Frequency domain low time-bandwidth product chirp synthesis for pulse compression side lobe reduction

Coded signals are commonly used in communication and radar systems. However, in ultrasonics the use of coded signals is still relatively uncommon. Linear frequency modulated chirps, employed to improve signal to noise ratio (SNR), exhibit autocorrelation sidelobes whose amplitude increase with decreasing time bandwidth product. This is important in pulse-echo ultrasonics where the chirps need to be short. The side lobes can be attenuated by windowing the chirp amplitude with a suitable window function, but this broadens the main lobe which lowers the resolution. We describe an alternative method for chirp generation in the frequency domain. The chirp is generated by applying a quadratic phase shift into a signal with predefined spectrum. The autocorrelation side lobes of these chirps are nearly identical with the original unchirped pulse. A sum of four sine modulated Gaussians were used to provide the initial spectrum for evaluating the frequency domain chirping. This method holds potential for use in NDT pulse-echo measurements and medical ultrasonics where short codes to improve SNR are needed.