The invention discloses an anti-symmetric
filter design method based on an anti-auto-inverse matrix theory, and belongs to the technical field of
digital signal processing. According to the method, a design problem of an antisymmetric filter is modeled into an
optimization problem of an
impulse response vector h, and an inverse self-inverse constraint h =-Jh (J is an inverse unit matrix) is applied, so that an optimization target minize | A -d | is constructed. An iterative solution technology of a generalized
coupling Sylster
transpose matrix equation is adopted, and through parameter initialization,
residual matrix updating, step length dynamic adjustment and anti-auto-
back projection operation, it is ensured that a filter coefficient strictly meets antisymmetry. Furthermore, the calculation complexity is reduced by using block calculation, fast multiplication and a
precondition technology, and the
frequency domain performance is optimized in combination with a weighted least square method and a
Lagrange multiplier method. According to the filter designed by the invention, the strict
linear phase characteristic is maintained, meanwhile, the stop-band attenuation can reach more than 50dB, the gradient of a
transition band is improved by 30%, and the group
delay fluctuation is controlled within 0.1 sampling point, so that the filter is suitable for medical image and
radar signal processing and high-fidelity audio systems, and has the characteristics of high calculation efficiency and excellent performance.