Lost knowledge refound: sharpened FIR filters

A scenario is presented in which an engineer in the field finds that there is a problem with the system specifications and a symmetric finite impulse response (FIR) filter in the software does not do the job; it needs reduced passband ripple or, maybe, more stopband attenuation. We present a simple method for transforming an FIR filter into one with better passband and stopband characteristics, while maintaining phase linearity. While filter sharpening may not be used often, it does have its place in an engineer's toolbox. An optimal filter has a shorter impulse response than a sharpened filter with the same passband and stopband ripple, and thus is more computationally efficient. However, filter sharpening can be used whenever a given filter response cannot be modified, such as a software code that makes use of an unchangeable filter subroutine. The scenario described is hypothetical, but all practicing engineers have been in situations where a problem needs to be solved without the full arsenal of normal design tools. Filter sharpening could be used when improved filtering is needed, but insufficient ROM space is available to store more filter coefficients, or as a way to reduce ROM requirements. In addition, in some hardware applications using filter ASICs, it may be easier to add additional chips to a design than it is to design a new ASIC.