Construction and Visualization of Ambiguity Functions for Arbitrary Signals

This implementation focuses on constructing and plotting ambiguity functions for arbitrary signals, validated through testing with Barker codes, linear frequency modulated (LFM) signals, and pulse signals. The ambiguity function serves as a fundamental mathematical tool for quantifying signal ambiguity, enabling comprehensive analysis of uncertainty principles in signal processing and communication system design. For Barker code signals, the ambiguity function characterizes the blurred boundaries between code symbols, facilitating optimal decoding strategy determination through cross-correlation analysis implemented via convolution algorithms in code. In linear frequency modulated (LFM) signals, the ambiguity function captures frequency domain uncertainties, supporting accurate frequency characteristic estimation through Doppler-tolerant waveform design using phase modulation techniques. For pulse signals, the ambiguity function simultaneously characterizes time-domain and frequency-domain properties, enabling evaluation of transmission performance and interference effects through matched filter implementations and time-frequency distribution computations. The implementation employs Fourier transform-based algorithms with windowing techniques for resolution control, incorporating 2D visualization methods for contour plotting and surface rendering of ambiguity diagrams. This approach provides deeper insights into signal properties, offering comprehensive references for advanced signal processing and communication system optimization. The code structure includes modular functions for signal generation, ambiguity calculation using FFT operations, and customizable plotting parameters for analytical flexibility.