Quantization noise analysis and error feedback implementation in frequency sampling FIR filters

This paper considers the problem of quantization noise in frequency sampling complex FIR filters. The error feedback (EFB) method - in which the discarded part of the word is appropriately fed back to the filter, so as to reduce the total effect, is utilized in order to reduce the quantization noise. We find conditions on the EFB scheme which pertain, separately, to each branch of the frequency sampling structure. These conditions ensure both noise reduction and the prevention of additional quantization, which may be created by EFB itself. The amount of improvement is a function of the filter characteristics and the specific implementation. Formulas for the improvement are developed and confirmed by simulation.