A class of orthogonal nonrecursive binomial filters

The discrete-time counterparts of the Hermite family of orthogonal functions are mentioned briefly in Milne's book [1]. We have investigated the time and frequency-domain properties of these sequences which we call the binomial sequences. It is shown here that these sequences, or digital filters based on them, can be generated using adders and delay elements only. No coefficient multipliers need be used, so that there is no attendant accuracy problem. Furthermore, the absence of multipliers permits substantial savings in the cost and complexity of these filters and a corresponding improvement in reliability. The frequency-domain behavior of these nonrecursive binomial filters suggests a number of applications as low-pass Gaussian filters or as inexpensive bandpass filters.