Fourier Transform Analysis of Signals

During the Fourier transform process of signals, we can obtain both amplitude and phase spectra, and visualize them through plotting. The amplitude spectrum reflects the magnitude of signal amplitudes at different frequencies, while the phase spectrum displays the phase information across various frequency components. Through analysis of both spectra, we gain deep insights into the frequency-domain characteristics of signals, providing crucial guidance for further signal processing and analysis. In practical implementation using programming languages like MATLAB or Python, the Fast Fourier Transform (FFT) algorithm is commonly employed for efficient computation. Key functions include fft() for transformation, abs() for amplitude calculation, and angle() for phase extraction. The implementation typically involves: 1. Applying FFT to convert time-domain signal to frequency-domain 2. Calculating amplitude spectrum using the magnitude of complex FFT results 3. Deriving phase spectrum from the angle of complex coefficients 4. Plotting both spectra using visualization functions like plot() or stem() The amplitude spectrum helps identify dominant frequency components and their relative strengths, while the phase spectrum reveals timing relationships between different frequency elements. This dual-spectrum analysis is fundamental in applications like filter design, spectral analysis, and signal reconstruction.