Efficient narrowband FIR and IFIR filters based on powers-of-two sigma-delta coefficient truncation

A new quantization scheme is presented for truncating the values of a high precision digital sequence to only a few non-zero bits. Sigma-delta modulation is used to round values to the nearest n-bit canonic signed-digit code (number representable as sum or difference of at most n powers-of-two) such that the quantization error is moved to higher frequencies. This technique can be applied to the impulse response of an FIR filter to truncate the coefficient values to a few non-zero bits; eliminating the need for multiplications. The resulting filter´s magnitude response will be accurate over low frequencies and is thus suitable for narrowband lowpass applications. Sigma-delta CSD truncation is applied to previous multiplier efficient approaches for narrowband filters (prefilter-equalizer, multirate) and examples are given which show an additional 4 to 64 times reduction in computational complexity. The sigma-delta CSD interpolated FIR (SCIFIR) filter is presented and examples are given which show an additional 29%-65% reduction in computational complexity over previously reported multiplier efficient IFIR designs