Decimation for Bandpass Sigma-Delta Analog-to-Digital Conversion

An efficient means for constructing a narrow bandpass filter for an analogto-digital converter based on a bandpass sigma-delta modulator is presented. It is shown that the filter can be made with very simple hardware, comparable to that required by an analog-to-digital converter using standard lowpass sigma-delta modulation. Introduction Bandpass sigma-delta modulation [1] is a variant of the more usual kind of sigma-delta modulation, lowpass sigma-delta modulation [2,3,4,5,6]. Lowpass sigma-delta modulation achieves an accurate representation of the input from DC to some small fraction of the sampling rate, whereas bandpass sigma-delta modulation is accurate in a narrow frequency band, typically at a significant fraction of the sampling rate. It is particularly suited to the simultaneous demodulation and analog-to-digital conversion of AM signals. The principles underlying bandpass sigma-delta modulation are identical to those of lowpass sigma-delta modulation [2]. Given a structure, one analyzes it by assuming that the quantizer is a source of additive white noise and deriving the transfer function, H, from this noise source to the output using ordinary linear system analysis. If we reverse this procedure, we turn analysis into synthesis. Figure 1 illustrates the process by which we convert H, the desired error transfer function, into a EA n modulator. The only prerequisite for this process is that H-l be strictly causal, or in terms of its z-transform, that H(m) = 1.