Radon Transform Implementation with Signal Parameter Extraction

The MATLAB code demonstrates Radon transform application for signal processing. Key implementation details include: Signal Generation: - Signal length N=800 with sampling frequency fs=200 Hz - Time vector t=n/fs where n=1:N - Two quadratic chirp signals: x1 = exp(j*2*pi*(5*t + 0.5*5*t.^2)) [Chirp rate: 5 Hz/s] x2 = exp(j*2*pi*(5*t + 0.5*15*t.^2)) [Chirp rate: 15 Hz/s] - Composite signal x = x1 + x2 Radon Transform Processing: - ambifunb(x) computes the ambiguity function for time-frequency analysis - htl(abs(naf)) performs Hough transform line detection on the ambiguity function magnitude - [wh, rho, theta] = htl(abs(naf)) returns Hough transform accumulator matrix and polar coordinates Visualization and Parameter Extraction: - colormap([0,0,0]) sets black colormap for better contrast - Peak detection: b=max(max(wh)) finds maximum value in accumulator - [u,a]=find(wh>=0.8*b) locates coordinates exceeding 80% of peak value - The peak coordinates are used to calculate initial frequencies and chirp slopes through Radon transform properties This implementation showcases how Radon transform can decompose composite signals and extract time-frequency parameters using Hough transform-based peak detection in the ambiguity function domain. The algorithm effectively separates signal components with different chirp characteristics through their distinct linear patterns in the transform domain.