Spectrum convolution theorem and spectra composition for Doppler ultrasound signals

The Doppler convolution theorem is studied by analyzing the received spectrum of a single scatter moving on arbitrary trajectories. For the homogeneous acoustical field and media without loss, the Doppler spectrum observed at receiver is a convolution of four sub-spectrums. The convolution equation is also used to analyze the Doppler received spectrum for some special cases. Particularly, it is shown that the coherent scattering gives rise to spectrum that might be different from that of single particle.