Fundamental Knowledge: Signal Spectrum Analysis

For any given signal, we can employ Fast Fourier Transform (FFT) to analyze its frequency spectrum. FFT is a mathematical algorithm widely used in signal processing and spectral analysis, which efficiently computes the Discrete Fourier Transform (DFT) by reducing the computational complexity from O(n²) to O(n log n). This implementation typically involves dividing the signal into smaller segments, applying butterfly operations, and combining the results through decimation-in-time or decimation-in-frequency approaches.

By performing Fourier transform on a signal, we can represent it as a superposition of frequency components, enabling better understanding of signal characteristics and spectral content. The FFT algorithm implementation commonly utilizes functions like fft() in MATLAB or numpy.fft.fft() in Python, which automatically handle windowing, zero-padding, and frequency bin calculations. This method effectively converts time-domain signals into frequency-domain representations, revealing amplitude and phase information across different frequencies.

Therefore, utilizing FFT for signal spectrum analysis represents a commonly used and efficient approach that facilitates in-depth investigation of signal properties in the frequency domain. The process typically involves preprocessing steps such as signal windowing to reduce spectral leakage, followed by FFT computation and magnitude/phase spectrum visualization using plotting functions.