Signal Spectrum Analysis Using FFT

In signal processing, we can utilize the FFT algorithm to perform spectral analysis of signals. Below are examples of common signal sequences with corresponding implementation insights: 1. Gaussian Sequence: The Gaussian sequence serves as a fundamental signal model characterized by a smooth, bell-shaped spectral profile. In implementation, we typically generate it using Gaussian distribution functions (e.g., numpy.random.normal() in Python or randn() in MATLAB) with adjustable standard deviation parameters to control spectral width. 2. Damped Sinusoidal Sequence: This sequence represents a sinusoidal signal with exponentially decaying amplitude, displaying gradually diminishing magnitude characteristics in the frequency domain. Code implementation involves combining sinusoidal functions with exponential decay terms (e.g., exp(-alpha*t)*sin(2*pi*f*t)), where damping factor alpha controls decay rate. 3. Triangular Wave Sequence: As a periodic signal, the triangular wave exhibits multiple harmonic components in its spectrum. Implementation commonly uses piecewise linear functions or built-in generators (e.g., scipy.signal.sawtooth() with width=0.5), where harmonic distribution depends on waveform symmetry. 4. Inverse Triangular Sequence: This periodic signal also demonstrates multiple harmonic characteristics in频谱, but with phase inversion compared to standard triangular waves. Code generation typically involves phase-shifting standard triangular waves by 180 degrees or modifying slope directions in piecewise linear functions. These examples demonstrate how different time-domain characteristics manifest in frequency-domain representations, helping develop practical understanding of spectral analysis in signal processing applications.