【Practical Exercise】Signal Spectrum Analysis Using MATLAB

# 1. Overview of MATLAB Signal Spectrum Analysis

Signal spectrum analysis is a powerful tool for understanding and analyzing the frequency components within a signal. It is widely applied in various fields, including audio processing, image processing, and biomedical engineering. MATLAB offers a comprehensive suite of tools for performing signal spectrum analysis, including data acquisition, preprocessing, Fourier transforms, and spectrum visualization.

# 2. Fundamentals of MATLAB Signal Spectrum Analysis

### 2.1 Definition and Properties of Signal Spectrum

**Definition:**

Signal spectrum refers to the process of decomposing a signal into its constituent frequency components. It reflects the amplitude and phase distribution of different frequency components within the signal.

**Properties:**

***Periodicity:** The spectrum of a periodic signal is also periodic.
***Symmetry:** The spectrum of a real signal is symmetric about the zero frequency.
***Energy Distribution:** The total energy of the signal is distributed across the various frequency components of the spectrum.
***Uniqueness:** For a given signal, its spectrum is unique.

### 2.2 Fourier Transform and Spectrum Analysis

**Fourier Transform:**

The Fourier transform converts a time-domain signal into a frequency-domain signal, revealing the amplitude and phase of the different frequency components within the signal.

**Spectrum Analysis:**

Spectrum analysis is the process of using the Fourier transform to decompose a signal into its frequency components and analyze these components.

**Code Block:**

% Define a time-domain signal
t = 0:0.01:1;
x = sin(2*pi*10*t) + sin(2*pi*20*t);

% Compute the Fourier transform
X = fft(x);

% Compute the magnitude and phase spectra
magnitude_spectrum = abs(X);
phase_spectrum = angle(X);

% Plot the spectrum
figure;
subplot(2,1,1);
plot(linspace(0, 1, length(X)), magnitude_spectrum);
title('Magnitude Spectrum');
xlabel('Frequency (Hz)');
ylabel('Magnitude');

subplot(2,1,2);
plot(linspace(0, 1, length(X)), phase_spectrum);
title('Phase Spectrum');
xlabel('Frequency (Hz)');
ylabel('Phase (rad)');

**Logical Analysis:**

* The `fft()` function performs the Fourier transform, converting the time-domain signal `x` into the frequency-domain signal `X`.
* `abs(X)` and `angle(X)` compute the magnitude and phase spectra, respectively.
* The magnitude and phase spectra are plotted, showcasing the amplitude and phase distribution of the different frequency components in the signal.

**Parameter Explanation:**

* `t`: Time-domain sampling points
* `x`: Time-domain signal
* `X`: Frequency-domain signal
* `magnitude_spectrum`: Magnitude spectrum
* `phase_spectrum`: Phase spectrum

# 3. Practical MATLAB Signal Spectrum Analysis

### 3.1 Signal Acquisition and Preprocessing

Signal acquisition is the first step in spectrum analysis and can be sourced from various origins, such as:

- Sensors (e.g., microphone, accelerometer)
- Files (e.g., WAV, CSV)
- Real-time streams (e.g., serial port, network