Variable digital filter design using the outer product expansion

Deng, Tian-Bo; Soma, Takashi

doi:10.1049/ip-vis:19941059

Cited by 34 publications

(27 citation statements)

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“…In deriving (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13), the range of integration is symmetrical about the origin. Equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) can readily be calculated by the reduction formula or in general numerical integration. The optimal weighted least square solution can be calculated from (2)(3)(4)(5)(6)…”

Section: Least Squares Design Of Fir Variable Digital Filtersmentioning

confidence: 99%

“…The spectral parameter method was first proposed by Zarour and Fahmy [14], where the poles and zeros of an infinite impulse response (IIR) filter are assumed to be polynomials of the spectral or tuning parameters. Most of the works on VDFs reported focus on the design of IIR VDFs, and methods for guaranteeing their stability [6], [13]. Unlike VDFs based on FIR filters, the design of IIR VDFs requires nonlinear optimization [6], [13], [14], which is rather time consuming.…”

Section: Design Of Iir Vdf Using Model Order Reductionmentioning

confidence: 99%

“…Most of the works on VDFs reported focus on the design of IIR VDFs, and methods for guaranteeing their stability [6], [13]. Unlike VDFs based on FIR filters, the design of IIR VDFs requires nonlinear optimization [6], [13], [14], which is rather time consuming. Another important problem of IIR VDFs with direct tuning of the poles and zeros of the digital filters is the undesirable transient response generated during parameter tuning.…”

Section: Design Of Iir Vdf Using Model Order Reductionmentioning

confidence: 99%

“…They find applications in different areas of signal processing and communications, e.g., fractional delay digital filters for timing adjustment in digital receivers [1], Manuscript [2]. Methods for designing variable digital filters can broadly be classified into two categories: transformation [3], [4] and spectral parameter approximation [6]- [10], [13], [14] methods.…”

Section: Introductionmentioning

confidence: 99%

“…The spectral parameter method was proposed by Zarour and Fahmy [14], where the poles and zeros of an infinite impulse response (IIR) filter are assumed to be polynomials of the spectral or tuning parameters. Most of the works on VDFs reported are focused on the design of IIR VDF (see [6], [13] and references therein), and methods for guaranteeing their stability [6]. More recently, the design of 1-D [5], [10], [21] and 2-D [7], [8] finite-impulse response (FIR) VDF (by parameterizing the impulse response as polynomials) have received considerably attention due to their simple design procedure and good filter performance.…”

Section: Introductionmentioning

confidence: 99%

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On the design and implementation of FIR and IIR digital filters with variable frequency characteristics

Pun

Chan

Yeung

et al. 2002

IEEE Trans. Circuits Syst. II

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This paper studies the design and implementation of finite-impulse response (FIR) and infinite-impulse response (IIR) variable digital filters (VDFs), whose frequency characteristics can be controlled continuously by some control or tuning parameters. A least squares (LS) approach is proposed for the design of FIR VDFs by expressing the impulse response of the filter as a linear combination of basis functions. It is shown that the optimal LS solution can be obtained by solving a system of linear equations. By choosing the basis functions as piecewise polynomials, VDFs with larger tuning range than that of ordinary polynomial based approach results. The proposed VDF can be efficiently implemented using the familiar Farrow structure. Making use of the FIR VDF so obtained, an Eigensystem Realization Algorithm (ERA)-based model reduction technique is proposed to approximate the FIR VDF by a stable IIR VDF with lower system order. The advantages of the model reduction approach are: 1) it is computational simple which only requires the computation of the singular value decomposition of a Hankel matrix; 2) the IIR VDF obtained is guaranteed to be stable; and 3) the frequency response such as the phase response of the FIR prototype is well preserved. Apart from the above advantages, the proposed IIR VDF does not suffer from undesirable transient response during parameter tuning found in other approaches based on direct tuning of filter parameters. For frequency selective VDFs, about 40% of the multiplications can be saved using the IIR VDFs. The implementation of the proposed FIR VDF using sum-of-powers-of-two (SOPOT) coefficient and the multiplier block (MB) technique are also studied. Results show that about two-third of the additions in implementing the multiplication of the SOPOT coefficients can be saved using the multiplier block, which leads to significant savings in hardware complexity.Index Terms-Design and implementation, finite-impulse response (FIR) filters, infinite-impulse response (IIR) filters, least squares design, model reduction, multiplier block, variable or tunable digital filters.

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Section: Least Squares Design Of Fir Variable Digital Filtersmentioning

confidence: 99%

Section: Design Of Iir Vdf Using Model Order Reductionmentioning

confidence: 99%

Section: Design Of Iir Vdf Using Model Order Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the design and implementation of FIR and IIR digital filters with variable frequency characteristics

Pun

Chan

Yeung

et al. 2002

IEEE Trans. Circuits Syst. II

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Fast algorithms for designing variable FIR notch filters

Routray

Swain

2007

Numerical Linear Algebra App

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SUMMARYThe paper presents fast algorithms for designing finite impulse response (FIR) notch filters. The aim is to design a digital FIR notch filter so that the magnitude of the filter has a deep notch at a specified frequency, and as the notch frequency changes, the filter coefficients should be able to track the notch fast in real time. The filter design problem is first converted into a convex optimization problem in the autocorrelation domain. The frequency response of the autocorrelation of the filter impulse response is compared with the desired filter response and the integral square error is minimized with respect to the unknown autocorrelation coefficients. Spectral factorization is used to calculate the coefficients of the filter. In the optimization process, the computational advantage is obtained by exploiting the structure of the Hessian matrix which consists of a Toeplitz plus a Hankel matrix. Two methods have been used for solving the Toeplitz-plus-Hankel system of equations. In the first method, the computational time is reduced by using Block-Levinson's recursion for solving the Toeplitz-plus-Hankel system of matrices. In the second method, the conjugate gradient method with different preconditioners is used to solve the system. Comparative studies demonstrate the computational advantages of the latter. Both these algorithms have been used to obtain the autocorrelation coefficients of notch filters with different orders. The original filter coefficients are found by spectral factorization and each of these filters have been tested for filtering synthetic as well as real-life signals.

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An efficient closed-form approach to the design of linear-phase FIR digital filters with variable-bandwidth characteristics

Kidambi

2006

Signal Processing

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Variable digital filter design using the outer product expansion

Cited by 34 publications

References 0 publications

On the design and implementation of FIR and IIR digital filters with variable frequency characteristics

On the design and implementation of FIR and IIR digital filters with variable frequency characteristics

Fast algorithms for designing variable FIR notch filters

An efficient closed-form approach to the design of linear-phase FIR digital filters with variable-bandwidth characteristics

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