A method for long impulse response digital filtering of an input data stream, by use of a digital filtering system. Where the input data stream is divided into zero-input signals and zero-state signals. One of the zero-input signals and a corresponding impulse response of the digital filtering system is converted to the frequency domain to determine a respective zero-input response of the digital filtering system. One of the zero-state signals is convolved with a corresponding impulse response of the digital filtering system to determine a respective zero-state response of the digital filtering system, wherein at least part of the zero-input signal precedes the zero-state signal. The zero-state response of the digital filtering system is added to the zero-input response of the digital filtering system to determine the response of the digital filtering system. Apparatus for effecting this method is also disclosed.