The host windowing technique for FIR digital filter design

A detailed description is given of a technique for designing finite duration impulse response digital filters in which one portion of the impulse response sequence is identified as a "host" filter which undergoes multiplication by a simple trigonometric window in order to implement the final "object" filter. This partitioning is found to be useful, both from the viewpoint of insight into error and transition width characteristics, and from the practical implementation aspect when variation of a frequency parameter (cutoff frequency for a low-pass filter or center frequency for a bandpass filter) is desired. Design results for families of variable filters are presented under conditions where the host filter has been preoptimized to give a close approximation to minimax behavior over a whole range of values for the variable frequency parameter-all for the price of a single initial host optimization procedure for the entire family, followed by a computationally easy modification method for any one member of the family. It is seen that useful performance guarantees can be offered to the user across a range of operating conditions, and that the penalty incurred is never more than a doubling of the peak error (and often much less) over that of minimax designs specifically and laboriously computed for each condition of the variable frequency. Therefore, high speed filter coefficient variation is found to be compatible with good quality filtering in a theoretical framework which readily admits extension to non-standard filter types such as arbitrary multiband filters. A glossary of terms is included at the end of the paper.