Time-Frequency Analysis Using the Ambiguity Function Method

The ambiguity function method proves highly effective for time-frequency analysis. This technique enables comprehensive examination of signal characteristics across both time and frequency domains, including spectral properties, transient responses, and periodic signal behaviors. Consequently, it finds widespread applications across multiple disciplines such as signal processing, image analysis, audio engineering, and biomedical engineering. From an implementation perspective, the ambiguity function typically involves mathematical operations like auto-correlation and Fourier transforms. Key computational steps include: 1. Calculating the auto-ambiguity function: A(τ,ν) = ∫ x(t)x*(t+τ)e^(-j2πνt) dt 2. Applying Fourier transform pairs to generate time-frequency representations 3. Implementing windowing functions for improved resolution Successful application requires specialized software tools. One particularly efficient implementation I utilized during my thesis research features optimized matrix operations for faster computation and includes visualization modules for clear time-frequency distribution plots. The program incorporates advanced windowing techniques and supports both continuous and discrete signal analysis through customizable parameter settings.