Windowed Fourier Transform Demonstration

This document provides a detailed MATLAB implementation guide for demonstrating the windowed Fourier transform process. We will process signals using both rectangular window and Hamming window functions, followed by Fourier transform analysis. Through this demonstration, you will gain comprehensive understanding of Fourier transform procedures with windowing techniques. The following sections detail the step-by-step implementation of windowed Fourier transform using MATLAB programming. Step 1: Data Preparation Before performing windowed Fourier transform, we need to prepare signal data. We will generate random signals using MATLAB's random number generation functions like randn() or rand(). These generated signals will serve as input for our Fourier transform operations. For example: signal = randn(1,N) creates an N-length random signal with normal distribution. Step 2: Window Application Once data is prepared, we apply window functions. Windowing is a signal segmentation technique that improves Fourier transform accuracy by reducing spectral leakage. In this demonstration, we implement both rectangular window (rectwin() function) and Hamming window (hamming() function). The rectangular window provides uniform weighting while Hamming window offers better side lobe suppression. Implementation: windowed_signal = original_signal .* window_vector. Step 3: Fourier Transform Execution After data preparation and window application, we perform Fourier transform using MATLAB's fft() function (Fast Fourier Transform). The fft() function efficiently computes the discrete Fourier transform of the windowed signal. We analyze the frequency spectrum using: spectrum = fft(windowed_signal). For magnitude analysis, we use abs(spectrum) and for phase analysis, angle(spectrum). Through this demonstration, you have learned how to implement windowed Fourier transform. We utilized MATLAB programming to demonstrate the complete process with both rectangular and Hamming window functions. This practical example enhances understanding of Fourier transform procedures and develops skills in signal processing applications. Happy coding!