Plotting Amplitude-Frequency Characteristics of Rectangular Window Functions

To plot the amplitude-frequency characteristics of rectangular window functions using MATLAB programming, we can implement a systematic approach with the following key steps: First, we generate rectangular windows of specified lengths (10, 20, 50, 100) using MATLAB's built-in rectangular window function or by creating unit impulse sequences. The rectangular window, also known as a boxcar window, can be created using the `rectwin` function or by defining a vector of ones with the desired length. The core implementation involves performing Fast Fourier Transform (FFT) analysis on each window function. We typically apply zero-padding to achieve smooth frequency domain plots, using FFT lengths significantly larger than the window length (e.g., 1024 or 2048 points) for better frequency resolution. For accurate amplitude-frequency characterization, we calculate the magnitude response using the `abs` function after FFT, and often plot the results in dB scale using `20*log10(abs(fft_result))` to better visualize side lobe characteristics. The frequency axis can be normalized or scaled to actual frequency units using appropriate sampling frequency assumptions. We can analyze how different window lengths affect key properties: longer windows provide better frequency resolution (narrower main lobe) but exhibit different side lobe behavior. The rectangular window typically shows high side lobe levels (-13 dB) but narrow main lobe width compared to other window types. The implementation should include comparative analysis of leakage effects - shorter windows tend to have more spectral leakage due to broader main lobes, while longer windows offer improved frequency selectivity but may introduce other artifacts. The code should demonstrate the fundamental trade-off between resolution (main lobe width) and leakage (side lobe levels) inherent in rectangular window functions. By examining the performance across different parameters, we can understand how window length selection impacts spectral analysis accuracy and optimize window function choices for specific applications like digital filter design, spectral estimation, or signal processing tasks. Key MATLAB functions involved: `rectwin`, `fft`, `abs`, `plot`, `xlabel`, `ylabel`, `title` for creating comprehensive visualizations of window function properties in both time and frequency domains.