A digital filter is disclosed, the filter comprising a device for determining the initial condition of a partial filter input, using a partitioned filter input signal, and partitioned filter input coefficients and a device for determining the initial condition of a partial filter output, using a partitioned filter output signal, and partitioned filter output coefficients, and a device for realising said digital filter as a sum of outputs of Finite Impulse Response ("FIR") filter elements, wherein inputs of the FIR filter elements are dependent upon said partial filter input initial condition and said partial filter output initial condition, and said current block of filter input signal values.