Time-Frequency Analysis Using the Ambiguity Function Method

The ambiguity function method serves as an effective tool for time-frequency analysis, especially suitable for processing non-stationary signals. Its core concept involves transforming a one-dimensional time signal into a two-dimensional time-frequency plane through mathematical operations, thereby simultaneously revealing both temporal and spectral characteristics of the signal.

When implementing the ambiguity function method, several key steps are typically involved. The first step is signal preprocessing, which includes necessary filtering and normalization operations to ensure analysis quality. Following this is the construction of the ambiguity function, usually achieved through specific mathematical transformations or kernel functions that map the signal to a joint time-frequency domain. Finally, result interpretation and visualization are crucial for understanding the signal's time-frequency properties.

This method proves particularly valuable in academic research as it not only clearly displays the time-frequency distribution of signals but also aids in identifying transient features and frequency-modulation patterns within the signal. Through appropriate parameter configuration and algorithm optimization, the ambiguity function method can be adapted to various signal types and analytical requirements.