Finite word-length effects of pipelined recursive digital filters /
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| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1992.
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| Subjects: | |
| Online Access: | Link to OAKTrust copy |
| Abstract: | Scattered Look-Ahead (SLA) pipelining has been proposed as a structure for high throughput recursive digital filtering, but their numerical properties have been largely misunderstood and unexplored. The Finite Word-Length (FWL) effects of SLA filters using fixed point arithmetic are analyzed in this dissertation. First and second-order Direct Form (DF) structures and second-order Minimum RoundOff Noise (MRON) structures are analyzed using general purpose and unified methodologies. In addition, two new state variable descriptions are introduced to effectively analyze the SLA structures. First, a specialized state variable description, called the Sectioned K and W Description (SKWD), is developed by sectioning the noise contributions of the non-recursive nodes. The resulting K[i] and W[i] matrices have the same dimensions as the system matrix, A. Second, a Non-Canonic State Variable Description (NCSVD) is introduced and is shown to be applicable to any computable signal flow graph. For SLA analysis, the NCSVD method requires matrices of dimension M times the non-SLA matrices, where M is the degree of look-ahead. Analytic closed form solutions for the RoundOff Noise (RON) and Coefficient Quantization Noise (CQN) of DF SLA filters are derived assuming independent pseudo-noise source models. CQN is shown to be interpreted as RON under the single length accumulation model, which enables the unification of quantization analysis. Moreover this model affords the practical building of internal registers in a digital filter, contrast to the previous pure theoretical derivations. Regions free from overflow limit cycles using Two's Complement Arithmetic (TCA) are obtained in both parameter space and in the z-domain for SLA filters. Results for zero-input quantization limit cycle stability using Two's Complement Truncation (TCT) and Rounding (R) are extended to DF SLA filters. Combining these results, the regions of global asymptotic stability of DF SLA filters are found. In consequence, the DF SLA structure is proved to have merits implementing high Q filters except at certain regions near the unit circle, which the structure is highly susceptible to RON and CQN. DF and MRON based structures are compared for the purpose of reducing complexity or improving numerical performance. To achieve very high throughput rates, the SLA structure is implemented using bit-parallel Most Significant Digit (MSD)-first Signed-Digit Number System (SDNS) array architectures. FWL effects using SDNS are compared with those of conventional arithmetic. |
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| Item Description: | Typescript (photocopy). Vita. "Major subject: Electrical Engineering." |
| Physical Description: | xiii, 141 leaves : illustrations ; 29 cm |
| Bibliography: | Includes bibliographical references. |