);

In this example, we use `audioread` to read the audio signal from a file and then convert it into a normalized spectrogram. After that, we load a pre-trained audio classification network `audiorecnet` and use it to classify the spectrogram.

In this way, MATLAB seamlessly combines signal processing with deep learning, providing powerful tools for solving various complex signal analysis problems.