Coefficient Inaccuracy in Transversal Filtering

Coefficient inaccuracy in transversal 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 By extending recent results on random trigonometric polynomials, we show that for random additive coefficient errors with variance σ², the error ΔH(ω) in frequency response for large n is such that where log denotes the natural logarithm. This result leads to an absolute bound on attainable stopband rejection for any band‐select transversal filter with given coefficient inaccuracy. In particular, the result places a definite limitation on the quality of band‐select filtering that can be achieved using a ccd split‐electrode filter. It also implies bounds for the peak sidelobes of random radar arrays.