Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then low-pass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, real-time performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.

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From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

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

A time-interleaved A-D converter (ADC) system is an effective way to implement a high-sampling-rate ADC with relatively slow circuits. In the system, several channel ADCs operate at interleaved sampling times as if they were effectively a single ADC operating at a much higher sampling rate. However, mismatches such as offset, gain mismatches among channel ADCs as well as timing skew of the clocks distributed to them degrade S/N of the ADC system as a whole. This paper analyzes the channel mismatch effects in the time-interleaved ADC system. Previous analysis showed the effect for each mismatch individually, however in this paper we derive explicit formulas for the mismatch effects when all of offset, gain and timing mismatches exist together. We have clarified that the gain and timing mismatch effects interact with each other but the offset mismatch effect is independent from them, and this can be seen clearly in frequency domain. We also discuss the bandwidth mismatch effect. The derived formulas can be used for calibration algorithms to compensate for the channel mismatch effects.

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Explicit analysis of channel mismatch effects in time-interleaved ADC systems

An in vivo imaging device is provided for producing real-time images of small, moving or stationary cavities and surrounding tissue structure. The imaging device includes a probe assembly of very small dimensions and preferably sufficiently small to fit within cavities having a diameter on the order of that of a human coronary artery. The probe assembly may be mounted to a positioning device such as a catheter, which allows for the use of, for example, conventional guiding catheters and guide wires.

Apparatus and method for imaging small cavities

Ultra-wide-band analog-to-digital (A/D) conversion is one of the most critical problems faced in communication, instrumentation, and radar systems. This paper presents a comprehensive analysis of the recently proposed time-stretched A/D converter. By reducing the signal bandwidth prior to digitization, this technique offers revolutionary enhancements in the performance of electronic converters. The paper starts with a fundamental-physics analysis of the time-wavelength transformation and the implication of time dilation on the signal-to-noise ratio. A detailed mathematical description of the time-stretch process is then constructed. It elucidates the influence of linear and nonlinear optical dispersion on the fidelity of the electrical signal. Design issues of a single-sideband time-stretch system, as they relate to broad-band operation, are examined. Problems arising from the nonuniform optical power spectral density are explained, and two methods for overcoming them are described. As proof of the concept, 120 GSa/s real-time digitization of a 20-GHz signal is demonstrated. Finally, design issues and performance features of a continuous-time time-stretch system are discussed.

Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations

High-speed monolithic converters normally use a variation of the flash technique, which 2/SUP n/ comparators in parallel to obtain a fast n-bit conversion. Although this method allows for high converter bandwidth, it is not very area efficient, and results in large die sizes for even modest resolution converters. In the technique presented here, a number of small but area efficient converters are operated in a time-interleaved fashion to achieve the bandwidth of a flash circuit, but in a substantially smaller area. This technique is analyzed with respect to noise and distortion resulting from nonideal array characteristics, and is demonstrated by way of a four-way array test-chip. This chip consists of four time-interleaved 7-bit weighted-capacitor A/D converters fabricated in a 10 /spl mu/m metal-gate CMOS process. Full 7-bit linearity is maintained up to a 2.5 MHz conversion rate, with operation at reduced linearity continuing to approximately 4 MHz. The design of this chip, and anticipated characteristics if fabricated in a modern 4-5 /spl mu/m process are described.

Time interleaved converter arrays

This paper will report on a CMOS channel filter which contains transmit, receive and 50/60Hz rejection filters and two 600-ohm output drivers on a single die, designed for either +5 or single +12v, where operating power with active amplifiers is under 40mW. Switched capacitor techniques are used.

W.C. Black

Papers

Time interleaved converter arrays

CMOS PCM channel filter