Methods for the transfer function design of multiple narrow-band bandpass sigma-delta modulators

This paper presents the design analysis of novel tunable narrow-band bandpass sigma-delta modulators, which can achieve concurrent multiple noise-shaping for multi-tone input signals. Four different design methodologies based on the noise transfer functions of comb filters, slink filters, multi-notch filters and fractional delay comb filters are applied for the design of these multiple-band sigma-delta modulators. The latter approach utilises conventional comb filters in conjunction with FIR, or allpass IIR fractional delay filters, to deliver the desired nulls for the quantisation noise transfer function. Detailed simulation results show that FIR fractional delay comb filter-based sigma-delta modulators tune accurately to most centre frequencies, but suffer from degraded resolution at frequencies close to Nyquist. However, superior accuracies are obtained from their allpass IIR fractional delay counterpart at the expense of a slight shift in noise-shaping bands at very high frequencies. The merits and drawbacks of each technique for the various sigma-delta topologies are assessed in terms of in-band signal-to-noise ratios, accuracy of tunability and coefficient complexity for ease of implementation.

Narrow-band variable center frequency single-loop and multistage sigma-delta modulators for bandpass signals

Oversampled narrow-band single-loop and multistage resonator-based bandpass sigma-delta (Σ-Δ) modulators that can accommodate different passband center to sampling frequency ratios are reported. These tunable bandpass configurations are designed by analytically determining and subsequently verifying through detailed empirical simulations the required compensation hardware to deliver enhanced noise-shaping. It is demonstrated that comparatively superior in-band signal-to-noise ratios and dynamic ranges are attributed to the inclusion of appropriate digital feedforward and feedback compensators within these structures.

Application of fractional delay filters to tune the centre frequency location of single-band sigma-delta modulators

This paper presents a novel technique for the design of narrow-band sigma-delta modulators with an embedded tunable centre frequency mechanism. This method demonstrates that the use of sum filters combined with a fractional delayer provide the flexibility of tuning the noise shaping band for any desired variable centre frequency input signal.

A comparative study of complex multiple-band noise-shaping sigma-delta modulators for multi-tone input signals

This paper presents a comparative study of complex single-bit and multi-bit sigma-delta modulators that are capable of providing concurrent multiple-band noise-shaping for multi-tone narrow-band input signals. The concepts applied for the three design methodologies are based on the noise transfer functions of complex comb, complex slink and complex multi-notch filters.

Increasing the variability of centre frequency locations in multiple-band sigma-delta modulators via the use of fractional delay filters

This paper presents the design analysis of novel tunable narrow-band bandpass sigma-delta modulators, that can achieve concurrent multiple noise-shaping for multi-tone input signals. This approach utilises conventional comb filters in conjunction with FIR, or allpass IIR fractional delay filters, to deliver the desired nulls for the quantisation noise transfer function. Detailed simulation results show that FIR fractional delay comb filter based sigma-delta modulators tune accurately to most centre frequencies, but suffer from degraded resolution at frequencies close to Nyquist. However, superior accuracies are obtained from their allpass IIR fractional delay counterpart at the expense of a slight shift in noise-shaping bands at very high frequencies.