Source Code for Fractional Fourier Transform

In this text, several crucial points are identified. First, we need to examine the source code implementation of the fractional Fourier transform. This source code serves as an essential tool for handling linear frequency modulation (LFM) signals. Through this implementation, which typically involves numerical computation methods and matrix operations, we can perform comprehensive analysis and processing of LFM signals to achieve deeper insights and more accurate results. The code structure generally includes core functions for signal transformation, parameter configuration modules, and visualization components. When processing LFM signals, this source code facilitates multiple functionalities including: spectral analysis through frequency domain transformation algorithms, frequency measurement using peak detection methods, and phase estimation via Hilbert transform techniques. The implementation often employs discrete fractional Fourier transform algorithms with optimized computational efficiency. Therefore, utilizing this source code enables better understanding and processing of LFM signals, thereby enhancing research capabilities and practical applications in this field through programmable signal processing workflows.