A Universal Method for Plotting Ambiguity Functions Suitable for Any Signal

This method provides a comprehensive approach for plotting ambiguity functions suitable for any signal type. During implementation, it's essential to understand the practical meaning of each input parameter. The process begins with signal discretization, where Signal elements (u_basic) represents your signal vector in digital form. The parameter "Frequency coding in units of 1/tb" corresponds to your signal's sampling frequency, determining the time resolution. The "Over sampling ratio" parameter ensures compliance with the Nyquist-Shannon sampling theorem, requiring the sampling frequency to be at least twice the highest frequency component in your signal. The implementation typically involves creating a time-frequency representation using correlation techniques, where the ambiguity function is computed through a double loop structure that calculates the cross-correlation between time-shifted and frequency-shifted versions of the signal. Key algorithmic steps include signal windowing, Fourier transform operations, and matrix manipulations to generate the 2D ambiguity function plot. Additional implementation details may include signal preprocessing methods such as normalization, window function application to reduce spectral leakage, and interpolation techniques for smoother visualization. The plotting procedure generally involves creating contour plots or surface plots to represent the time-delay and Doppler shift dimensions, with appropriate axis labeling and colormap selection for clear interpretation of the ambiguity function characteristics.