New Fractional Ambiguity Function Integrated with CNN-Based Machine Learning for Signal Classification

2026-06-06

AI Summary

This work addresses the limitations of conventional time–frequency representations in signal classification, which suffer from insufficient resolution and localization capabilities. To overcome these challenges, the study proposes a novel fractional ambiguity function (NFrAF) based on the fractional Fourier transform and, for the first time, employs it as an input representation for convolutional neural networks to classify linear frequency-modulated signals. Compared with traditional spectrograms and the classical ambiguity function, NFrAF demonstrates superior time–frequency concentration and enhanced information representation. Experimental results on simulated datasets show that the proposed method significantly improves classification accuracy, thereby validating the effectiveness and superiority of NFrAF as a data-driven representation for signal analysis.

Abstract

A new fractional ambiguity function (NFrAF) derived from the fractional Fourier transform is introduced as a generalization of the classical ambiguity function. The fundamental analytical properties of the NFrAF, including symmetry, marginality, and Moyal type identities, are rigorously established. After verifying its ability to detect and localize monocomponent and multicomponent linear frequency modulated (LFM) signals, the NFrAF is integrated into a convolutional neural network based machine learning framework for signal classification. Owing to its superior time frequency resolution and localization, the NFrAF provides a more informative input representation than conventional methods such as the spectrogram and classical ambiguity function. Experimental results on simulated datasets demonstrate consistent improvements in classification accuracy, highlighting the effectiveness of the proposed representation for data driven signal analysis.

Problem

• signal classification
• fractional ambiguity function
• time-frequency representation
• linear frequency modulated signals
• machine learning

Innovation

• fractional ambiguity function
• convolutional neural network
• time-frequency representation
• signal classification
• fractional Fourier transform