Signal Spectrum Analysis Using FFT

In digital signal processing, FFT (Fast Fourier Transform) serves as a fundamental algorithm for spectral analysis of signals. FFT efficiently computes the Discrete Fourier Transform (DFT), enabling the transformation of signals from the time domain to the frequency domain. This conversion reveals the signal's frequency components and their respective magnitudes. The algorithm typically operates with O(n log n) complexity, significantly faster than the direct DFT implementation's O(n²) complexity. Code implementation often involves pre-optimized library functions (such as fft() in MATLAB or numpy.fft.fft() in Python) that handle windowing, zero-padding, and frequency bin calculations automatically. Through spectral analysis, engineers can identify dominant frequencies, noise components, and signal characteristics that are essential for filtering, modulation analysis, and system identification. Proper implementation requires consideration of sampling rate, frequency resolution, and spectral leakage mitigation through window functions. Thus, FFT-based spectral analysis represents a critical step in digital signal processing workflows, providing valuable insights for signal interpretation and subsequent processing operations.