Stabilization of 2-D recursive digital filters by the DHT method

Damera-Venkata, Niranjan; Venkataraman, M.; Hrishikesh, M.S.; Reddy, P. Siva Kota

doi:10.1109/82.749104

Cited by 10 publications

(11 citation statements)

References 9 publications

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“…There are few methods by which the 1-D recursive digital filter can be stabilized. The popular methods are Least Squares Inverse (LSI) [5,7] and Discrete Hilbert Transform (DHT) methods [8] . It has been shown [8] that DHT method of stabilization will yield stable polynomials if the original polynomial does not have zeros on the unit circle.…”

Section: -D Recursive Digital Filter Stability Theorems and Stabilizmentioning

confidence: 99%

“…The popular methods are Least Squares Inverse (LSI) [5,7] and Discrete Hilbert Transform (DHT) methods [8] . It has been shown [8] that DHT method of stabilization will yield stable polynomials if the original polynomial does not have zeros on the unit circle. Likewise, it is well known [5,[9][10][11] that the LSI of a 1-D polynomial that does not have zeros on the unit circle is always stable.…”

Section: -D Recursive Digital Filter Stability Theorems and Stabilizmentioning

confidence: 99%

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A Novel Approach for Testing Stability of 1-D Recursive Digital Filters Based on Lagrange Multipliers

Santhi¹,

Gangatharan²,

Ponnavaikko³

2008

American J. of Applied Sciences

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Digital filters have found their way into many products from every day consumer items such as mobile phones to advanced maritime and military communications and avionics systems. Design of digital filters faces two fundamental problems, their stability and synthesis. Recursive filters have more stability problems than nonrecursive filters. Stability of a filter can be determined by the location of the zero valued region of the denominator polynomial of its transfer function. Stability of recursive filters has been studied by many researchers for the past three decades. Several theorems on stability testing and stabilizing recursive digital filters have been already proposed. We present a new approach to test the stability problem of the one-dimensional (1-D) recursive digital filters using Lagrange Multipliers. This method not only tests the stability of recursive digital filters, but also provides the stable version of the filter's transfer function if found to be unstable

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Section: -D Recursive Digital Filter Stability Theorems and Stabilizmentioning

confidence: 99%

Section: -D Recursive Digital Filter Stability Theorems and Stabilizmentioning

confidence: 99%

A Novel Approach for Testing Stability of 1-D Recursive Digital Filters Based on Lagrange Multipliers

Santhi¹,

Gangatharan²,

Ponnavaikko³

2008

American J. of Applied Sciences

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“…In our case, since the rational prototype function ( ) from (6) contains only even powers of frequency , that is, only powers of 2 , we will derive a convenient expression for Ω = ( 1 cos + 2 sin ) 2 , according to mapping (11):…”

Section: Design Methodsmentioning

confidence: 99%

“…A class of tunable 2D digital filters is discussed in [7]. The stability problem for 2D filters and stabilization methods are treated in papers like [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Design of Adjustable Square-Shaped 2D IIR Filters

Matei

2013

ISRN Signal Processing

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This paper proposes an analytical design method for two-dimensional square-shaped IIR filters. The designed 2D filters are adjustable since their bandwidth and orientation are specified by parameters appearing explicitly in the filter matrices. The design relies on a zero-phase low-pass 1D prototype filter. To this filter a frequency transformation is next applied, which yields a 2D filter with the desired square shape in the frequency plane. The proposed method combines the analytical approach with numerical approximations. Since the prototype transfer function is factorized into partial functions, the 2D filter also will be described by a factorized transfer function, which is an advantage in implementation.

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“…Another problem with the design of 2D recursive digital filters is to ensure their 2 EURASIP Journal on Advances in Signal Processing stability at the beginning stage of the design [5] since it is computationally tedious to take care of stability constraints during the approximation stage. So it would be advantageous to devise a technique by which the stability problem is detached from the approximation one, and it is here that stabilization methods come into play [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Stabilization of 2D NSHP Recursive Digital Filters with Guaranteed Stability Using PLSI Polynomials

Santhi

Ponnavaikko

Gangatharan

2009

EURASIP J. Adv. Signal Process.

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Two-dimensional digital filters have gained wide acceptance in recent years. For recursive filters, nonsymmetric half-plane versions (also known as semicausal) are more general than quarter-plane versions (also known as causal) in approximating arbitrary magnitude characteristics. The major problem in designing two-dimensional recursive filters is to guarantee their stability with the expected magnitude response. In general, it is very difficult to take stability constraints into account during the stage of approximation. This is the reason why it is useful to develop techniques, by which stability problem can be separated from the approximation problem. In this way, at the end of approximation process, if the filter becomes unstable, there is a need for stabilization procedures that produce a stable filter with similar magnitude response as that of the unstable filter. This paper, demonstrates a stabilization procedure for a two-dimensional nonsymmetric half-plane recursive filters based on planar least squares inverse (PLSI) polynomials. The paper's findings prove that, a new way of form-preserving transformation can be used to obtain stable PLSI polynomials. Therefore obtaining PLSI polynomial is computationally less involved with the proposed formpreserving transformation as compared to existing methods, and the stability of the resulting filters is guaranteed.

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Stabilization of 2-D recursive digital filters by the DHT method

Cited by 10 publications

References 9 publications

A Novel Approach for Testing Stability of 1-D Recursive Digital Filters Based on Lagrange Multipliers

A Novel Approach for Testing Stability of 1-D Recursive Digital Filters Based on Lagrange Multipliers

Design of Adjustable Square-Shaped 2D IIR Filters

Stabilization of 2D NSHP Recursive Digital Filters with Guaranteed Stability Using PLSI Polynomials

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