Coefficient inaccuracy in FIR filters

Coefficient inaccuracy in FIR filters is known to degrade the frequency response particularly in stopband regions. The magnitude of the stopband degradation increases with the number of stages N, the length of the impulse response. A widely used formula for the error in frequency response is proportional to . Recently, we have found that for random additive coefficient errors with variance σ², the maximum error in frequency response for large N is given by . This result is applied to an empirical formula relating the minimum number of stages, N, to specified lowpass filter performance parameters. The results lead to absolute bounds on attainable stopband rejection for band-select FIR filters. The realization of transversal filters with charge-coupled devices (CCD\´s) is particularly relevant to this study.