Digital Sampling of Sinusoidal Signals Using MATLAB and DFT Transformation

We can utilize MATLAB to perform digital sampling of sinusoidal signals and apply Discrete Fourier Transform (DFT) to the sampled data. The implementation begins by defining a sinusoidal signal with specific parameters (frequency, amplitude, and phase) and selecting an appropriate sampling rate that satisfies the Nyquist criterion to avoid aliasing. The sampling process can be implemented using MATLAB's built-in functions or by creating time vectors with defined sampling intervals. For DFT analysis, we employ MATLAB's fft() function, which efficiently computes the Discrete Fourier Transform. The algorithm transforms the time-domain sampled signal into frequency-domain representation, revealing the signal's spectral components. Key implementation steps include proper signal windowing to reduce spectral leakage and frequency axis calibration for accurate frequency interpretation. This process enables comprehensive frequency domain analysis of sinusoidal signals, allowing researchers to extract spectral characteristics, identify harmonic components, and perform subsequent signal processing operations such as filtering or spectral modification. The MATLAB implementation provides both numerical results and visual representations through plotting functions for enhanced signal analysis.