Applying progressive phase shifts steers a beam array off-center

Evidence

From the shift theorem, we know that a shift in the spatial domain leads to a linear (progressive) phase change in the Fourier domain and vice versa. Thus, a progressive phase shift in the spatial domain would result in a linear shift of the function in Ω space. This would result in the main lobe moving off the central axis, thus steering the main beam to an off-centre angle. However, the visible region would remain in the same place. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2895

Categorization

• DEFINE: This is the working principle behind phased-array beam steering — phase differences, not physical movement, redirect the beam.