Spectral Analysis

Fourier Analysis · Axiom Academy

Understanding the frequency content and power distribution of signals The Power Spectral Density (PSD) measures how power is distributed across frequency components. It's obtained by taking the squared magnitude of the Fourier transform, revealing which frequencies contain the most energy. Key insight: The PSD reveals dominant frequencies in a signal. Peaks in the spectrum indicate frequency components with high energy content. Signals are classified as either energy signals or power signals based on their total energy and average power characteristics. Practical note: Most real-world signals we analyze are power signals since they persist over time, while energy signals are typically short-duration events. 3. Windowing and Spectral Leakage When analyzing finite-length signals, abrupt truncation causes spectral leakage—frequency content "leaks" into adjacent frequencies. Windowing functions smooth the signal edges to reduce this artifact. Trade-off: Windows reduce leakage but decrease frequency resolution. Choose windows based on whether you need better frequency resolution or lower sidelobes. 4. Practical Spectral Estimation Real spectral estimation combines multiple techniques: using the FFT for efficient computation, applying windows to reduce leakage, averaging multiple segments to reduce variance, and choosing appropriate frequency resolution.

This is the written version of the interactive lesson above. See the full Fourier Analysis course.