【Practical Exercise】Analysis and Processing of Microwave Signals Using MATLAB

# 1. Introduction to MATLAB

MATLAB (Matrix Laboratory) is an interactive programming environment designed for numerical computation, data analysis, and visualization. Developed by MathWorks, it is widely used in engineering, science, and finance. MATLAB is renowned for its powerful matrix manipulation capabilities and an extensive collection of toolboxes, making it an ideal tool for managing complex data and solving technical problems.

# 2.1 Time-Domain Analysis

Time-domain analysis is a fundamental technique in microwave signal analysis. It involves directly observing the changes in a signal over time to extract its characteristics. The primary methods of time-domain analysis include waveform visualization and statistical characteristic analysis.

### 2.1.1 Waveform Visualization

Waveform visualization is the most straightforward method of time-domain analysis. It involves plotting the amplitude-versus-time curve to display the changes in a signal over time. Waveform visualization helps us observe the signal's shape, amplitude, period, and phase.

MATLAB provides various functions for waveform visualization, such as `plot`, `stem`, and `stairs`. These functions can draw different types of waveforms, like sine waves, square waves, and pulse waves.

% Generate a sine wave signal
t = 0:0.01:1;
y = sin(2*pi*10*t);

% Plot the sine wave
plot(t, y);
xlabel('Time (s)');
ylabel('Amplitude');
title('Sine Wave Form');

### 2.1.2 Statistical Characteristic Analysis

Statistical ***mon statistical measures include mean, variance, peak factor, and waveform factor.

MATLAB provides various functions for statistical characteristic analysis, such as `mean`, `std`, and `max`. These functions can calculate the signal's mean, variance, and peak values.

% Compute the statistics of the sine wave signal
mean_y = mean(y);
std_y = std(y);
max_y = max(y);

% Print the statistics
fprintf('Mean: %.2f\n', mean_y);
fprintf('Variance: %.2f\n', std_y);
fprintf('Peak: %.2f\n', max_y);

# 3. Microwave Signal Processing

### 3.1 Filtering

Filtering is a basic and important task in microwave signal processing, used to extract the desired information from a signal or to remove unwanted noise.

**3.1.1 Digital Filter Design**

Digital filters are implemented using digital signal processing techniques. They have the following advantages:

- Programmability: Filter characteristics can be easily modified as needed.
- Stability: Unaffected by component tolerances and environmental changes.
- Low Cost: Lower implementation cost compared to analog filters.

MATLAB provides various functions for designing digital filters, such as `designfilt` and `fdatool`. These functions allow users to specify filter type (such as low-pass, high-pass, band-pass, or band-stop), cutoff frequency, and order.

**Code Block: Using `designfilt` to Design a Low-Pass Filter**

% Design a low-pass filter with a cutoff frequency of 100 Hz
Fs = 1000; % Sampling frequency
Fpass = 100; % Passband frequency
Apass = 1; % Passband gain
Astop = 60; % Stopband attenuation
N = 10; % Filter order
[b, a] = designfilt('lowpassfir', 'PassbandFrequency', Fpass, 'StopbandFrequency', Fpass*1.2, ...
     'PassbandRipple', Apass, 'StopbandAttenuation', Astop, 'SampleRate', Fs, 'DesignMethod', 'kaiserwin');

**Code Logic Analysis:**

- The `designfilt` function is used for designing filters.
- `'lowpassfir'` specifies the filter type as a low-pass finite impulse response (FIR) filter.
- `'PassbandFrequency'` and `'StopbandFrequency'` specify the passband and stopband cutoff frequencies.
- `'PassbandRipple'` and `'StopbandAttenuation'` specify the passband gain and stopband attenuation.
- `'SampleRate'` specifies the sampling frequency.
- `'DesignMethod'` specifies the filter design method (in this case, Kaiser window).

**3.1.2 Filter Application**

Once a filter is designed, it can be applied to a signal to extract the desired information or remove noise.

**Code Block: Using the `filter` Function to Apply a Low-Pass Filter**

% Remove noise from a signal
x = noisy_signal; % Noisy signal
y