A design method of 3‐D fir digital filters detecting linear trajectory signals using the rotation and interpolation in the signal domain

Abstract This paper proposes a method for designing an FIR digital filter which extracts an object moving in a fixed direction at a fixed speed on a plane (linear trajectory signal) with some margins concerning direction and speed independently. Signals to be considered are 3‐D signals on the 2‐D space‐time coordinates. The method herein enables processing by FIR‐type prototype filter of cubic‐symmetric characteristics by rotating signal data and designing a prototype filter in the digital domain directly. Since this design method is not based on optimization design such as an iterative algorithm but finds filter coefficients in an analytical manner, the computation time is extremely short. In addition, since it is a direct design in the digital domain, it does not require s‐z transformation such as bilinear transformation and thus it is not affected by distortion caused by it. Moreover, because of the FIR type its feature is that we do not need to consider a stability check or phase distortion.