this paper is the study of four real, linear, possibly constrained minimum norm approximation problems, which arise in connection with the design of linear-phase nonrecursive digital lters and are distinguished by the type of used trigonometric approximation functions. In case of unconstrained minimax designs these problems are normally solved by the Parks-McClellan algorithm, which is a straightforward adaptation of the second algorithm of Remez to these problems and which is one of the most popular tools in lter design. In this paper the four types of approximation problems are investigated for all L

This paper compares command shaping techniques for controlling residual vibration of high-performance machines. Input shaping generates vibration-reducing shaped commands through convolution of an impulse sequence with the desired command. Because input shaping has similarities to notch filtering, it is compared here with a variety of FIR and IIR filters. Several types of input shapers are presented and shown to be more effective than any of the conventional filters. Introduction Control of machine vibration becomes very important as designers attempt to push the state of the art with faster, lighter machines. Many researchers have examined different controller configurations in order to control machines without exciting resonances. Even with a sophisticated controller it is difficult to rapidly move flexible machines without deflections and vibrations. A more achievable goal is to eliminate residual vibration once the machine has achieved a desired setpoint. Input shaping is a comm...

fFor equiripple filters, the relation among the filter length N +1, the transition bandwidth 1!, and the optimal passband and stopband errors ffi p and ffi s has been a secret for more than 20 years. This paper is aimed at solving this mystery. We derive the exact asymptotic results in the weightfree case ffi p = ffi s = ffi, which enables us to interpret and improve the existing empirical formulas. Our main results are finally combined into formula (17). In the transition band, the filter response is discovered to be asymptotically close to a scaled error function. The main tools are potential theory in the complex plane and asymptotic analysis.

A hierarchical watermarking approach is developed that incorporates an ownership identification .directly into the design development process. This approach oftrs a high degree of tamper resistance and provides easy, noninvasive copy detection. We present two FIR digital filter cores, one watermarked at the algorithm level and the second at the algorithm and architecture levels. A unique ownership signature (watermark) is placed at each level. At the algorithm level, the watermark is embedded in the filter coefficients during the development of the transfer function. At the architecture level, we use circuit transformations to watermark the design. Experimental results show approximately 7% area overhead of the algorithm-level watermarked design over a nonwatermarked design. The cost of area for the design watermarked at both the algorithm and architecture levels is less than 40%.

The four main design problems for nonrecursive digital filters in the frequency domain are properly formulated as approximation problems and studied in regard to the existence of solutions and the convergence of the approximation errors. These are the problems of approximating a frequency response and a magnitude response and the problems of simultaneously approximating a magnitude and phase response and a magnitude and group response delay respectively. The errors are measured by an arbitrary L p - resp. l p -norm, 1 p 1; and constraints on the filter coefficients are permitted. The topic of this first part of the paper is the approximation of a prescribed frequency response where linear-phase filters are considered separately.

. High quality sound reproduction by loudspeakers is increasingly problematic if the dimensions of the loudspeaker decrease. To produce enough power, large diaphragm excursions are needed which give rise to significant distortions especially at very low frequencies. Instead of improving the mechanical construction of the transducer we apply a feedforward nonlinear digital inverse circuit. Results of two 2 nd order Volterra compensators show a significant reduction of the second order harmonics, leaving higher order distortions unchanged. The structure of the realization influences the performance considerably. Two realization structures are considered, and the error caused by the differentiators in the output of the compensators are compared. Both algorithms are implemented in real--time on a Digital Signal Processor (DSP) for on-line testing with the transducer. 1. Introduction Because audio reproduction elements tend to decrease in size there is a search for smaller loudspeakers a...

Abstract—This paper studies the basic design challenges associated with multirate sensor arrays. A multirate sensor array is a sensor array in which each sensor node communicates a low-resolution measurement to a central processing unit. The objective is to design the individual sensor nodes and the central processing unit such that, at the end, a unified high-resolution measurement is reconstructed. A multirate sensor array can be modeled as an analysis filterbank in discrete-time. Using this model, the design problem is reduced to solving the following two problems: a) how to design the sensor nodes such that the time-delay of arrival (TDOA) between the sensors can be estimated and b) how to design a synthesis filterbank to fuse the low-rate data sent by the sensor nodes given the TDOA? In this paper, we consider a basic two-channel sensor array. We show that it is possible to estimate the TDOA between the sensors if the analysis filters incorporated in the array satisfy specific phase-response requirements. We then provide practical sample designs that satisfy these requirements. We prove, however, that a fixed synthesis filterbank cannot reconstruct the desired high-resolution measurement for all TDOA values. As a result, we suggest a fusion system that uses different sets of synthesis filters for even and odd TDOAs. Finally, we use the optimality theory to design optimal synthesis filters. Index Terms—Delay estimation, filterbanks, FIR filters, optimization, multirate systems, multisensor systems, sensor fusion, sensor networks. I.

We compute approximate Fekete points for weighted polynomial interpolation, by a recent algorithm based on QR factorizations of Vandermonde matrices. We consider in particular the case of univariate and bivariate functions with prescribed poles or other singularities, which are absorbed in the basis by a weight function. Moreover, we apply the method to the construction of real and complex weighted polynomial filters, where the relevant concept is that of weighted norm.

Conjugate quadrature filters (CQF's) have applications to wavelet construction and signal processing. We show that any continuous frequency response (Fourier transform) P of a CQF p can be uniformly approximated by the frequency response Q of CQF q having finite length. Our first proof uses Hardy space theory and the parametrization of CQF's by the infinite dimensional Lie group of paraunitary matrices. Our second proof uses a differential equation method to approximate CQF's by CQF's having factorial decay, followed by a phase retreival method to approximate CQF's having factorial decay by CQF's having finite support. 1 Introduction We let Z; R; C; and T denote the integers, reals, complex numbers, and unit circle. A conjugate quadrature filter (CQF) is a sequence p whose Fourier transform P is a measurable function that satisfies jP (w)j 2 + jP (\Gammaw)j 2 = 1; w 2 T : (1.1) These filters, having either finite or infinite support, have applications to wavelet construction and...

The cerebrated Kalman-Yakubovi c-Popov (KYP) lemma establishes the equivalence between a frequency domain inequality (FDI) and a linear matrix inequality (LMI), and has played one of the most fundamental roles in systems and control theory. This paper generalizes the KYP lemma in two aspects --- the frequency range and the class of systems --- and unifies various existing versions by a single theorem. In particular, our result covers FDIs in finite frequency intervals for both continuous/discrete-time settings as opposed to the standard infinite frequency range. The class of systems for which FDIs are considered is no longer constrained to be proper, and nonproper transfer functions including polynomials can also be treated. We study implications of this generalization, and develop a proper interface between the basic result and various engineering applications. Specifically, it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain/phase properties in several frequency ranges. The method is illustrated by numerical design examples of digital filters and PID controllers. 1