Low Group Delay Interpolation Filter For Delta-Sigma Converters

Abstract

This paper shows how a relaxation of the high frequency requirements can help reducing the latency in linear phase interpolation filter, with an audio production system perspective. The reduced need for attenuation is justified when the interpolation filter is followed by a noise-shaping Delta-Sigma loop and an analog filtering stage. This is done by using a non-constant error weight of the stop-band. In order to use the Parks-McClellan method for finite impulse response filter design from Matlab, the stop-band is divided and weighted logarithmically. Quantitative results are shown for different example filter design, limited to situations where the Parks-McClellan converges well. It has been found that the shorter the filter length needed to respect a given filter template, the more relative group delay reduction can be achieved by relaxing the high frequency requirement. For filter size of the order of 100, reduction of group delay of 30% can be expected. For sake of simplicity, the Delta-Sigma loop is discussed but not analysed here. The idea is demonstrated in the context of Digital-to-Analog converters (DAC) but by duality could be applicable also to Analog-to-Digital converters (ADC). The main performance metric used is a relative reduction of the impulse response group delay. The results are also presented as impulse responses and power spectrum examples. The presented approach may be generalised to complex and non-linear phase filters and does not prevent the use of polyphase structures.