545 research outputs found
Wordlength optimization for linear digital signal processing
Published versio
SWATI: Synthesizing Wordlengths Automatically Using Testing and Induction
In this paper, we present an automated technique SWATI: Synthesizing
Wordlengths Automatically Using Testing and Induction, which uses a combination
of Nelder-Mead optimization based testing, and induction from examples to
automatically synthesize optimal fixedpoint implementation of numerical
routines. The design of numerical software is commonly done using
floating-point arithmetic in design-environments such as Matlab. However, these
designs are often implemented using fixed-point arithmetic for speed and
efficiency reasons especially in embedded systems. The fixed-point
implementation reduces implementation cost, provides better performance, and
reduces power consumption. The conversion from floating-point designs to
fixed-point code is subject to two opposing constraints: (i) the word-width of
fixed-point types must be minimized, and (ii) the outputs of the fixed-point
program must be accurate. In this paper, we propose a new solution to this
problem. Our technique takes the floating-point program, specified accuracy and
an implementation cost model and provides the fixed-point program with
specified accuracy and optimal implementation cost. We demonstrate the
effectiveness of our approach on a set of examples from the domain of automated
control, robotics and digital signal processing
Non-uniform wordlength delay lines for FIR filters
When FIR filters are designed floating point arithmetic is generally used. However when implemented on hardware such as ASICs, fixed point arithmetic must be used to minimise cost and power requirements. Research to minimise hardware costs has mainly focused on the quantization effects of fixed point wordlengths for the coefficients, multipliers and adders of FIR filters, but with the actual data delays assigned a uniform wordlength and essentially not optimised. This paper proposes that the wordlengths of the delay line can be non-uniform with a minimal increase in quantization noise for parallel implementation of FIR filters where there are differences in the magnitudes of the coefficients. A non-uniform delay line allows hardware savings in terms of delay register wordlengths, delay signal wordlengths and multiplier wordlengths. Results for an FIR design are presented which demonstrate the hardware savingswhen using a non-uniform wordlength delay lin
Design of Multistage Decimation Filters Using Cyclotomic Polynomials: Optimization and Design Issues
This paper focuses on the design of multiplier-less decimation filters
suitable for oversampled digital signals. The aim is twofold. On one hand, it
proposes an optimization framework for the design of constituent decimation
filters in a general multistage decimation architecture. The basic building
blocks embedded in the proposed filters belong, for a simple reason, to the
class of cyclotomic polynomials (CPs): the first 104 CPs have a z-transfer
function whose coefficients are simply {-1,0,+1}. On the other hand, the paper
provides a bunch of useful techniques, most of which stemming from some key
properties of CPs, for designing the proposed filters in a variety of
architectures. Both recursive and non-recursive architectures are discussed by
focusing on a specific decimation filter obtained as a result of the
optimization algorithm.
Design guidelines are provided with the aim to simplify the design of the
constituent decimation filters in the multistage chain.Comment: Submitted to CAS-I, July 07; 11 pages, 5 figures, 3 table
Optimal controllers for finite wordlength implementation
When a controller is implemented in a digital computer, with A/D and D/A conversion, the numerical errors of the computation can drastically affect the performance of the control system. There exists realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Since, in general, there is no upper bound, it is important to have a systematic way of reducing these effects. Optimum controller designs are developed which take account of the digital round-off errors in the controller implementation and in the A/D and D/A converters. These results provide a natural extension to the Linear Quadratic Gaussian (LQG) theory since they reduce to the standard LQG controller when infinite precision computation is used. But for finite precision the separation principle does not hold
The digital implementation of control compensators : the coefficient wordlength issue
Bibliography: leaves 32-34."October, 1979."NASA Ames Grant NGL-22-009-124by Paul Moroney, Alan S. Willsky, Paul K. Houpt
Optimum wordlength allocation
Published versio
On the Implementation of Efficient Channel Filters for Wideband Receivers by Optimizing Common Subexpression Elimination Methods
No abstract availabl
Roundoff noise minimization in a modified direct-form delta operator IIR structure
Among various direct-form delta operator realized filter structures, the delta transposed direct-form II (δDFIIt) has been shown to produce the lowest roundoff noise gain in finite wordlength implementations. Recent analyses focus on the optimization of the free parameter Δ of the delta operator, with scaling of the structure to prevent arithmetic overflow. This paper proposes a modified δDFIIt second-order section in which the Δs and filter coefficients at different branches are separately scaled to achieve improved roundoff noise gain minimization. Expressions for the filter coefficients are derived, and reduction of roundoff noise gain is verified by numerical examples.published_or_final_versio
The wordlength determination problem of linear time invariant systems with multiple outputs - A geometric programming approach
IEEE International Symposium on Circuits and Systems, Island of Kos, Greece, 21-24 May 2006This paper proposes two new methods for optimizing hardware resources in finite wordlength implementation of multiple-output (MO) linear time invariant systems. The hardware complexity is measured by the exact internal wordlength used for each intermediate data. The first method relaxes the wordlength from integer to real-value and formulates the design problem as a geometric programming, from which an optimal solution of the relaxed problem can be determined. The second method is based on a discrete optimization method called the Marginal Analysis method, and it yields the desired wordlengths in integer values. By combining these two methods, a hybrid method is also proposed, which is found to be very effective for large scale MO systems. Design example shows that the proposed algorithms offer better results and a lower design complexity than conventional methods. © 2006 IEEE.published_or_final_versio
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