Using sigma-delta A/D methods, high resolution can be obtained for only low to medium signal bandwidths. This article describes conventional A/D conversion, as well as its performance modeling. We then look at the technique of oversampling, which can be used to improve the resolution of classical A/D methods. We discuss how sigma-delta converters use the technique of noise shaping in addition to oversampling to allow high resolution conversion of relatively low bandwidth signals. We examine the use of sigma-delta converters to convert narrowband bandpass signals with high resolution. Several parallel sigma-delta converters, which offer the potential of extending high resolution conversion to signals with higher bandwidths, are also described.

An overview of sigma-delta converters

: The paper addresses the issue of the send-on-delta data collecting strategy to capture information from the environment. Send-on-delta concept is the signal-dependent temporal sampling scheme, where the sampling is triggered if the signal deviates by delta defined as the significant change of its value. It is an attractive scheme for wireless sensor networking due to effective energy consumption. The quantitative evaluations of send-on-delta scheme for a general type continuous-time bandlimited signal are presented in the paper. The bounds on the mean traffic of reports for a given signal, and assumed sampling resolution, are evaluated. Furthermore, the send-on-delta effectiveness, defined as the reduction of the mean rate of reports in comparison to the periodic sampling for a given resolution, is derived. It is shown that the lower bound of the send-on-delta effectiveness (i.e. the guaranteed reduction) is independent of the sampling resolution, and constitutes the built-in feature of the input signal. The calculation of the effectiveness for standard signals, that model the state evolution of dynamic environment in time, is exemplified. Finally, the example of send-on-delta programming is shown.

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Send-On-Delta Concept: An Event-Based Data Reporting Strategy

A sampling scheme that is based on multiple level-crossings is presented. This scheme generates samples of the input signal that are nonuniformly spaced in time by recording the time instants at which the signal crosses any of the fixed quantization levels. The nonuniform sample sequence is transformed to uniform samples by polynomial interpolation. The resolution is further increased by employing decimation. Various trade-offs involved in terms of speed, resolution and hardware complexity are discussed.

A level-crossing sampling scheme for A/D conversion

This paper introduces a filterbank interpretation of various sampling strategies, which leads to efficient interpolation and reconstruction methods An identity, which is referred to as the interpolation identity, is developed and is used to obtain particularly efficient discrete-time systems for interpolation of generalized samples as well as a class of nonuniform samples, to uniform Nyquist samples, either for further processing in that form or for conversion to continuous time The interpolation identity also leads to new sampling strategies including an extension of Papoulis' (1977) generalized sampling expansion

/pdf/filterbank-reconstruction-of-bandlimited-signals-from-46ygr8t34n.pdf

Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples

This work is a contribution to a drastic change in standard signal processing chains. The main objective is to reduce the power consumption by one or two orders of magnitude. Integrated Smart Devices and Communicating Objects are application domains targeted by this work. In this context, we present a new class of Analog-to-Digital Converters (ADCs), based on an irregular sampling of the analog signal, and an asynchronous design. Because they are not conventional, a complete design methodology is presented. It determines their characteristics given the required effective number of bits and the analog signal properties. it is shown that our approach leads to a significant reduction in terms of hardware complexity and power consumption. A prototype has been designed for speech applications, using the STMicroelectronics 0.18-/spl mu/m CMOS technology. Electrical simulations prove that the factor of merit is increased by more than one order of magnitude compared to synchronous Nyquist ADCs.

A new class of asynchronous A/D converters based on time quantization

A multi band approach to oversampled noise shaping analog to digital conversion is described. The multi band A/D converter breaks the signal band into several smaller bands and uses a different band reject noise shaping transfer function for each band. A FIR filter bank attenuates the out-of-band noise for each band and reconstructs the signal. This approach allows performance improvements over conventional noise shaping A/D converters which convert the entire signal band using one noise shaping transfer function. A design example and simulation results where a signal with 512 kHz bandwidth is converted to about 16 bits of resolution is presented. >

Multi band sigma delta analog to digital conversion

The use of complex noise transfer functions for bandpass sigma delta modulation is described and compared with real transfer functions. For bandpass signals centered at higher frequencies, the use of complex noise transfer functions (NTFs) allows performance improvements over a modulator of the same order using real transfer functions. Results are presented that show the performance improvement possible using complex second order modulators.

Performance of complex noise transfer functions in bandpass and multi band sigma delta systems

A sigma-delta modulation architecture which breaks the signal band into smaller bands and uses a different band reject noise shaping transfer function per band is described. Operating at 1.024 MHz and 64 kHz signal bandwidth with 2nd order modulators, the resolution of the architecture is 4.5 bits higher than that of a standard 2nd order sigma delta ( Sigma Delta 2).

Multiband sigma-delta modulation

A signal acquisition technique that will provide a favorable tradeoff between speed and resolution is described. This technique is based on recording the time instants at which the input signal crosses any of the fixed quantization levels and extracting additional information from the nonuniform sample sequence by means of digital signal processing methods. The proposed concepts are verified using both software simulation and board level hardware implementation. The proposed scheme offers significant benefits in the VLSI implementation, mainly in terms of reduced power consumption and smaller chip area. >

H.V. Sorensen

Papers

A level-crossing sampling scheme for A/D conversion

Multi band sigma delta analog to digital conversion

Performance of complex noise transfer functions in bandpass and multi band sigma delta systems

Multiband sigma-delta modulation

A non-uniform sampling technique for A/D conversion