Reduced-complexity digital sinusoid generators and oversampled data converters

Citation

Flanagan, Michael J. (1995) Reduced-complexity digital sinusoid generators and oversampled data converters. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SP61-8895. https://resolver.caltech.edu/CaltechETD:etd-10022007-131456

Abstract

This thesis separately addresses two important issues in signal processing: digital sinusoid generators and oversampled data converters. The first part of the thesis addresses noise additive, or dithering, techniques that exponentially reduce the complexity of digital sinusoid generators for a given level of spur performance. With the appropriate dither signals the quantization noise can be rendered nearly white and free of large spurs, or periodic error components, without recourse to large look-up tables. New analysis shows that when the phase dither signal is the sum of M uniform white variates, the phase spurs are at a level of -6(M + 1) dBc per look-up phase bit instead of the usual -6 dBc per phase bit in a non-dithered system. This exponentially reduces the complexity of the digital sinusoid generator for a given spur requirement at the expense of linearly increasing the nearly-white quantization noise.

The second part of the thesis presents two metric-based approaches to the design of over-sampled data converters (ODCs). The first approach leads to an architecture which is derived based on the minimization of a causal, constrained-memory, power-spectral-distortion metric. This architecture is compared to standard ΔΣ modulators and shown to have superior noise performance under some conditions.

Another metric-based approach to the design of ODCs uses a more general distortion metric and incorporates elements of vector quantization, eigensystems and analysis of the discrete prolate spheroidal wave functions. This enables the application of vector quantization theory to oversampled data converters. A vector-quantizer-based ODC architecture called the eigenmodulator is motivated and analyzed. Rate-distortion results are presented for the important case of a band-limited Gaussian input. When both the complexity of the eigenmodulator and the oversampling ratio become large, it is shown that the distribution of the output vectors in an important transform space becomes joint Gaussian. This is shown to be important in light of the centroid condition for an optimal vector quantizer. The implication of this result on the choice of output scaling for the single-bit data converter is addressed.

Thesis Files