In discrete multitone（DMT）modulation systems

a cyclic prefix（CP）is inserted before every symbol block being transmitted

to ensure the independence of each subchannel and alleviate the interference between consecutive symbol blocks The length of the CP is equal to the memory length of the impulse response of the effective channel Using a long CP reduces the throughput of the system largely To avoid using a long CP

an finite impulse response filter is used to shorten the length of the effective channel impulse response An algorithm used to calculate the coefficients of the optimal shortening impulse response filter（SIRF）was given in However

this algorithm requires that the length of the SIRF must be smaller than or equal to the memory length of the target impulse response In this paper

we modify this algorithm and make it suitable for calculating the coefficients of the SIRF with arbitrary length