Multi-dimensional finite impulse response filters ale disclosed in hybrid and transpose forms. Multi-dimensional signals can be expressed in a vector (ox matrix) form to allow multi-dimensional signals to be processed collectively. Known hybrid and transpose FIR filters are extended to the multi-dimensional case to allow multi-dimensional signals to be processed with reduced redundancies. The input signals are vectors with multidimensional components. The disclosed FIR filters include multipliers that perform matrix multiplications with multiple coefficients, and adders for performing vector additions with multiple inputs and outputs. The z-transforms are provided for the disclosed hybrid and transpose multi-dimensional FIR filters.