Discrete Fourier Transform (DFT) and Spectral Analysis with MATLAB Implementation

This article discusses the implementation of Discrete Fourier Transform (DFT) and spectral analysis using MATLAB programming. We begin by defining the signal function h(t) = e^(-a*t)*sin(2πft), where 'a' represents the damping coefficient and 'f' denotes the frequency parameter. The implementation involves computing both Discrete Fourier Transform (DFT) and Inverse Discrete Fourier Transform (IDFT) with visualization of their respective plots. The MATLAB implementation includes key steps such as signal sampling using appropriate sampling rates, zero-padding for frequency resolution enhancement, and applying DFT algorithms. We calculate the amplitude spectrum using abs() function on DFT results and phase spectrum through angle() function. For main frequency detection, the code employs peak finding algorithms like findpeaks() function to identify dominant frequency components in the power spectrum. Furthermore, we explore optimization techniques for DFT computation efficiency, particularly through Fast Fourier Transform (FFT) algorithm implementation. By utilizing fft() and ifft() functions in MATLAB, we can significantly accelerate spectral analysis processes and handle larger datasets. The article also covers windowing techniques (e.g., Hanning window) to reduce spectral leakage and improve frequency resolution. These enhancements provide comprehensive explanations of DFT and spectral analysis implementation processes, offering readers detailed technical insights and practical MATLAB coding approaches for signal processing applications. The code structure includes proper parameter initialization, loop optimization, and result visualization using plot() and stem() functions for clear spectral representation.