FAM Algorithm for Cyclic Spectrum Analysis

This article explores the FAM (Fast Algorithm for cyclic spectral analysis) method, which enables efficient and accurate computation of cyclic spectra. Cyclic spectrum analysis serves as a fundamental tool in signal processing for frequency-domain characterization of signals. The FAM algorithm accelerates cyclic spectrum calculation through optimized FFT operations and cyclic autocorrelation implementations, typically achieved via nested loops for frequency smoothing and cyclic frequency resolution. Key computational steps involve signal segmentation, Fourier transform operations, and conjugate multiplication with spectral correlation indexing. This approach significantly reduces computational complexity from O(N³) to O(N²logN) compared to direct methods. Notably, the FAM algorithm's modular structure allows extensions to multidimensional signal processing applications, including image analysis (through 2D cyclic statistics) and speech recognition systems (via joint time-frequencycyclostationary features). The implementation typically involves MATLAB or Python functions for windowing, FFT convolution, and cyclic frequency accumulation loops.